Multiscale optical simulation settings: challenging applications handled with an iterative ray-tracing FDTD interface method.

PubMed

Leiner, Claude; Nemitz, Wolfgang; Schweitzer, Susanne; Kuna, Ladislav; Wenzl, Franz P; Hartmann, Paul; Satzinger, Valentin; Sommer, Christian

2016-03-20

We show that with an appropriate combination of two optical simulation techniques-classical ray-tracing and the finite difference time domain method-an optical device containing multiple diffractive and refractive optical elements can be accurately simulated in an iterative simulation approach. We compare the simulation results with experimental measurements of the device to discuss the applicability and accuracy of our iterative simulation procedure.

Computationally efficient finite-difference modal method for the solution of Maxwell's equations.

PubMed

Semenikhin, Igor; Zanuccoli, Mauro

2013-12-01

In this work, a new implementation of the finite-difference (FD) modal method (FDMM) based on an iterative approach to calculate the eigenvalues and corresponding eigenfunctions of the Helmholtz equation is presented. Two relevant enhancements that significantly increase the speed and accuracy of the method are introduced. First of all, the solution of the complete eigenvalue problem is avoided in favor of finding only the meaningful part of eigenmodes by using iterative methods. Second, a multigrid algorithm and Richardson extrapolation are implemented. Simultaneous use of these techniques leads to an enhancement in terms of accuracy, which allows a simple method such as the FDMM with a typical three-point difference scheme to be significantly competitive with an analytical modal method.

Integrated Collaborative Model in Research and Education with Emphasis on Small Satellite Technology

DTIC Science & Technology

1996-01-01

feedback; the number of iterations in a complete iteration is referred to as loop depth or iteration depth, g (i). A data packet or packet is data...loop depth, g (i)) is either a finite (constant or variable) or an infinite value. 1) Finite loop depth, variable number of iterations Some problems...design time. The time needed for the first packet to leave and a new initial data to be introduced to the iteration is min(R * ( g (k) * (N+I) + k-1

An implicit-iterative solution of the heat conduction equation with a radiation boundary condition

NASA Technical Reports Server (NTRS)

Williams, S. D.; Curry, D. M.

1977-01-01

For the problem of predicting one-dimensional heat transfer between conducting and radiating mediums by an implicit finite difference method, four different formulations were used to approximate the surface radiation boundary condition while retaining an implicit formulation for the interior temperature nodes. These formulations are an explicit boundary condition, a linearized boundary condition, an iterative boundary condition, and a semi-iterative boundary method. The results of these methods in predicting surface temperature on the space shuttle orbiter thermal protection system model under a variety of heating rates were compared. The iterative technique caused the surface temperature to be bounded at each step. While the linearized and explicit methods were generally more efficient, the iterative and semi-iterative techniques provided a realistic surface temperature response without requiring step size control techniques.

Development Of A Navier-Stokes Computer Code

NASA Technical Reports Server (NTRS)

Yoon, Seokkwan; Kwak, Dochan

1993-01-01

Report discusses aspects of development of CENS3D computer code, solving three-dimensional Navier-Stokes equations of compressible, viscous, unsteady flow. Implements implicit finite-difference or finite-volume numerical-integration scheme, called "lower-upper symmetric-Gauss-Seidel" (LU-SGS), offering potential for very low computer time per iteration and for fast convergence.

Iterative methods for mixed finite element equations

NASA Technical Reports Server (NTRS)

Nakazawa, S.; Nagtegaal, J. C.; Zienkiewicz, O. C.

1985-01-01

Iterative strategies for the solution of indefinite system of equations arising from the mixed finite element method are investigated in this paper with application to linear and nonlinear problems in solid and structural mechanics. The augmented Hu-Washizu form is derived, which is then utilized to construct a family of iterative algorithms using the displacement method as the preconditioner. Two types of iterative algorithms are implemented. Those are: constant metric iterations which does not involve the update of preconditioner; variable metric iterations, in which the inverse of the preconditioning matrix is updated. A series of numerical experiments is conducted to evaluate the numerical performance with application to linear and nonlinear model problems.

Material nonlinear analysis via mixed-iterative finite element method

NASA Technical Reports Server (NTRS)

Sutjahjo, Edhi; Chamis, Christos C.

1992-01-01

The performance of elastic-plastic mixed-iterative analysis is examined through a set of convergence studies. Membrane and bending behaviors are tested using 4-node quadrilateral finite elements. The membrane result is excellent, which indicates the implementation of elastic-plastic mixed-iterative analysis is appropriate. On the other hand, further research to improve bending performance of the method seems to be warranted.

Parallel iterative methods for sparse linear and nonlinear equations

NASA Technical Reports Server (NTRS)

Saad, Youcef

1989-01-01

As three-dimensional models are gaining importance, iterative methods will become almost mandatory. Among these, preconditioned Krylov subspace methods have been viewed as the most efficient and reliable, when solving linear as well as nonlinear systems of equations. There has been several different approaches taken to adapt iterative methods for supercomputers. Some of these approaches are discussed and the methods that deal more specifically with general unstructured sparse matrices, such as those arising from finite element methods, are emphasized.

Iterative methods for 3D implicit finite-difference migration using the complex Padé approximation

NASA Astrophysics Data System (ADS)

Costa, Carlos A. N.; Campos, Itamara S.; Costa, Jessé C.; Neto, Francisco A.; Schleicher, Jörg; Novais, Amélia

2013-08-01

Conventional implementations of 3D finite-difference (FD) migration use splitting techniques to accelerate performance and save computational cost. However, such techniques are plagued with numerical anisotropy that jeopardises the correct positioning of dipping reflectors in the directions not used for the operator splitting. We implement 3D downward continuation FD migration without splitting using a complex Padé approximation. In this way, the numerical anisotropy is eliminated at the expense of a computationally more intensive solution of a large-band linear system. We compare the performance of the iterative stabilized biconjugate gradient (BICGSTAB) and that of the multifrontal massively parallel direct solver (MUMPS). It turns out that the use of the complex Padé approximation not only stabilizes the solution, but also acts as an effective preconditioner for the BICGSTAB algorithm, reducing the number of iterations as compared to the implementation using the real Padé expansion. As a consequence, the iterative BICGSTAB method is more efficient than the direct MUMPS method when solving a single term in the Padé expansion. The results of both algorithms, here evaluated by computing the migration impulse response in the SEG/EAGE salt model, are of comparable quality.

A discourse on sensitivity analysis for discretely-modeled structures

NASA Technical Reports Server (NTRS)

Adelman, Howard M.; Haftka, Raphael T.

1991-01-01

A descriptive review is presented of the most recent methods for performing sensitivity analysis of the structural behavior of discretely-modeled systems. The methods are generally but not exclusively aimed at finite element modeled structures. Topics included are: selections of finite difference step sizes; special consideration for finite difference sensitivity of iteratively-solved response problems; first and second derivatives of static structural response; sensitivity of stresses; nonlinear static response sensitivity; eigenvalue and eigenvector sensitivities for both distinct and repeated eigenvalues; and sensitivity of transient response for both linear and nonlinear structural response.

Domain decomposition methods for systems of conservation laws: Spectral collocation approximations

NASA Technical Reports Server (NTRS)

Quarteroni, Alfio

1989-01-01

Hyperbolic systems of conversation laws are considered which are discretized in space by spectral collocation methods and advanced in time by finite difference schemes. At any time-level a domain deposition method based on an iteration by subdomain procedure was introduced yielding at each step a sequence of independent subproblems (one for each subdomain) that can be solved simultaneously. The method is set for a general nonlinear problem in several space variables. The convergence analysis, however, is carried out only for a linear one-dimensional system with continuous solutions. A precise form of the error reduction factor at each iteration is derived. Although the method is applied here to the case of spectral collocation approximation only, the idea is fairly general and can be used in a different context as well. For instance, its application to space discretization by finite differences is straight forward.

Robust non-fragile finite-frequency H∞ static output-feedback control for active suspension systems

NASA Astrophysics Data System (ADS)

Wang, Gang; Chen, Changzheng; Yu, Shenbo

2017-07-01

This paper deals with the problem of non-fragile H∞ static output-feedback control of vehicle active suspension systems with finite-frequency constraint. The control objective is to improve ride comfort within the given frequency range and ensure the hard constraints in the time-domain. Moreover, in order to enhance the robustness of the controller, the control gain perturbation is also considered in controller synthesis. Firstly, a new non-fragile H∞ finite-frequency control condition is established by using generalized Kalman-Yakubovich-Popov (GKYP) lemma. Secondly, the static output-feedback control gain is directly derived by using a non-iteration algorithm. Different from the existing iteration LMI results, the static output-feedback design is simple and less conservative. Finally, the proposed control algorithm is applied to a quarter-car active suspension model with actuator dynamics, numerical results are made to show the effectiveness and merits of the proposed method.

Parallel processing in finite element structural analysis

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.

1987-01-01

A brief review is made of the fundamental concepts and basic issues of parallel processing. Discussion focuses on parallel numerical algorithms, performance evaluation of machines and algorithms, and parallelism in finite element computations. A computational strategy is proposed for maximizing the degree of parallelism at different levels of the finite element analysis process including: 1) formulation level (through the use of mixed finite element models); 2) analysis level (through additive decomposition of the different arrays in the governing equations into the contributions to a symmetrized response plus correction terms); 3) numerical algorithm level (through the use of operator splitting techniques and application of iterative processes); and 4) implementation level (through the effective combination of vectorization, multitasking and microtasking, whenever available).

Time-Dependent Parabolic Finite Difference Formulation for Harmonic Sound Propagation in a Two-Dimensional Duct with Flow

NASA Technical Reports Server (NTRS)

Kreider, Kevin L.; Baumeister, Kenneth J.

1996-01-01

An explicit finite difference real time iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for future large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable for a harmonic monochromatic sound field, a parabolic (in time) approximation is introduced to reduce the order of the governing equation. The analysis begins with a harmonic sound source radiating into a quiescent duct. This fully explicit iteration method then calculates stepwise in time to obtain the 'steady state' harmonic solutions of the acoustic field. For stability, applications of conventional impedance boundary conditions requires coupling to explicit hyperbolic difference equations at the boundary. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Three-dimensional local grid refinement for block-centered finite-difference groundwater models using iteratively coupled shared nodes: A new method of interpolation and analysis of errors

USGS Publications Warehouse

Mehl, S.; Hill, M.C.

2004-01-01

This paper describes work that extends to three dimensions the two-dimensional local-grid refinement method for block-centered finite-difference groundwater models of Mehl and Hill [Development and evaluation of a local grid refinement method for block-centered finite-difference groundwater models using shared nodes. Adv Water Resour 2002;25(5):497-511]. In this approach, the (parent) finite-difference grid is discretized more finely within a (child) sub-region. The grid refinement method sequentially solves each grid and uses specified flux (parent) and specified head (child) boundary conditions to couple the grids. Iteration achieves convergence between heads and fluxes of both grids. Of most concern is how to interpolate heads onto the boundary of the child grid such that the physics of the parent-grid flow is retained in three dimensions. We develop a new two-step, "cage-shell" interpolation method based on the solution of the flow equation on the boundary of the child between nodes shared with the parent grid. Error analysis using a test case indicates that the shared-node local grid refinement method with cage-shell boundary head interpolation is accurate and robust, and the resulting code is used to investigate three-dimensional local grid refinement of stream-aquifer interactions. Results reveal that (1) the parent and child grids interact to shift the true head and flux solution to a different solution where the heads and fluxes of both grids are in equilibrium, (2) the locally refined model provided a solution for both heads and fluxes in the region of the refinement that was more accurate than a model without refinement only if iterations are performed so that both heads and fluxes are in equilibrium, and (3) the accuracy of the coupling is limited by the parent-grid size - A coarse parent grid limits correct representation of the hydraulics in the feedback from the child grid.

A finite difference scheme for the equilibrium equations of elastic bodies

NASA Technical Reports Server (NTRS)

Phillips, T. N.; Rose, M. E.

1984-01-01

A compact difference scheme is described for treating the first-order system of partial differential equations which describe the equilibrium equations of an elastic body. An algebraic simplification enables the solution to be obtained by standard direct or iterative techniques.

Application of Four-Point Newton-EGSOR iteration for the numerical solution of 2D Porous Medium Equations

NASA Astrophysics Data System (ADS)

Chew, J. V. L.; Sulaiman, J.

2017-09-01

Partial differential equations that are used in describing the nonlinear heat and mass transfer phenomena are difficult to be solved. For the case where the exact solution is difficult to be obtained, it is necessary to use a numerical procedure such as the finite difference method to solve a particular partial differential equation. In term of numerical procedure, a particular method can be considered as an efficient method if the method can give an approximate solution within the specified error with the least computational complexity. Throughout this paper, the two-dimensional Porous Medium Equation (2D PME) is discretized by using the implicit finite difference scheme to construct the corresponding approximation equation. Then this approximation equation yields a large-sized and sparse nonlinear system. By using the Newton method to linearize the nonlinear system, this paper deals with the application of the Four-Point Newton-EGSOR (4NEGSOR) iterative method for solving the 2D PMEs. In addition to that, the efficiency of the 4NEGSOR iterative method is studied by solving three examples of the problems. Based on the comparative analysis, the Newton-Gauss-Seidel (NGS) and the Newton-SOR (NSOR) iterative methods are also considered. The numerical findings show that the 4NEGSOR method is superior to the NGS and the NSOR methods in terms of the number of iterations to get the converged solutions, the time of computation and the maximum absolute errors produced by the methods.

A Note on Multigrid Theory for Non-nested Grids and/or Quadrature

NASA Technical Reports Server (NTRS)

Douglas, C. C.; Douglas, J., Jr.; Fyfe, D. E.

1996-01-01

We provide a unified theory for multilevel and multigrid methods when the usual assumptions are not present. For example, we do not assume that the solution spaces or the grids are nested. Further, we do not assume that there is an algebraic relationship between the linear algebra problems on different levels. What we provide is a computationally useful theory for adaptively changing levels. Theory is provided for multilevel correction schemes, nested iteration schemes, and one way (i.e., coarse to fine grid with no correction iterations) schemes. We include examples showing the applicability of this theory: finite element examples using quadrature in the matrix assembly and finite volume examples with non-nested grids. Our theory applies directly to other discretizations as well.

Finite-difference fluid dynamics computer mathematical models for the design and interpretation of experiments for space flight. [atmospheric general circulation experiment, convection in a float zone, and the Bridgman-Stockbarger crystal growing system

NASA Technical Reports Server (NTRS)

Roberts, G. O.; Fowlis, W. W.; Miller, T. L.

1984-01-01

Numerical methods are used to design a spherical baroclinic flow model experiment of the large scale atmosphere flow for Spacelab. The dielectric simulation of radial gravity is only dominant in a low gravity environment. Computer codes are developed to study the processes at work in crystal growing systems which are also candidates for space flight. Crystalline materials rarely achieve their potential properties because of imperfections and component concentration variations. Thermosolutal convection in the liquid melt can be the cause of these imperfections. Such convection is suppressed in a low gravity environment. Two and three dimensional finite difference codes are being used for this work. Nonuniform meshes and implicit iterative methods are used. The iterative method for steady solutions is based on time stepping but has the options of different time steps for velocity and temperature and of a time step varying smoothly with position according to specified powers of the mesh spacings. This allows for more rapid convergence. The code being developed for the crystal growth studies allows for growth of the crystal as the solid-liquid interface. The moving interface is followed using finite differences; shape variations are permitted. For convenience in applying finite differences in the solid and liquid, a time dependent coordinate transformation is used to make this interface a coordinate surface.

Iterative solution of the inverse Cauchy problem for an elliptic equation by the conjugate gradient method

NASA Astrophysics Data System (ADS)

Vasil'ev, V. I.; Kardashevsky, A. M.; Popov, V. V.; Prokopev, G. A.

2017-10-01

This article presents results of computational experiment carried out using a finite-difference method for solving the inverse Cauchy problem for a two-dimensional elliptic equation. The computational algorithm involves an iterative determination of the missing boundary condition from the override condition using the conjugate gradient method. The results of calculations are carried out on the examples with exact solutions as well as at specifying an additional condition with random errors are presented. Results showed a high efficiency of the iterative method of conjugate gradients for numerical solution

Accuracy Improvement for Light-Emitting-Diode-Based Colorimeter by Iterative Algorithm

NASA Astrophysics Data System (ADS)

Yang, Pao-Keng

2011-09-01

We present a simple algorithm, combining an interpolating method with an iterative calculation, to enhance the resolution of spectral reflectance by removing the spectral broadening effect due to the finite bandwidth of the light-emitting diode (LED) from it. The proposed algorithm can be used to improve the accuracy of a reflective colorimeter using multicolor LEDs as probing light sources and is also applicable to the case when the probing LEDs have different bandwidths in different spectral ranges, to which the powerful deconvolution method cannot be applied.

The use of Galerkin finite-element methods to solve mass-transport equations

USGS Publications Warehouse

Grove, David B.

1977-01-01

The partial differential equation that describes the transport and reaction of chemical solutes in porous media was solved using the Galerkin finite-element technique. These finite elements were superimposed over finite-difference cells used to solve the flow equation. Both convection and flow due to hydraulic dispersion were considered. Linear and Hermite cubic approximations (basis functions) provided satisfactory results: however, the linear functions were computationally more efficient for two-dimensional problems. Successive over relaxation (SOR) and iteration techniques using Tchebyschef polynomials were used to solve the sparce matrices generated using the linear and Hermite cubic functions, respectively. Comparisons of the finite-element methods to the finite-difference methods, and to analytical results, indicated that a high degree of accuracy may be obtained using the method outlined. The technique was applied to a field problem involving an aquifer contaminated with chloride, tritium, and strontium-90. (Woodard-USGS)

A 3D finite-difference BiCG iterative solver with the Fourier-Jacobi preconditioner for the anisotropic EIT/EEG forward problem.

PubMed

Turovets, Sergei; Volkov, Vasily; Zherdetsky, Aleksej; Prakonina, Alena; Malony, Allen D

2014-01-01

The Electrical Impedance Tomography (EIT) and electroencephalography (EEG) forward problems in anisotropic inhomogeneous media like the human head belongs to the class of the three-dimensional boundary value problems for elliptic equations with mixed derivatives. We introduce and explore the performance of several new promising numerical techniques, which seem to be more suitable for solving these problems. The proposed numerical schemes combine the fictitious domain approach together with the finite-difference method and the optimally preconditioned Conjugate Gradient- (CG-) type iterative method for treatment of the discrete model. The numerical scheme includes the standard operations of summation and multiplication of sparse matrices and vector, as well as FFT, making it easy to implement and eligible for the effective parallel implementation. Some typical use cases for the EIT/EEG problems are considered demonstrating high efficiency of the proposed numerical technique.

Parallelization of implicit finite difference schemes in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Decker, Naomi H.; Naik, Vijay K.; Nicoules, Michel

1990-01-01

Implicit finite difference schemes are often the preferred numerical schemes in computational fluid dynamics, requiring less stringent stability bounds than the explicit schemes. Each iteration in an implicit scheme involves global data dependencies in the form of second and higher order recurrences. Efficient parallel implementations of such iterative methods are considerably more difficult and non-intuitive. The parallelization of the implicit schemes that are used for solving the Euler and the thin layer Navier-Stokes equations and that require inversions of large linear systems in the form of block tri-diagonal and/or block penta-diagonal matrices is discussed. Three-dimensional cases are emphasized and schemes that minimize the total execution time are presented. Partitioning and scheduling schemes for alleviating the effects of the global data dependencies are described. An analysis of the communication and the computation aspects of these methods is presented. The effect of the boundary conditions on the parallel schemes is also discussed.

Extrapolation techniques applied to matrix methods in neutron diffusion problems

NASA Technical Reports Server (NTRS)

Mccready, Robert R

1956-01-01

A general matrix method is developed for the solution of characteristic-value problems of the type arising in many physical applications. The scheme employed is essentially that of Gauss and Seidel with appropriate modifications needed to make it applicable to characteristic-value problems. An iterative procedure produces a sequence of estimates to the answer; and extrapolation techniques, based upon previous behavior of iterants, are utilized in speeding convergence. Theoretically sound limits are placed on the magnitude of the extrapolation that may be tolerated. This matrix method is applied to the problem of finding criticality and neutron fluxes in a nuclear reactor with control rods. The two-dimensional finite-difference approximation to the two-group neutron fluxes in a nuclear reactor with control rods. The two-dimensional finite-difference approximation to the two-group neutron-diffusion equations is treated. Results for this example are indicated.

A one-dimensional nonlinear problem of thermoelasticity in extended thermodynamics

NASA Astrophysics Data System (ADS)

Rawy, E. K.

2018-06-01

We solve a nonlinear, one-dimensional initial boundary-value problem of thermoelasticity in generalized thermodynamics. A Cattaneo-type evolution equation for the heat flux is used, which differs from the one used extensively in the literature. The hyperbolic nature of the associated linear system is clarified through a study of the characteristic curves. Progressive wave solutions with two finite speeds are noted. A numerical treatment is presented for the nonlinear system using a three-step, quasi-linearization, iterative finite-difference scheme for which the linear system of equations is the initial step in the iteration. The obtained results are discussed in detail. They clearly show the hyperbolic nature of the system, and may be of interest in investigating thermoelastic materials, not only at low temperatures, but also during high temperature processes involving rapid changes in temperature as in laser treatment of surfaces.

Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation

NASA Astrophysics Data System (ADS)

Agarwal, P.; El-Sayed, A. A.

2018-06-01

In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sense. The Chebyshev collocation method with the (NSFD) method is used to convert the problem into a system of algebraic equations. These equations solved numerically using Newton's iteration method. The applicability, reliability, and efficiency of the presented technique are demonstrated through some given numerical examples.

Four-level conservative finite-difference schemes for Boussinesq paradigm equation

NASA Astrophysics Data System (ADS)

Kolkovska, N.

2013-10-01

In this paper a two-parametric family of four level conservative finite difference schemes is constructed for the multidimensional Boussinesq paradigm equation. The schemes are explicit in the sense that no inner iterations are needed for evaluation of the numerical solution. The preservation of the discrete energy with this method is proved. The schemes have been numerically tested on one soliton propagation model and two solitons interaction model. The numerical experiments demonstrate that the proposed family of schemes has second order of convergence in space and time steps in the discrete maximal norm.

A Finite-Orbit-Width Fokker-Planck solver for modeling of RF Current Drive in ITER

NASA Astrophysics Data System (ADS)

Petrov, Yu. V.; Harvey, R. W.

2017-10-01

The bounce-average (BA) finite-difference Fokker-Planck (FP) code CQL3D now includes the essential physics to describe the RF heating of Finite-Orbit-Width (FOW) ions in tokamaks. The FP equation is reformulated in terms of constants-of-motion coordinates, which we select to be particle speed, pitch angle, and major radius on the equatorial plane thus obtaining the distribution function directly at this location. A recent development is the capability to obtain solution simultaneously for FOW ions and Zero-Orbit-Width (ZOW) electrons. As a practical application, the code is used for simulation of alpha-particle heating by high-harmonic waves in ITER scenarios. Coupling of high harmonic or helicon fast waves power to electrons is a promising current drive (CD) scenario for high beta plasmas. However, the efficiency of current drive can be diminished by parasitic channeling of RF power into fast ions such as alphas or NBI-produced deuterons, through finite Larmor-radius effects. Based on simulations, we formulate conditions where the fast ions absorb less than 10% of RF power. Supported by USDOE Grants ER54649, ER54744, and SC0006614.

Comparing mass balance and adjoint methods for inverse modeling of nitrogen dioxide columns for global nitrogen oxide emissions

NASA Astrophysics Data System (ADS)

Cooper, Matthew; Martin, Randall V.; Padmanabhan, Akhila; Henze, Daven K.

2017-04-01

Satellite observations offer information applicable to top-down constraints on emission inventories through inverse modeling. Here we compare two methods of inverse modeling for emissions of nitrogen oxides (NOx) from nitrogen dioxide (NO2) columns using the GEOS-Chem chemical transport model and its adjoint. We treat the adjoint-based 4D-Var modeling approach for estimating top-down emissions as a benchmark against which to evaluate variations on the mass balance method. We use synthetic NO2 columns generated from known NOx emissions to serve as "truth." We find that error in mass balance inversions can be reduced by up to a factor of 2 with an iterative process that uses finite difference calculations of the local sensitivity of NO2 columns to a change in emissions. In a simplified experiment to recover local emission perturbations, horizontal smearing effects due to NOx transport are better resolved by the adjoint approach than by mass balance. For more complex emission changes, or at finer resolution, the iterative finite difference mass balance and adjoint methods produce similar global top-down inventories when inverting hourly synthetic observations, both reducing the a priori error by factors of 3-4. Inversions of simulated satellite observations from low Earth and geostationary orbits also indicate that both the mass balance and adjoint inversions produce similar results, reducing a priori error by a factor of 3. As the iterative finite difference mass balance method provides similar accuracy as the adjoint method, it offers the prospect of accurately estimating top-down NOx emissions using models that do not have an adjoint.

A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems, Part 2: Derivation of finite-element equations and comparisons with analytical solutions

USGS Publications Warehouse

Cooley, Richard L.

1992-01-01

MODFE, a modular finite-element model for simulating steady- or unsteady-state, area1 or axisymmetric flow of ground water in a heterogeneous anisotropic aquifer is documented in a three-part series of reports. In this report, part 2, the finite-element equations are derived by minimizing a functional of the difference between the true and approximate hydraulic head, which produces equations that are equivalent to those obtained by either classical variational or Galerkin techniques. Spatial finite elements are triangular with linear basis functions, and temporal finite elements are one dimensional with linear basis functions. Physical processes that can be represented by the model include (1) confined flow, unconfined flow (using the Dupuit approximation), or a combination of both; (2) leakage through either rigid or elastic confining units; (3) specified recharge or discharge at points, along lines, or areally; (4) flow across specified-flow, specified-head, or head-dependent boundaries; (5) decrease of aquifer thickness to zero under extreme water-table decline and increase of aquifer thickness from zero as the water table rises; and (6) head-dependent fluxes from springs, drainage wells, leakage across riverbeds or confining units combined with aquifer dewatering, and evapotranspiration. The matrix equations produced by the finite-element method are solved by the direct symmetric-Doolittle method or the iterative modified incomplete-Cholesky conjugate-gradient method. The direct method can be efficient for small- to medium-sized problems (less than about 500 nodes), and the iterative method is generally more efficient for larger-sized problems. Comparison of finite-element solutions with analytical solutions for five example problems demonstrates that the finite-element model can yield accurate solutions to ground-water flow problems.

Numerical solution of nonlinear partial differential equations of mixed type. [finite difference approximation

NASA Technical Reports Server (NTRS)

Jameson, A.

1976-01-01

A review is presented of some recently developed numerical methods for the solution of nonlinear equations of mixed type. The methods considered use finite difference approximations to the differential equation. Central difference formulas are employed in the subsonic zone and upwind difference formulas are used in the supersonic zone. The relaxation method for the small disturbance equation is discussed and a description is given of difference schemes for the potential flow equation in quasi-linear form. Attention is also given to difference schemes for the potential flow equation in conservation form, the analysis of relaxation schemes by the time dependent analogy, the accelerated iterative method, and three-dimensional calculations.

Assessment of the measurement performance of the in-vessel system of gap 6 of the ITER plasma position reflectometer using a finite-difference time-domain Maxwell full-wave code.

PubMed

da Silva, F; Heuraux, S; Ricardo, E; Quental, P; Ferreira, J

2016-11-01

We conducted a first assessment of the measurement performance of the in-vessel components at gap 6 of the ITER plasma position reflectometry with the aid of a synthetic Ordinary Mode (O-mode) broadband frequency-modulated continuous-wave reflectometer implemented with REFMUL, a 2D finite-difference time-domain full-wave Maxwell code. These simulations take into account the system location within the vacuum vessel as well as its access to the plasma. The plasma case considered is a baseline scenario from Fusion for Energy. We concluded that for the analyzed scenario, (i) the plasma curvature and non-equatorial position of the antenna have neglectable impact on the measurements; (ii) the cavity-like space surrounding the antenna can cause deflection and splitting of the probing beam; and (iii) multi-reflections on the blanket wall cause a substantial error preventing the system from operating within the required error margin.

Numerical solution of Euler's equation by perturbed functionals

NASA Technical Reports Server (NTRS)

Dey, S. K.

1985-01-01

A perturbed functional iteration has been developed to solve nonlinear systems. It adds at each iteration level, unique perturbation parameters to nonlinear Gauss-Seidel iterates which enhances its convergence properties. As convergence is approached these parameters are damped out. Local linearization along the diagonal has been used to compute these parameters. The method requires no computation of Jacobian or factorization of matrices. Analysis of convergence depends on properties of certain contraction-type mappings, known as D-mappings. In this article, application of this method to solve an implicit finite difference approximation of Euler's equation is studied. Some representative results for the well known shock tube problem and compressible flows in a nozzle are given.

Efficient stabilization and acceleration of numerical simulation of fluid flows by residual recombination

NASA Astrophysics Data System (ADS)

Citro, V.; Luchini, P.; Giannetti, F.; Auteri, F.

2017-09-01

The study of the stability of a dynamical system described by a set of partial differential equations (PDEs) requires the computation of unstable states as the control parameter exceeds its critical threshold. Unfortunately, the discretization of the governing equations, especially for fluid dynamic applications, often leads to very large discrete systems. As a consequence, matrix based methods, like for example the Newton-Raphson algorithm coupled with a direct inversion of the Jacobian matrix, lead to computational costs too large in terms of both memory and execution time. We present a novel iterative algorithm, inspired by Krylov-subspace methods, which is able to compute unstable steady states and/or accelerate the convergence to stable configurations. Our new algorithm is based on the minimization of the residual norm at each iteration step with a projection basis updated at each iteration rather than at periodic restarts like in the classical GMRES method. The algorithm is able to stabilize any dynamical system without increasing the computational time of the original numerical procedure used to solve the governing equations. Moreover, it can be easily inserted into a pre-existing relaxation (integration) procedure with a call to a single black-box subroutine. The procedure is discussed for problems of different sizes, ranging from a small two-dimensional system to a large three-dimensional problem involving the Navier-Stokes equations. We show that the proposed algorithm is able to improve the convergence of existing iterative schemes. In particular, the procedure is applied to the subcritical flow inside a lid-driven cavity. We also discuss the application of Boostconv to compute the unstable steady flow past a fixed circular cylinder (2D) and boundary-layer flow over a hemispherical roughness element (3D) for supercritical values of the Reynolds number. We show that Boostconv can be used effectively with any spatial discretization, be it a finite-difference, finite-volume, finite-element or spectral method.

The Mixed Finite Element Multigrid Method for Stokes Equations

PubMed Central

Muzhinji, K.; Shateyi, S.; Motsa, S. S.

2015-01-01

The stable finite element discretization of the Stokes problem produces a symmetric indefinite system of linear algebraic equations. A variety of iterative solvers have been proposed for such systems in an attempt to construct efficient, fast, and robust solution techniques. This paper investigates one of such iterative solvers, the geometric multigrid solver, to find the approximate solution of the indefinite systems. The main ingredient of the multigrid method is the choice of an appropriate smoothing strategy. This study considers the application of different smoothers and compares their effects in the overall performance of the multigrid solver. We study the multigrid method with the following smoothers: distributed Gauss Seidel, inexact Uzawa, preconditioned MINRES, and Braess-Sarazin type smoothers. A comparative study of the smoothers shows that the Braess-Sarazin smoothers enhance good performance of the multigrid method. We study the problem in a two-dimensional domain using stable Hood-Taylor Q 2-Q 1 pair of finite rectangular elements. We also give the main theoretical convergence results. We present the numerical results to demonstrate the efficiency and robustness of the multigrid method and confirm the theoretical results. PMID:25945361

Polynomial elimination theory and non-linear stability analysis for the Euler equations

NASA Technical Reports Server (NTRS)

Kennon, S. R.; Dulikravich, G. S.; Jespersen, D. C.

1986-01-01

Numerical methods are presented that exploit the polynomial properties of discretizations of the Euler equations. It is noted that most finite difference or finite volume discretizations of the steady-state Euler equations produce a polynomial system of equations to be solved. These equations are solved using classical polynomial elimination theory, with some innovative modifications. This paper also presents some preliminary results of a new non-linear stability analysis technique. This technique is applicable to determining the stability of polynomial iterative schemes. Results are presented for applying the elimination technique to a one-dimensional test case. For this test case, the exact solution is computed in three iterations. The non-linear stability analysis is applied to determine the optimal time step for solving Burgers' equation using the MacCormack scheme. The estimated optimal time step is very close to the time step that arises from a linear stability analysis.

Generalization of analytical tools for helicopter-rotor airfoils

NASA Technical Reports Server (NTRS)

Gibbs, E. H.

1979-01-01

A state-of-the-art finite difference boundary-layer program incorporated into the NYU Transonic Analysis Program is described. Some possible treatments for the trailing edge region were investigated. Findings indicate the trailing edge region, still within the scope of an iterative potential flow, boundary layer program, appears feasible.

Subresolution Displacements in Finite Difference Simulations of Ultrasound Propagation and Imaging.

PubMed

Pinton, Gianmarco F

2017-03-01

Time domain finite difference simulations are used extensively to simulate wave propagation. They approximate the wave field on a discrete domain with a grid spacing that is typically on the order of a tenth of a wavelength. The smallest displacements that can be modeled by this type of simulation are thus limited to discrete values that are integer multiples of the grid spacing. This paper presents a method to represent continuous and subresolution displacements by varying the impedance of individual elements in a multielement scatterer. It is demonstrated that this method removes the limitations imposed by the discrete grid spacing by generating a continuum of displacements as measured by the backscattered signal. The method is first validated on an ideal perfect correlation case with a single scatterer. It is subsequently applied to a more complex case with a field of scatterers that model an acoustic radiation force-induced displacement used in ultrasound elasticity imaging. A custom finite difference simulation tool is used to simulate propagation from ultrasound imaging pulses in the scatterer field. These simulated transmit-receive events are then beamformed into images, which are tracked with a correlation-based algorithm to determine the displacement. A linear predictive model is developed to analytically describe the relationship between element impedance and backscattered phase shift. The error between model and simulation is λ/ 1364 , where λ is the acoustical wavelength. An iterative method is also presented that reduces the simulation error to λ/ 5556 over one iteration. The proposed technique therefore offers a computationally efficient method to model continuous subresolution displacements of a scattering medium in ultrasound imaging. This method has applications that include ultrasound elastography, blood flow, and motion tracking. This method also extends generally to finite difference simulations of wave propagation, such as electromagnetic or seismic waves.

Finite element analysis of elasto-plastic soils. Report no. 4: Finite element analysis of elasto-plastic frictional materials for application to lunar earth sciences

NASA Technical Reports Server (NTRS)

Marr, W. A., Jr.

1972-01-01

The behavior of finite element models employing different constitutive relations to describe the stress-strain behavior of soils is investigated. Three models, which assume small strain theory is applicable, include a nondilatant, a dilatant and a strain hardening constitutive relation. Two models are formulated using large strain theory and include a hyperbolic and a Tresca elastic perfectly plastic constitutive relation. These finite element models are used to analyze retaining walls and footings. Methods of improving the finite element solutions are investigated. For nonlinear problems better solutions can be obtained by using smaller load increment sizes and more iterations per load increment than by increasing the number of elements. Suitable methods of treating tension stresses and stresses which exceed the yield criteria are discussed.

Transient analysis of 1D inhomogeneous media by dynamic inhomogeneous finite element method

NASA Astrophysics Data System (ADS)

Yang, Zailin; Wang, Yao; Hei, Baoping

2013-12-01

The dynamic inhomogeneous finite element method is studied for use in the transient analysis of onedimensional inhomogeneous media. The general formula of the inhomogeneous consistent mass matrix is established based on the shape function. In order to research the advantages of this method, it is compared with the general finite element method. A linear bar element is chosen for the discretization tests of material parameters with two fictitious distributions. And, a numerical example is solved to observe the differences in the results between these two methods. Some characteristics of the dynamic inhomogeneous finite element method that demonstrate its advantages are obtained through comparison with the general finite element method. It is found that the method can be used to solve elastic wave motion problems with a large element scale and a large number of iteration steps.

Iterative design of one- and two-dimensional FIR digital filters. [Finite duration Impulse Response

NASA Technical Reports Server (NTRS)

Suk, M.; Choi, K.; Algazi, V. R.

1976-01-01

The paper describes a new iterative technique for designing FIR (finite duration impulse response) digital filters using a frequency weighted least squares approximation. The technique is as easy to implement (via FFT) and as effective in two dimensions as in one dimension, and there are virtually no limitations on the class of filter frequency spectra approximated. An adaptive adjustment of the frequency weight to achieve other types of design approximation such as Chebyshev type design is discussed.

A finite difference solution for the propagation of sound in near sonic flows

NASA Technical Reports Server (NTRS)

Hariharan, S. I.; Lester, H. C.

1983-01-01

An explicit time/space finite difference procedure is used to model the propagation of sound in a quasi one-dimensional duct containing high Mach number subsonic flow. Nonlinear acoustic equations are derived by perturbing the time-dependent Euler equations about a steady, compressible mean flow. The governing difference relations are based on a fourth-order, two-step (predictor-corrector) MacCormack scheme. The solution algorithm functions by switching on a time harmonic source and allowing the difference equations to iterate to a steady state. The principal effect of the non-linearities was to shift acoustical energy to higher harmonics. With increased source strengths, wave steepening was observed. This phenomenon suggests that the acoustical response may approach a shock behavior at at higher sound pressure level as the throat Mach number aproaches unity. On a peak level basis, good agreement between the nonlinear finite difference and linear finite element solutions was observed, even through a peak sound pressure level of about 150 dB occurred in the throat region. Nonlinear steady state waveform solutions are shown to be in excellent agreement with a nonlinear asymptotic theory.

Inversion of potential field data using the finite element method on parallel computers

NASA Astrophysics Data System (ADS)

Gross, L.; Altinay, C.; Shaw, S.

2015-11-01

In this paper we present a formulation of the joint inversion of potential field anomaly data as an optimization problem with partial differential equation (PDE) constraints. The problem is solved using the iterative Broyden-Fletcher-Goldfarb-Shanno (BFGS) method with the Hessian operator of the regularization and cross-gradient component of the cost function as preconditioner. We will show that each iterative step requires the solution of several PDEs namely for the potential fields, for the adjoint defects and for the application of the preconditioner. In extension to the traditional discrete formulation the BFGS method is applied to continuous descriptions of the unknown physical properties in combination with an appropriate integral form of the dot product. The PDEs can easily be solved using standard conforming finite element methods (FEMs) with potentially different resolutions. For two examples we demonstrate that the number of PDE solutions required to reach a given tolerance in the BFGS iteration is controlled by weighting regularization and cross-gradient but is independent of the resolution of PDE discretization and that as a consequence the method is weakly scalable with the number of cells on parallel computers. We also show a comparison with the UBC-GIF GRAV3D code.

The aggregated unfitted finite element method for elliptic problems

NASA Astrophysics Data System (ADS)

Badia, Santiago; Verdugo, Francesc; Martín, Alberto F.

2018-07-01

Unfitted finite element techniques are valuable tools in different applications where the generation of body-fitted meshes is difficult. However, these techniques are prone to severe ill conditioning problems that obstruct the efficient use of iterative Krylov methods and, in consequence, hinders the practical usage of unfitted methods for realistic large scale applications. In this work, we present a technique that addresses such conditioning problems by constructing enhanced finite element spaces based on a cell aggregation technique. The presented method, called aggregated unfitted finite element method, is easy to implement, and can be used, in contrast to previous works, in Galerkin approximations of coercive problems with conforming Lagrangian finite element spaces. The mathematical analysis of the new method states that the condition number of the resulting linear system matrix scales as in standard finite elements for body-fitted meshes, without being affected by small cut cells, and that the method leads to the optimal finite element convergence order. These theoretical results are confirmed with 2D and 3D numerical experiments.

Particle-based simulation of charge transport in discrete-charge nano-scale systems: the electrostatic problem

PubMed Central

2012-01-01

The fast and accurate computation of the electric forces that drive the motion of charged particles at the nanometer scale represents a computational challenge. For this kind of system, where the discrete nature of the charges cannot be neglected, boundary element methods (BEM) represent a better approach than finite differences/finite elements methods. In this article, we compare two different BEM approaches to a canonical electrostatic problem in a three-dimensional space with inhomogeneous dielectrics, emphasizing their suitability for particle-based simulations: the iterative method proposed by Hoyles et al. and the Induced Charge Computation introduced by Boda et al. PMID:22338640

Particle-based simulation of charge transport in discrete-charge nano-scale systems: the electrostatic problem.

PubMed

Berti, Claudio; Gillespie, Dirk; Eisenberg, Robert S; Fiegna, Claudio

2012-02-16

The fast and accurate computation of the electric forces that drive the motion of charged particles at the nanometer scale represents a computational challenge. For this kind of system, where the discrete nature of the charges cannot be neglected, boundary element methods (BEM) represent a better approach than finite differences/finite elements methods. In this article, we compare two different BEM approaches to a canonical electrostatic problem in a three-dimensional space with inhomogeneous dielectrics, emphasizing their suitability for particle-based simulations: the iterative method proposed by Hoyles et al. and the Induced Charge Computation introduced by Boda et al.

Combining the modified Skyrme-like model and the local density approximation to determine the symmetry energy of nuclear matter

NASA Astrophysics Data System (ADS)

Liu, Jian; Ren, Zhongzhou; Xu, Chang

2018-07-01

Combining the modified Skyrme-like model and the local density approximation model, the slope parameter L of symmetry energy is extracted from the properties of finite nuclei with an improved iterative method. The calculations of the iterative method are performed within the framework of the spherical symmetry. By choosing 200 neutron rich nuclei on 25 isotopic chains as candidates, the slope parameter is constrained to be 50 MeV < L < 62 MeV. The validity of this method is examined by the properties of finite nuclei. Results show that reasonable descriptions on the properties of finite nuclei and nuclear matter can be obtained together.

A finite element solver for 3-D compressible viscous flows

NASA Technical Reports Server (NTRS)

Reddy, K. C.; Reddy, J. N.; Nayani, S.

1990-01-01

Computation of the flow field inside a space shuttle main engine (SSME) requires the application of state of the art computational fluid dynamic (CFD) technology. Several computer codes are under development to solve 3-D flow through the hot gas manifold. Some algorithms were designed to solve the unsteady compressible Navier-Stokes equations, either by implicit or explicit factorization methods, using several hundred or thousands of time steps to reach a steady state solution. A new iterative algorithm is being developed for the solution of the implicit finite element equations without assembling global matrices. It is an efficient iteration scheme based on a modified nonlinear Gauss-Seidel iteration with symmetric sweeps. The algorithm is analyzed for a model equation and is shown to be unconditionally stable. Results from a series of test problems are presented. The finite element code was tested for couette flow, which is flow under a pressure gradient between two parallel plates in relative motion. Another problem that was solved is viscous laminar flow over a flat plate. The general 3-D finite element code was used to compute the flow in an axisymmetric turnaround duct at low Mach numbers.

Development of iterative techniques for the solution of unsteady compressible viscous flows

NASA Technical Reports Server (NTRS)

Sankar, Lakshmi N.; Hixon, Duane

1991-01-01

Efficient iterative solution methods are being developed for the numerical solution of two- and three-dimensional compressible Navier-Stokes equations. Iterative time marching methods have several advantages over classical multi-step explicit time marching schemes, and non-iterative implicit time marching schemes. Iterative schemes have better stability characteristics than non-iterative explicit and implicit schemes. Thus, the extra work required by iterative schemes can also be designed to perform efficiently on current and future generation scalable, missively parallel machines. An obvious candidate for iteratively solving the system of coupled nonlinear algebraic equations arising in CFD applications is the Newton method. Newton's method was implemented in existing finite difference and finite volume methods. Depending on the complexity of the problem, the number of Newton iterations needed per step to solve the discretized system of equations can, however, vary dramatically from a few to several hundred. Another popular approach based on the classical conjugate gradient method, known as the GMRES (Generalized Minimum Residual) algorithm is investigated. The GMRES algorithm was used in the past by a number of researchers for solving steady viscous and inviscid flow problems with considerable success. Here, the suitability of this algorithm is investigated for solving the system of nonlinear equations that arise in unsteady Navier-Stokes solvers at each time step. Unlike the Newton method which attempts to drive the error in the solution at each and every node down to zero, the GMRES algorithm only seeks to minimize the L2 norm of the error. In the GMRES algorithm the changes in the flow properties from one time step to the next are assumed to be the sum of a set of orthogonal vectors. By choosing the number of vectors to a reasonably small value N (between 5 and 20) the work required for advancing the solution from one time step to the next may be kept to (N+1) times that of a noniterative scheme. Many of the operations required by the GMRES algorithm such as matrix-vector multiplies, matrix additions and subtractions can all be vectorized and parallelized efficiently.

Adaptive implicit-explicit and parallel element-by-element iteration schemes

NASA Technical Reports Server (NTRS)

Tezduyar, T. E.; Liou, J.; Nguyen, T.; Poole, S.

1989-01-01

Adaptive implicit-explicit (AIE) and grouped element-by-element (GEBE) iteration schemes are presented for the finite element solution of large-scale problems in computational mechanics and physics. The AIE approach is based on the dynamic arrangement of the elements into differently treated groups. The GEBE procedure, which is a way of rewriting the EBE formulation to make its parallel processing potential and implementation more clear, is based on the static arrangement of the elements into groups with no inter-element coupling within each group. Various numerical tests performed demonstrate the savings in the CPU time and memory.

Solution algorithms for nonlinear transient heat conduction analysis employing element-by-element iterative strategies

NASA Technical Reports Server (NTRS)

Winget, J. M.; Hughes, T. J. R.

1985-01-01

The particular problems investigated in the present study arise from nonlinear transient heat conduction. One of two types of nonlinearities considered is related to a material temperature dependence which is frequently needed to accurately model behavior over the range of temperature of engineering interest. The second nonlinearity is introduced by radiation boundary conditions. The finite element equations arising from the solution of nonlinear transient heat conduction problems are formulated. The finite element matrix equations are temporally discretized, and a nonlinear iterative solution algorithm is proposed. Algorithms for solving the linear problem are discussed, taking into account the form of the matrix equations, Gaussian elimination, cost, and iterative techniques. Attention is also given to approximate factorization, implementational aspects, and numerical results.

Iterative methods for elliptic finite element equations on general meshes

NASA Technical Reports Server (NTRS)

Nicolaides, R. A.; Choudhury, Shenaz

1986-01-01

Iterative methods for arbitrary mesh discretizations of elliptic partial differential equations are surveyed. The methods discussed are preconditioned conjugate gradients, algebraic multigrid, deflated conjugate gradients, an element-by-element techniques, and domain decomposition. Computational results are included.

Application of viscous-inviscid interaction methods to transonic turbulent flows

NASA Technical Reports Server (NTRS)

Lee, D.; Pletcher, R. H.

1986-01-01

Two different viscous-inviscid interaction schemes were developed for the analysis of steady, turbulent, transonic, separated flows over axisymmetric bodies. The viscous and inviscid solutions are coupled through the displacement concept using a transpiration velocity approach. In the semi-inverse interaction scheme, the viscous and inviscid equations are solved in an explicitly separate manner and the displacement thickness distribution is iteratively updated by a simple coupling algorithm. In the simultaneous interaction method, local solutions of viscous and inviscid equations are treated simultaneously, and the displacement thickness is treated as an unknown and is obtained as a part of the solution through a global iteration procedure. The inviscid flow region is described by a direct finite-difference solution of a velocity potential equation in conservative form. The potential equation is solved on a numerically generated mesh by an approximate factorization (AF2) scheme in the semi-inverse interaction method and by a successive line overrelaxation (SLOR) scheme in the simultaneous interaction method. The boundary-layer equations are used for the viscous flow region. The continuity and momentum equations are solved inversely in a coupled manner using a fully implicit finite-difference scheme.

A Build-Up Interior Method for Linear Programming: Affine Scaling Form

DTIC Science & Technology

1990-02-01

initiating a major iteration imply convergence in a finite number of iterations. Each iteration t of the Dikin algorithm starts with an interior dual...this variant with the affine scaling method of Dikin [5] (in dual form). We have also looked into the analogous variant for the related Karmarkar’s...4] G. B. Dantzig, Linear Programming and Extensions (Princeton University Press, Princeton, NJ, 1963). [5] I. I. Dikin , "Iterative solution of

Group iterative methods for the solution of two-dimensional time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Balasim, Alla Tareq; Ali, Norhashidah Hj. Mohd.

2016-06-01

Variety of problems in science and engineering may be described by fractional partial differential equations (FPDE) in relation to space and/or time fractional derivatives. The difference between time fractional diffusion equations and standard diffusion equations lies primarily in the time derivative. Over the last few years, iterative schemes derived from the rotated finite difference approximation have been proven to work well in solving standard diffusion equations. However, its application on time fractional diffusion counterpart is still yet to be investigated. In this paper, we will present a preliminary study on the formulation and analysis of new explicit group iterative methods in solving a two-dimensional time fractional diffusion equation. These methods were derived from the standard and rotated Crank-Nicolson difference approximation formula. Several numerical experiments were conducted to show the efficiency of the developed schemes in terms of CPU time and iteration number. At the request of all authors of the paper an updated version of this article was published on 7 July 2016. The original version supplied to AIP Publishing contained an error in Table 1 and References 15 and 16 were incomplete. These errors have been corrected in the updated and republished article.

A Finite-Orbit-Width Fokker-Planck solver for modeling of energetic particle interactions with waves, with application to Helicons in ITER

NASA Astrophysics Data System (ADS)

Petrov, Yuri V.; Harvey, R. W.

2017-10-01

The bounce-average (BA) finite-difference Fokker-Planck (FP) code CQL3D [1,2] now includes the essential physics to describe the RF heating of Finite-Orbit-Width (FOW) ions in tokamaks. The FP equation is reformulated in terms of Constants-Of-Motion coordinates, which we select to be particle speed, pitch angle, and major radius on the equatorial plane thus obtaining the distribution function directly at this location. Full-orbit, low collisionality neoclassical radial transport emerges from averaging the local friction and diffusion coefficients along guiding center orbits. Similarly, the BA of local quasilinear RF diffusion terms gives rise to additional radial transport. The local RF electric field components needed for the BA operator are usually obtained by a ray-tracing code, such as GENRAY, or in conjunction with full-wave codes. As a new, practical application, the CQL3D-FOW version is used for simulation of alpha-particle heating by high-harmonic waves in ITER. Coupling of high harmonic or helicon fast waves power to electrons is a promising current drive (CD) scenario for high beta plasmas. However, the efficiency of current drive can be diminished by parasitic channeling of RF power into fast ions, such as alphas, through finite Larmor-radius effects. We investigate possibilities to reduce the fast ion heating in CD scenarios.

Exploiting parallel computing with limited program changes using a network of microcomputers

NASA Technical Reports Server (NTRS)

Rogers, J. L., Jr.; Sobieszczanski-Sobieski, J.

1985-01-01

Network computing and multiprocessor computers are two discernible trends in parallel processing. The computational behavior of an iterative distributed process in which some subtasks are completed later than others because of an imbalance in computational requirements is of significant interest. The effects of asynchronus processing was studied. A small existing program was converted to perform finite element analysis by distributing substructure analysis over a network of four Apple IIe microcomputers connected to a shared disk, simulating a parallel computer. The substructure analysis uses an iterative, fully stressed, structural resizing procedure. A framework of beams divided into three substructures is used as the finite element model. The effects of asynchronous processing on the convergence of the design variables are determined by not resizing particular substructures on various iterations.

A time dependent difference theory for sound propagation in ducts with flow. [characteristic of inlet and exhaust ducts of turbofan engines

NASA Technical Reports Server (NTRS)

Baumeister, K. J.

1979-01-01

A time dependent numerical solution of the linearized continuity and momentum equation was developed for sound propagation in a two dimensional straight hard or soft wall duct with a sheared mean flow. The time dependent governing acoustic difference equations and boundary conditions were developed along with a numerical determination of the maximum stable time increments. A harmonic noise source radiating into a quiescent duct was analyzed. This explicit iteration method then calculated stepwise in real time to obtain the transient as well as the steady state solution of the acoustic field. Example calculations were presented for sound propagation in hard and soft wall ducts, with no flow and plug flow. Although the problem with sheared flow was formulated and programmed, sample calculations were not examined. The time dependent finite difference analysis was found to be superior to the steady state finite difference and finite element techniques because of shorter solution times and the elimination of large matrix storage requirements.

Algorithmic vs. finite difference Jacobians for infrared atmospheric radiative transfer

NASA Astrophysics Data System (ADS)

Schreier, Franz; Gimeno García, Sebastián; Vasquez, Mayte; Xu, Jian

2015-10-01

Jacobians, i.e. partial derivatives of the radiance and transmission spectrum with respect to the atmospheric state parameters to be retrieved from remote sensing observations, are important for the iterative solution of the nonlinear inverse problem. Finite difference Jacobians are easy to implement, but computationally expensive and possibly of dubious quality; on the other hand, analytical Jacobians are accurate and efficient, but the implementation can be quite demanding. GARLIC, our "Generic Atmospheric Radiation Line-by-line Infrared Code", utilizes algorithmic differentiation (AD) techniques to implement derivatives w.r.t. atmospheric temperature and molecular concentrations. In this paper, we describe our approach for differentiation of the high resolution infrared and microwave spectra and provide an in-depth assessment of finite difference approximations using "exact" AD Jacobians as a reference. The results indicate that the "standard" two-point finite differences with 1 K and 1% perturbation for temperature and volume mixing ratio, respectively, can exhibit substantial errors, and central differences are significantly better. However, these deviations do not transfer into the truncated singular value decomposition solution of a least squares problem. Nevertheless, AD Jacobians are clearly recommended because of the superior speed and accuracy.

DENSITY-DEPENDENT FLOW IN ONE-DIMENSIONAL VARIABLY-SATURATED MEDIA

EPA Science Inventory

A one-dimensional finite element is developed to simulate density-dependent flow of saltwater in variably saturated media. The flow and solute equations were solved in a coupled mode (iterative), in a partially coupled mode (non-iterative), and in a completely decoupled mode. P...

Computational aspects of helicopter trim analysis and damping levels from Floquet theory

NASA Technical Reports Server (NTRS)

Gaonkar, Gopal H.; Achar, N. S.

1992-01-01

Helicopter trim settings of periodic initial state and control inputs are investigated for convergence of Newton iteration in computing the settings sequentially and in parallel. The trim analysis uses a shooting method and a weak version of two temporal finite element methods with displacement formulation and with mixed formulation of displacements and momenta. These three methods broadly represent two main approaches of trim analysis: adaptation of initial-value and finite element boundary-value codes to periodic boundary conditions, particularly for unstable and marginally stable systems. In each method, both the sequential and in-parallel schemes are used and the resulting nonlinear algebraic equations are solved by damped Newton iteration with an optimally selected damping parameter. The impact of damped Newton iteration, including earlier-observed divergence problems in trim analysis, is demonstrated by the maximum condition number of the Jacobian matrices of the iterative scheme and by virtual elimination of divergence. The advantages of the in-parallel scheme over the conventional sequential scheme are also demonstrated.

Moving mesh finite element simulation for phase-field modeling of brittle fracture and convergence of Newton's iteration

NASA Astrophysics Data System (ADS)

Zhang, Fei; Huang, Weizhang; Li, Xianping; Zhang, Shicheng

2018-03-01

A moving mesh finite element method is studied for the numerical solution of a phase-field model for brittle fracture. The moving mesh partial differential equation approach is employed to dynamically track crack propagation. Meanwhile, the decomposition of the strain tensor into tensile and compressive components is essential for the success of the phase-field modeling of brittle fracture but results in a non-smooth elastic energy and stronger nonlinearity in the governing equation. This makes the governing equation much more difficult to solve and, in particular, Newton's iteration often fails to converge. Three regularization methods are proposed to smooth out the decomposition of the strain tensor. Numerical examples of fracture propagation under quasi-static load demonstrate that all of the methods can effectively improve the convergence of Newton's iteration for relatively small values of the regularization parameter but without compromising the accuracy of the numerical solution. They also show that the moving mesh finite element method is able to adaptively concentrate the mesh elements around propagating cracks and handle multiple and complex crack systems.

A Parallel Fast Sweeping Method for the Eikonal Equation

NASA Astrophysics Data System (ADS)

Baker, B.

2017-12-01

Recently, there has been an exciting emergence of probabilistic methods for travel time tomography. Unlike gradient-based optimization strategies, probabilistic tomographic methods are resistant to becoming trapped in a local minimum and provide a much better quantification of parameter resolution than, say, appealing to ray density or performing checkerboard reconstruction tests. The benefits associated with random sampling methods however are only realized by successive computation of predicted travel times in, potentially, strongly heterogeneous media. To this end this abstract is concerned with expediting the solution of the Eikonal equation. While many Eikonal solvers use a fast marching method, the proposed solver will use the iterative fast sweeping method because the eight fixed sweep orderings in each iteration are natural targets for parallelization. To reduce the number of iterations and grid points required the high-accuracy finite difference stencil of Nobel et al., 2014 is implemented. A directed acyclic graph (DAG) is created with a priori knowledge of the sweep ordering and finite different stencil. By performing a topological sort of the DAG sets of independent nodes are identified as candidates for concurrent updating. Additionally, the proposed solver will also address scalability during earthquake relocation, a necessary step in local and regional earthquake tomography and a barrier to extending probabilistic methods from active source to passive source applications, by introducing an asynchronous parallel forward solve phase for all receivers in the network. Synthetic examples using the SEG over-thrust model will be presented.

The Development of a Finite Volume Method for Modeling Sound in Coastal Ocean Environment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Long, Wen; Yang, Zhaoqing; Copping, Andrea E.

: As the rapid growth of marine renewable energy and off-shore wind energy, there have been concerns that the noises generated from construction and operation of the devices may interfere marine animals’ communication. In this research, a underwater sound model is developed to simulate sound prorogation generated by marine-hydrokinetic energy (MHK) devices or offshore wind (OSW) energy platforms. Finite volume and finite difference methods are developed to solve the 3D Helmholtz equation of sound propagation in the coastal environment. For finite volume method, the grid system consists of triangular grids in horizontal plane and sigma-layers in vertical dimension. A 3Dmore » sparse matrix solver with complex coefficients is formed for solving the resulting acoustic pressure field. The Complex Shifted Laplacian Preconditioner (CSLP) method is applied to efficiently solve the matrix system iteratively with MPI parallelization using a high performance cluster. The sound model is then coupled with the Finite Volume Community Ocean Model (FVCOM) for simulating sound propagation generated by human activities in a range-dependent setting, such as offshore wind energy platform constructions and tidal stream turbines. As a proof of concept, initial validation of the finite difference solver is presented for two coastal wedge problems. Validation of finite volume method will be reported separately.« less

Finite-beta equilibria for Wendelstein 7-X configurations using the Princeton Iterative Equilibrium Solver code

NASA Astrophysics Data System (ADS)

Arndt, S.; Merkel, P.; Monticello, D. A.; Reiman, A. H.

1999-04-01

Fixed- and free-boundary equilibria for Wendelstein 7-X (W7-X) [W. Lotz et al., Plasma Physics and Controlled Nuclear Fusion Research 1990 (Proc. 13th Int. Conf. Washington, DC, 1990), (International Atomic Energy Agency, Vienna, 1991), Vol. 2, p. 603] configurations are calculated using the Princeton Iterative Equilibrium Solver (PIES) [A. H. Reiman et al., Comput. Phys. Commun., 43, 157 (1986)] to deal with magnetic islands and stochastic regions. Usually, these W7-X configurations require a large number of iterations for PIES convergence. Here, two methods have been successfully tested in an attempt to decrease the number of iterations needed for convergence. First, periodic sequences of different blending parameters are used. Second, the initial guess is vastly improved by using results of the Variational Moments Equilibrium Code (VMEC) [S. P. Hirshmann et al., Phys. Fluids 26, 3553 (1983)]. Use of these two methods have allowed verification of the Hamada condition and tendency of "self-healing" of islands has been observed.

Three dimensional iterative beam propagation method for optical waveguide devices

NASA Astrophysics Data System (ADS)

Ma, Changbao; Van Keuren, Edward

2006-10-01

The finite difference beam propagation method (FD-BPM) is an effective model for simulating a wide range of optical waveguide structures. The classical FD-BPMs are based on the Crank-Nicholson scheme, and in tridiagonal form can be solved using the Thomas method. We present a different type of algorithm for 3-D structures. In this algorithm, the wave equation is formulated into a large sparse matrix equation which can be solved using iterative methods. The simulation window shifting scheme and threshold technique introduced in our earlier work are utilized to overcome the convergence problem of iterative methods for large sparse matrix equation and wide-angle simulations. This method enables us to develop higher-order 3-D wide-angle (WA-) BPMs based on Pade approximant operators and the multistep method, which are commonly used in WA-BPMs for 2-D structures. Simulations using the new methods will be compared to the analytical results to assure its effectiveness and applicability.

RAXBOD- INVISCID TRANSONIC FLOW OVER AXISYMMETRIC BODIES

NASA Technical Reports Server (NTRS)

Keller, J. D.

1994-01-01

The problem of axisymmetric transonic flow is of interest not only because of the practical application to missile and launch vehicle aerodynamics, but also because of its relation to fully three-dimensional flow in terms of the area rule. The RAXBOD computer program was developed for the analysis of steady, inviscid, irrotational, transonic flow over axisymmetric bodies in free air. RAXBOD uses a finite-difference relaxation method to numerically solve the exact formulation of the disturbance velocity potential with exact surface boundary conditions. Agreement with available experimental results has been good in cases where viscous effects and wind-tunnel wall interference are not important. The governing second-order partial differential equation describing the flow potential is replaced by a system of finite difference equations, including Jameson's "rotated" difference scheme at supersonic points. A stretching is applied to both the normal and tangential coordinates such that the infinite physical space is mapped onto a finite computational space. The boundary condition at infinity can be applied directly and there is no need for an asymptotic far-field solution. The system of finite difference equations is solved by a column relaxation method. In order to obtain both rapid convergence and any desired resolution, the relaxation is performed iteratively on successively refined grids. Input to RAXBOD consists of a description of the body geometry, the free stream conditions, and the desired resolution control parameters. Output from RAXBOD includes computed geometric parameters in the normal and tangential directions, iteration history information, drag coefficients, flow field data in the computational plane, and coordinates of the sonic line. This program is written in FORTRAN IV for batch execution and has been implemented on a CDC 6600 computer with an overlayed central memory requirement of approximately 40K (octal) of 60 bit words. Optional plotted output can be generated for the Calcomp plotting system. The RAXBOD program was developed in 1976.

POSTPROCESSING MIXED FINITE ELEMENT METHODS FOR SOLVING CAHN-HILLIARD EQUATION: METHODS AND ERROR ANALYSIS

PubMed Central

Wang, Wansheng; Chen, Long; Zhou, Jie

2015-01-01

A postprocessing technique for mixed finite element methods for the Cahn-Hilliard equation is developed and analyzed. Once the mixed finite element approximations have been computed at a fixed time on the coarser mesh, the approximations are postprocessed by solving two decoupled Poisson equations in an enriched finite element space (either on a finer grid or a higher-order space) for which many fast Poisson solvers can be applied. The nonlinear iteration is only applied to a much smaller size problem and the computational cost using Newton and direct solvers is negligible compared with the cost of the linear problem. The analysis presented here shows that this technique remains the optimal rate of convergence for both the concentration and the chemical potential approximations. The corresponding error estimate obtained in our paper, especially the negative norm error estimates, are non-trivial and different with the existing results in the literatures. PMID:27110063

Iterative and multigrid methods in the finite element solution of incompressible and turbulent fluid flow

NASA Astrophysics Data System (ADS)

Lavery, N.; Taylor, C.

1999-07-01

Multigrid and iterative methods are used to reduce the solution time of the matrix equations which arise from the finite element (FE) discretisation of the time-independent equations of motion of the incompressible fluid in turbulent motion. Incompressible flow is solved by using the method of reduce interpolation for the pressure to satisfy the Brezzi-Babuska condition. The k-l model is used to complete the turbulence closure problem. The non-symmetric iterative matrix methods examined are the methods of least squares conjugate gradient (LSCG), biconjugate gradient (BCG), conjugate gradient squared (CGS), and the biconjugate gradient squared stabilised (BCGSTAB). The multigrid algorithm applied is based on the FAS algorithm of Brandt, and uses two and three levels of grids with a V-cycling schedule. These methods are all compared to the non-symmetric frontal solver. Copyright

An efficient flexible-order model for 3D nonlinear water waves

NASA Astrophysics Data System (ADS)

Engsig-Karup, A. P.; Bingham, H. B.; Lindberg, O.

2009-04-01

The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211-228] is extended to three dimensions (3D). In order to obtain an optimal scaling of the solution effort multigrid is employed to precondition a GMRES iterative solution of the discretized Laplace problem. A robust multigrid method based on Gauss-Seidel smoothing is found to require special treatment of the boundary conditions along solid boundaries, and in particular on the sea bottom. A new discretization scheme using one layer of grid points outside the fluid domain is presented and shown to provide convergent solutions over the full physical and discrete parameter space of interest. Linear analysis of the fundamental properties of the scheme with respect to accuracy, robustness and energy conservation are presented together with demonstrations of grid independent iteration count and optimal scaling of the solution effort. Calculations are made for 3D nonlinear wave problems for steep nonlinear waves and a shoaling problem which show good agreement with experimental measurements and other calculations from the literature.

High-performance finite-difference time-domain simulations of C-Mod and ITER RF antennas

NASA Astrophysics Data System (ADS)

Jenkins, Thomas G.; Smithe, David N.

2015-12-01

Finite-difference time-domain methods have, in recent years, developed powerful capabilities for modeling realistic ICRF behavior in fusion plasmas [1, 2, 3, 4]. When coupled with the power of modern high-performance computing platforms, such techniques allow the behavior of antenna near and far fields, and the flow of RF power, to be studied in realistic experimental scenarios at previously inaccessible levels of resolution. In this talk, we present results and 3D animations from high-performance FDTD simulations on the Titan Cray XK7 supercomputer, modeling both Alcator C-Mod's field-aligned ICRF antenna and the ITER antenna module. Much of this work focuses on scans over edge density, and tailored edge density profiles, to study dispersion and the physics of slow wave excitation in the immediate vicinity of the antenna hardware and SOL. An understanding of the role of the lower-hybrid resonance in low-density scenarios is emerging, and possible implications of this for the NSTX launcher and power balance are also discussed. In addition, we discuss ongoing work centered on using these simulations to estimate sputtering and impurity production, as driven by the self-consistent sheath potentials at antenna surfaces.

High-performance finite-difference time-domain simulations of C-Mod and ITER RF antennas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jenkins, Thomas G., E-mail: tgjenkins@txcorp.com; Smithe, David N., E-mail: smithe@txcorp.com

Finite-difference time-domain methods have, in recent years, developed powerful capabilities for modeling realistic ICRF behavior in fusion plasmas [1, 2, 3, 4]. When coupled with the power of modern high-performance computing platforms, such techniques allow the behavior of antenna near and far fields, and the flow of RF power, to be studied in realistic experimental scenarios at previously inaccessible levels of resolution. In this talk, we present results and 3D animations from high-performance FDTD simulations on the Titan Cray XK7 supercomputer, modeling both Alcator C-Mod’s field-aligned ICRF antenna and the ITER antenna module. Much of this work focuses on scansmore » over edge density, and tailored edge density profiles, to study dispersion and the physics of slow wave excitation in the immediate vicinity of the antenna hardware and SOL. An understanding of the role of the lower-hybrid resonance in low-density scenarios is emerging, and possible implications of this for the NSTX launcher and power balance are also discussed. In addition, we discuss ongoing work centered on using these simulations to estimate sputtering and impurity production, as driven by the self-consistent sheath potentials at antenna surfaces.« less

Iterative Methods to Solve Linear RF Fields in Hot Plasma

NASA Astrophysics Data System (ADS)

Spencer, Joseph; Svidzinski, Vladimir; Evstatiev, Evstati; Galkin, Sergei; Kim, Jin-Soo

2014-10-01

Most magnetic plasma confinement devices use radio frequency (RF) waves for current drive and/or heating. Numerical modeling of RF fields is an important part of performance analysis of such devices and a predictive tool aiding design and development of future devices. Prior attempts at this modeling have mostly used direct solvers to solve the formulated linear equations. Full wave modeling of RF fields in hot plasma with 3D nonuniformities is mostly prohibited, with memory demands of a direct solver placing a significant limitation on spatial resolution. Iterative methods can significantly increase spatial resolution. We explore the feasibility of using iterative methods in 3D full wave modeling. The linear wave equation is formulated using two approaches: for cold plasmas the local cold plasma dielectric tensor is used (resolving resonances by particle collisions), while for hot plasmas the conductivity kernel (which includes a nonlocal dielectric response) is calculated by integrating along test particle orbits. The wave equation is discretized using a finite difference approach. The initial guess is important in iterative methods, and we examine different initial guesses including the solution to the cold plasma wave equation. Work is supported by the U.S. DOE SBIR program.

Solution of a tridiagonal system of equations on the finite element machine

NASA Technical Reports Server (NTRS)

Bostic, S. W.

1984-01-01

Two parallel algorithms for the solution of tridiagonal systems of equations were implemented on the Finite Element Machine. The Accelerated Parallel Gauss method, an iterative method, and the Buneman algorithm, a direct method, are discussed and execution statistics are presented.

The L sub 1 finite element method for pure convection problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan

1991-01-01

The least squares (L sub 2) finite element method is introduced for 2-D steady state pure convection problems with smooth solutions. It is proven that the L sub 2 method has the same stability estimate as the original equation, i.e., the L sub 2 method has better control of the streamline derivative. Numerical convergence rates are given to show that the L sub 2 method is almost optimal. This L sub 2 method was then used as a framework to develop an iteratively reweighted L sub 2 finite element method to obtain a least absolute residual (L sub 1) solution for problems with discontinuous solutions. This L sub 1 finite element method produces a nonoscillatory, nondiffusive and highly accurate numerical solution that has a sharp discontinuity in one element on both coarse and fine meshes. A robust reweighting strategy was also devised to obtain the L sub 1 solution in a few iterations. A number of examples solved by using triangle and bilinear elements are presented.

A Kernel-free Boundary Integral Method for Elliptic Boundary Value Problems ⋆

PubMed Central

Ying, Wenjun; Henriquez, Craig S.

2013-01-01

This paper presents a class of kernel-free boundary integral (KFBI) methods for general elliptic boundary value problems (BVPs). The boundary integral equations reformulated from the BVPs are solved iteratively with the GMRES method. During the iteration, the boundary and volume integrals involving Green's functions are approximated by structured grid-based numerical solutions, which avoids the need to know the analytical expressions of Green's functions. The KFBI method assumes that the larger regular domain, which embeds the original complex domain, can be easily partitioned into a hierarchy of structured grids so that fast elliptic solvers such as the fast Fourier transform (FFT) based Poisson/Helmholtz solvers or those based on geometric multigrid iterations are applicable. The structured grid-based solutions are obtained with standard finite difference method (FDM) or finite element method (FEM), where the right hand side of the resulting linear system is appropriately modified at irregular grid nodes to recover the formal accuracy of the underlying numerical scheme. Numerical results demonstrating the efficiency and accuracy of the KFBI methods are presented. It is observed that the number of GM-RES iterations used by the method for solving isotropic and moderately anisotropic BVPs is independent of the sizes of the grids that are employed to approximate the boundary and volume integrals. With the standard second-order FEMs and FDMs, the KFBI method shows a second-order convergence rate in accuracy for all of the tested Dirichlet/Neumann BVPs when the anisotropy of the diffusion tensor is not too strong. PMID:23519600

An iterative truncation method for unbounded electromagnetic problems using varying order finite elements

NASA Astrophysics Data System (ADS)

Paul, Prakash

2009-12-01

The finite element method (FEM) is used to solve three-dimensional electromagnetic scattering and radiation problems. Finite element (FE) solutions of this kind contain two main types of error: discretization error and boundary error. Discretization error depends on the number of free parameters used to model the problem, and on how effectively these parameters are distributed throughout the problem space. To reduce the discretization error, the polynomial order of the finite elements is increased, either uniformly over the problem domain or selectively in those areas with the poorest solution quality. Boundary error arises from the condition applied to the boundary that is used to truncate the computational domain. To reduce the boundary error, an iterative absorbing boundary condition (IABC) is implemented. The IABC starts with an inexpensive boundary condition and gradually improves the quality of the boundary condition as the iteration continues. An automatic error control (AEC) is implemented to balance the two types of error. With the AEC, the boundary condition is improved when the discretization error has fallen to a low enough level to make this worth doing. The AEC has these characteristics: (i) it uses a very inexpensive truncation method initially; (ii) it allows the truncation boundary to be very close to the scatterer/radiator; (iii) it puts more computational effort on the parts of the problem domain where it is most needed; and (iv) it can provide as accurate a solution as needed depending on the computational price one is willing to pay. To further reduce the computational cost, disjoint scatterers and radiators that are relatively far from each other are bounded separately and solved using a multi-region method (MRM), which leads to savings in computational cost. A simple analytical way to decide whether the MRM or the single region method will be computationally cheaper is also described. To validate the accuracy and savings in computation time, different shaped metallic and dielectric obstacles (spheres, ogives, cube, flat plate, multi-layer slab etc.) are used for the scattering problems. For the radiation problems, waveguide excited antennas (horn antenna, waveguide with flange, microstrip patch antenna) are used. Using the AEC the peak reduction in computation time during the iteration is typically a factor of 2, compared to the IABC using the same element orders throughout. In some cases, it can be as high as a factor of 4.

High-performance equation solvers and their impact on finite element analysis

NASA Technical Reports Server (NTRS)

Poole, Eugene L.; Knight, Norman F., Jr.; Davis, D. Dale, Jr.

1990-01-01

The role of equation solvers in modern structural analysis software is described. Direct and iterative equation solvers which exploit vectorization on modern high-performance computer systems are described and compared. The direct solvers are two Cholesky factorization methods. The first method utilizes a novel variable-band data storage format to achieve very high computation rates and the second method uses a sparse data storage format designed to reduce the number of operations. The iterative solvers are preconditioned conjugate gradient methods. Two different preconditioners are included; the first uses a diagonal matrix storage scheme to achieve high computation rates and the second requires a sparse data storage scheme and converges to the solution in fewer iterations that the first. The impact of using all of the equation solvers in a common structural analysis software system is demonstrated by solving several representative structural analysis problems.

High-performance equation solvers and their impact on finite element analysis

NASA Technical Reports Server (NTRS)

Poole, Eugene L.; Knight, Norman F., Jr.; Davis, D. D., Jr.

1992-01-01

The role of equation solvers in modern structural analysis software is described. Direct and iterative equation solvers which exploit vectorization on modern high-performance computer systems are described and compared. The direct solvers are two Cholesky factorization methods. The first method utilizes a novel variable-band data storage format to achieve very high computation rates and the second method uses a sparse data storage format designed to reduce the number od operations. The iterative solvers are preconditioned conjugate gradient methods. Two different preconditioners are included; the first uses a diagonal matrix storage scheme to achieve high computation rates and the second requires a sparse data storage scheme and converges to the solution in fewer iterations that the first. The impact of using all of the equation solvers in a common structural analysis software system is demonstrated by solving several representative structural analysis problems.

2-D Fused Image Reconstruction approach for Microwave Tomography: a theoretical assessment using FDTD Model.

PubMed

Bindu, G; Semenov, S

2013-01-01

This paper describes an efficient two-dimensional fused image reconstruction approach for Microwave Tomography (MWT). Finite Difference Time Domain (FDTD) models were created for a viable MWT experimental system having the transceivers modelled using thin wire approximation with resistive voltage sources. Born Iterative and Distorted Born Iterative methods have been employed for image reconstruction with the extremity imaging being done using a differential imaging technique. The forward solver in the imaging algorithm employs the FDTD method of solving the time domain Maxwell's equations with the regularisation parameter computed using a stochastic approach. The algorithm is tested with 10% noise inclusion and successful image reconstruction has been shown implying its robustness.

A preconditioner for the finite element computation of incompressible, nonlinear elastic deformations

NASA Astrophysics Data System (ADS)

Whiteley, J. P.

2017-10-01

Large, incompressible elastic deformations are governed by a system of nonlinear partial differential equations. The finite element discretisation of these partial differential equations yields a system of nonlinear algebraic equations that are usually solved using Newton's method. On each iteration of Newton's method, a linear system must be solved. We exploit the structure of the Jacobian matrix to propose a preconditioner, comprising two steps. The first step is the solution of a relatively small, symmetric, positive definite linear system using the preconditioned conjugate gradient method. This is followed by a small number of multigrid V-cycles for a larger linear system. Through the use of exemplar elastic deformations, the preconditioner is demonstrated to facilitate the iterative solution of the linear systems arising. The number of GMRES iterations required has only a very weak dependence on the number of degrees of freedom of the linear systems.

Higher-order finite-difference formulation of periodic Orbital-free Density Functional Theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghosh, Swarnava; Suryanarayana, Phanish, E-mail: phanish.suryanarayana@ce.gatech.edu

2016-02-15

We present a real-space formulation and higher-order finite-difference implementation of periodic Orbital-free Density Functional Theory (OF-DFT). Specifically, utilizing a local reformulation of the electrostatic and kernel terms, we develop a generalized framework for performing OF-DFT simulations with different variants of the electronic kinetic energy. In particular, we propose a self-consistent field (SCF) type fixed-point method for calculations involving linear-response kinetic energy functionals. In this framework, evaluation of both the electronic ground-state and forces on the nuclei are amenable to computations that scale linearly with the number of atoms. We develop a parallel implementation of this formulation using the finite-difference discretization.more » We demonstrate that higher-order finite-differences can achieve relatively large convergence rates with respect to mesh-size in both the energies and forces. Additionally, we establish that the fixed-point iteration converges rapidly, and that it can be further accelerated using extrapolation techniques like Anderson's mixing. We validate the accuracy of the results by comparing the energies and forces with plane-wave methods for selected examples, including the vacancy formation energy in Aluminum. Overall, the suitability of the proposed formulation for scalable high performance computing makes it an attractive choice for large-scale OF-DFT calculations consisting of thousands of atoms.« less

Iterative learning control with applications in energy generation, lasers and health care.

PubMed

Rogers, E; Tutty, O R

2016-09-01

Many physical systems make repeated executions of the same finite time duration task. One example is a robot in a factory or warehouse whose task is to collect an object in sequence from a location, transfer it over a finite duration, place it at a specified location or on a moving conveyor and then return for the next one and so on. Iterative learning control was especially developed for systems with this mode of operation and this paper gives an overview of this control design method using relatively recent relevant applications in wind turbines, free-electron lasers and health care, as exemplars to demonstrate its applicability.

A Huygens immersed-finite-element particle-in-cell method for modeling plasma-surface interactions with moving interface

NASA Astrophysics Data System (ADS)

Cao, Huijun; Cao, Yong; Chu, Yuchuan; He, Xiaoming; Lin, Tao

2018-06-01

Surface evolution is an unavoidable issue in engineering plasma applications. In this article an iterative method for modeling plasma-surface interactions with moving interface is proposed and validated. In this method, the plasma dynamics is simulated by an immersed finite element particle-in-cell (IFE-PIC) method, and the surface evolution is modeled by the Huygens wavelet method which is coupled with the iteration of the IFE-PIC method. Numerical experiments, including prototypical engineering applications, such as the erosion of Hall thruster channel wall, are presented to demonstrate features of this Huygens IFE-PIC method for simulating the dynamic plasma-surface interactions.

Internal and external axial corner flows

NASA Technical Reports Server (NTRS)

Kutler, P.; Shankar, V.; Anderson, D. A.; Sorenson, R. L.

1975-01-01

The inviscid, internal, and external axial corner flows generated by two intersecting wedges traveling supersonically are obtained by use of a second-order shock-capturing, finite-difference approach. The governing equations are solved iteratively in conical coordinates to yield the complicated wave structure of the internal corner and the simple peripheral shock of the external corner. The numerical results for the internal flows compare favorably with existing experimental data.

Recent advances in two-phase flow numerics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mahaffy, J.H.; Macian, R.

1997-07-01

The authors review three topics in the broad field of numerical methods that may be of interest to individuals modeling two-phase flow in nuclear power plants. The first topic is iterative solution of linear equations created during the solution of finite volume equations. The second is numerical tracking of macroscopic liquid interfaces. The final area surveyed is the use of higher spatial difference techniques.

Non-iterative determination of the stress-density relation from ramp wave data through a window

NASA Astrophysics Data System (ADS)

Dowling, Evan; Fratanduono, Dayne; Swift, Damian

2017-06-01

In the canonical ramp compression experiment, a smoothly-increasing load is applied the surface of the sample, and the particle velocity history is measured at interfaces two or more different distances into the sample. The velocity histories are used to deduce a stress-density relation by correcting for perturbations caused by reflected release waves, usually via the iterative Lagrangian analysis technique of Rothman and Maw. We previously described a non-iterative (recursive) method of analysis, which was more stable and orders of magnitude faster than iteration, but was subject to the limitation that the free surface velocity had to be sampled at uniform intervals. We have now developed more general recursive algorithms suitable for analyzing ramp data through a finite-impedance window. Free surfaces can be treated seamlessly, and the need for uniform velocity sampling has been removed. These calculations require interpolation of partially-released states using the partially-constructed isentrope, making them slower than the previous free-surface scheme, but they are still much faster than iterative analysis. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Highly efficient and exact method for parallelization of grid-based algorithms and its implementation in DelPhi

PubMed Central

Li, Chuan; Li, Lin; Zhang, Jie; Alexov, Emil

2012-01-01

The Gauss-Seidel method is a standard iterative numerical method widely used to solve a system of equations and, in general, is more efficient comparing to other iterative methods, such as the Jacobi method. However, standard implementation of the Gauss-Seidel method restricts its utilization in parallel computing due to its requirement of using updated neighboring values (i.e., in current iteration) as soon as they are available. Here we report an efficient and exact (not requiring assumptions) method to parallelize iterations and to reduce the computational time as a linear/nearly linear function of the number of CPUs. In contrast to other existing solutions, our method does not require any assumptions and is equally applicable for solving linear and nonlinear equations. This approach is implemented in the DelPhi program, which is a finite difference Poisson-Boltzmann equation solver to model electrostatics in molecular biology. This development makes the iterative procedure on obtaining the electrostatic potential distribution in the parallelized DelPhi several folds faster than that in the serial code. Further we demonstrate the advantages of the new parallelized DelPhi by computing the electrostatic potential and the corresponding energies of large supramolecular structures. PMID:22674480

Quantized Iterative Learning Consensus Tracking of Digital Networks With Limited Information Communication.

PubMed

Xiong, Wenjun; Yu, Xinghuo; Chen, Yao; Gao, Jie

2017-06-01

This brief investigates the quantized iterative learning problem for digital networks with time-varying topologies. The information is first encoded as symbolic data and then transmitted. After the data are received, a decoder is used by the receiver to get an estimate of the sender's state. Iterative learning quantized communication is considered in the process of encoding and decoding. A sufficient condition is then presented to achieve the consensus tracking problem in a finite interval using the quantized iterative learning controllers. Finally, simulation results are given to illustrate the usefulness of the developed criterion.

Computer program for solving laminar, transitional, or turbulent compressible boundary-layer equations for two-dimensional and axisymmetric flow

NASA Technical Reports Server (NTRS)

Harris, J. E.; Blanchard, D. K.

1982-01-01

A numerical algorithm and computer program are presented for solving the laminar, transitional, or turbulent two dimensional or axisymmetric compressible boundary-layer equations for perfect-gas flows. The governing equations are solved by an iterative three-point implicit finite-difference procedure. The software, program VGBLP, is a modification of the approach presented in NASA TR R-368 and NASA TM X-2458, respectively. The major modifications are: (1) replacement of the fourth-order Runge-Kutta integration technique with a finite-difference procedure for numerically solving the equations required to initiate the parabolic marching procedure; (2) introduction of the Blottner variable-grid scheme; (3) implementation of an iteration scheme allowing the coupled system of equations to be converged to a specified accuracy level; and (4) inclusion of an iteration scheme for variable-entropy calculations. These modifications to the approach presented in NASA TR R-368 and NASA TM X-2458 yield a software package with high computational efficiency and flexibility. Turbulence-closure options include either two-layer eddy-viscosity or mixing-length models. Eddy conductivity is modeled as a function of eddy viscosity through a static turbulent Prandtl number formulation. Several options are provided for specifying the static turbulent Prandtl number. The transitional boundary layer is treated through a streamwise intermittency function which modifies the turbulence-closure model. This model is based on the probability distribution of turbulent spots and ranges from zero to unity for laminar and turbulent flow, respectively. Several test cases are presented as guides for potential users of the software.

Large Deviations and Quasipotential for Finite State Mean Field Interacting Particle Systems

DTIC Science & Technology

2014-05-01

The conclusion then follows by applying Lemma 4.4.2. 132 119 4.4.1 Iterative solver: The widest neighborhood structure We employ Gauss - Seidel ...nearest neighborhood structure described in Section 4.4.2. We use Gauss - Seidel iterative method for our numerical experiments. The Gauss - Seidel ...x ∈ Bh, M x ∈ Sh\\Bh, where M ∈ (V,∞) is a very large number, so that the iteration (4.5.1) converges quickly. For simplicity, we restrict our

Low Density Parity Check Codes Based on Finite Geometries: A Rediscovery and More

NASA Technical Reports Server (NTRS)

Kou, Yu; Lin, Shu; Fossorier, Marc

1999-01-01

Low density parity check (LDPC) codes with iterative decoding based on belief propagation achieve astonishing error performance close to Shannon limit. No algebraic or geometric method for constructing these codes has been reported and they are largely generated by computer search. As a result, encoding of long LDPC codes is in general very complex. This paper presents two classes of high rate LDPC codes whose constructions are based on finite Euclidean and projective geometries, respectively. These classes of codes a.re cyclic and have good constraint parameters and minimum distances. Cyclic structure adows the use of linear feedback shift registers for encoding. These finite geometry LDPC codes achieve very good error performance with either soft-decision iterative decoding based on belief propagation or Gallager's hard-decision bit flipping algorithm. These codes can be punctured or extended to obtain other good LDPC codes. A generalization of these codes is also presented.

Updating finite element dynamic models using an element-by-element sensitivity methodology

NASA Technical Reports Server (NTRS)

Farhat, Charbel; Hemez, Francois M.

1993-01-01

A sensitivity-based methodology for improving the finite element model of a given structure using test modal data and a few sensors is presented. The proposed method searches for both the location and sources of the mass and stiffness errors and does not interfere with the theory behind the finite element model while correcting these errors. The updating algorithm is derived from the unconstrained minimization of the squared L sub 2 norms of the modal dynamic residuals via an iterative two-step staggered procedure. At each iteration, the measured mode shapes are first expanded assuming that the model is error free, then the model parameters are corrected assuming that the expanded mode shapes are exact. The numerical algorithm is implemented in an element-by-element fashion and is capable of 'zooming' on the detected error locations. Several simulation examples which demonstate the potential of the proposed methodology are discussed.

A split finite element algorithm for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Baker, A. J.

1979-01-01

An accurate and efficient numerical solution algorithm is established for solution of the high Reynolds number limit of the Navier-Stokes equations governing the multidimensional flow of a compressible essentially inviscid fluid. Finite element interpolation theory is used within a dissipative formulation established using Galerkin criteria within the Method of Weighted Residuals. An implicit iterative solution algorithm is developed, employing tensor product bases within a fractional steps integration procedure, that significantly enhances solution economy concurrent with sharply reduced computer hardware demands. The algorithm is evaluated for resolution of steep field gradients and coarse grid accuracy using both linear and quadratic tensor product interpolation bases. Numerical solutions for linear and nonlinear, one, two and three dimensional examples confirm and extend the linearized theoretical analyses, and results are compared to competitive finite difference derived algorithms.

Low speed airfoil design and analysis

NASA Technical Reports Server (NTRS)

Eppler, R.; Somers, D. M.

1979-01-01

A low speed airfoil design and analysis program was developed which contains several unique features. In the design mode, the velocity distribution is not specified for one but many different angles of attack. Several iteration options are included which allow the trailing edge angle to be specified while other parameters are iterated. For airfoil analysis, a panel method is available which uses third-order panels having parabolic vorticity distributions. The flow condition is satisfied at the end points of the panels. Both sharp and blunt trailing edges can be analyzed. The integral boundary layer method with its laminar separation bubble analog, empirical transition criterion, and precise turbulent boundary layer equations compares very favorably with other methods, both integral and finite difference. Comparisons with experiment for several airfoils over a very wide Reynolds number range are discussed. Applications to high lift airfoil design are also demonstrated.

Finite difference method accelerated with sparse solvers for structural analysis of the metal-organic complexes

NASA Astrophysics Data System (ADS)

Guda, A. A.; Guda, S. A.; Soldatov, M. A.; Lomachenko, K. A.; Bugaev, A. L.; Lamberti, C.; Gawelda, W.; Bressler, C.; Smolentsev, G.; Soldatov, A. V.; Joly, Y.

2016-05-01

Finite difference method (FDM) implemented in the FDMNES software [Phys. Rev. B, 2001, 63, 125120] was revised. Thorough analysis shows, that the calculated diagonal in the FDM matrix consists of about 96% zero elements. Thus a sparse solver would be more suitable for the problem instead of traditional Gaussian elimination for the diagonal neighbourhood. We have tried several iterative sparse solvers and the direct one MUMPS solver with METIS ordering turned out to be the best. Compared to the Gaussian solver present method is up to 40 times faster and allows XANES simulations for complex systems already on personal computers. We show applicability of the software for metal-organic [Fe(bpy)3]2+ complex both for low spin and high spin states populated after laser excitation.

A computer code for three-dimensional incompressible flows using nonorthogonal body-fitted coordinate systems

NASA Technical Reports Server (NTRS)

Chen, Y. S.

1986-01-01

In this report, a numerical method for solving the equations of motion of three-dimensional incompressible flows in nonorthogonal body-fitted coordinate (BFC) systems has been developed. The equations of motion are transformed to a generalized curvilinear coordinate system from which the transformed equations are discretized using finite difference approximations in the transformed domain. The hybrid scheme is used to approximate the convection terms in the governing equations. Solutions of the finite difference equations are obtained iteratively by using a pressure-velocity correction algorithm (SIMPLE-C). Numerical examples of two- and three-dimensional, laminar and turbulent flow problems are employed to evaluate the accuracy and efficiency of the present computer code. The user's guide and computer program listing of the present code are also included.

Numerical Characterization of Piezoceramics Using Resonance Curves

PubMed Central

Pérez, Nicolás; Buiochi, Flávio; Brizzotti Andrade, Marco Aurélio; Adamowski, Julio Cezar

2016-01-01

Piezoelectric materials characterization is a challenging problem involving physical concepts, electrical and mechanical measurements and numerical optimization techniques. Piezoelectric ceramics such as Lead Zirconate Titanate (PZT) belong to the 6 mm symmetry class, which requires five elastic, three piezoelectric and two dielectric constants to fully represent the material properties. If losses are considered, the material properties can be represented by complex numbers. In this case, 20 independent material constants are required to obtain the full model. Several numerical methods have been used to adjust the theoretical models to the experimental results. The continuous improvement of the computer processing ability has allowed the use of a specific numerical method, the Finite Element Method (FEM), to iteratively solve the problem of finding the piezoelectric constants. This review presents the recent advances in the numerical characterization of 6 mm piezoelectric materials from experimental electrical impedance curves. The basic strategy consists in measuring the electrical impedance curve of a piezoelectric disk, and then combining the Finite Element Method with an iterative algorithm to find a set of material properties that minimizes the difference between the numerical impedance curve and the experimental one. Different methods to validate the results are also discussed. Examples of characterization of some common piezoelectric ceramics are presented to show the practical application of the described methods. PMID:28787875

Numerical Characterization of Piezoceramics Using Resonance Curves.

PubMed

Pérez, Nicolás; Buiochi, Flávio; Brizzotti Andrade, Marco Aurélio; Adamowski, Julio Cezar

2016-01-27

Piezoelectric materials characterization is a challenging problem involving physical concepts, electrical and mechanical measurements and numerical optimization techniques. Piezoelectric ceramics such as Lead Zirconate Titanate (PZT) belong to the 6 mm symmetry class, which requires five elastic, three piezoelectric and two dielectric constants to fully represent the material properties. If losses are considered, the material properties can be represented by complex numbers. In this case, 20 independent material constants are required to obtain the full model. Several numerical methods have been used to adjust the theoretical models to the experimental results. The continuous improvement of the computer processing ability has allowed the use of a specific numerical method, the Finite Element Method (FEM), to iteratively solve the problem of finding the piezoelectric constants. This review presents the recent advances in the numerical characterization of 6 mm piezoelectric materials from experimental electrical impedance curves. The basic strategy consists in measuring the electrical impedance curve of a piezoelectric disk, and then combining the Finite Element Method with an iterative algorithm to find a set of material properties that minimizes the difference between the numerical impedance curve and the experimental one. Different methods to validate the results are also discussed. Examples of characterization of some common piezoelectric ceramics are presented to show the practical application of the described methods.

Iterative learning control with applications in energy generation, lasers and health care

PubMed Central

Tutty, O. R.

2016-01-01

Many physical systems make repeated executions of the same finite time duration task. One example is a robot in a factory or warehouse whose task is to collect an object in sequence from a location, transfer it over a finite duration, place it at a specified location or on a moving conveyor and then return for the next one and so on. Iterative learning control was especially developed for systems with this mode of operation and this paper gives an overview of this control design method using relatively recent relevant applications in wind turbines, free-electron lasers and health care, as exemplars to demonstrate its applicability. PMID:27713654

Nonlinear analysis of composite thin-walled helicopter blades

NASA Astrophysics Data System (ADS)

Kalfon, J. P.; Rand, O.

Nonlinear theoretical modeling of laminated thin-walled composite helicopter rotor blades is presented. The derivation is based on nonlinear geometry with a detailed treatment of the body loads in the axial direction which are induced by the rotation. While the in-plane warping is neglected, a three-dimensional generic out-of-plane warping distribution is included. The formulation may also handle varying thicknesses and mass distribution along the cross-sectional walls. The problem is solved by successive iterations in which a system of equations is constructed and solved for each cross-section. In this method, the differential equations in the spanwise directions are formulated and solved using a finite-differences scheme which allows simple adaptation of the spanwise discretization mesh during iterations.

2-D Fused Image Reconstruction approach for Microwave Tomography: a theoretical assessment using FDTD Model

PubMed Central

Bindu, G.; Semenov, S.

2013-01-01

This paper describes an efficient two-dimensional fused image reconstruction approach for Microwave Tomography (MWT). Finite Difference Time Domain (FDTD) models were created for a viable MWT experimental system having the transceivers modelled using thin wire approximation with resistive voltage sources. Born Iterative and Distorted Born Iterative methods have been employed for image reconstruction with the extremity imaging being done using a differential imaging technique. The forward solver in the imaging algorithm employs the FDTD method of solving the time domain Maxwell’s equations with the regularisation parameter computed using a stochastic approach. The algorithm is tested with 10% noise inclusion and successful image reconstruction has been shown implying its robustness. PMID:24058889

The MHOST finite element program: 3-D inelastic analysis methods for hot section components. Volume 1: Theoretical manual

NASA Technical Reports Server (NTRS)

Nakazawa, Shohei

1991-01-01

Formulations and algorithms implemented in the MHOST finite element program are discussed. The code uses a novel concept of the mixed iterative solution technique for the efficient 3-D computations of turbine engine hot section components. The general framework of variational formulation and solution algorithms are discussed which were derived from the mixed three field Hu-Washizu principle. This formulation enables the use of nodal interpolation for coordinates, displacements, strains, and stresses. Algorithmic description of the mixed iterative method includes variations for the quasi static, transient dynamic and buckling analyses. The global-local analysis procedure referred to as the subelement refinement is developed in the framework of the mixed iterative solution, of which the detail is presented. The numerically integrated isoparametric elements implemented in the framework is discussed. Methods to filter certain parts of strain and project the element discontinuous quantities to the nodes are developed for a family of linear elements. Integration algorithms are described for linear and nonlinear equations included in MHOST program.

Parallel Domain Decomposition Formulation and Software for Large-Scale Sparse Symmetrical/Unsymmetrical Aeroacoustic Applications

NASA Technical Reports Server (NTRS)

Nguyen, D. T.; Watson, Willie R. (Technical Monitor)

2005-01-01

The overall objectives of this research work are to formulate and validate efficient parallel algorithms, and to efficiently design/implement computer software for solving large-scale acoustic problems, arised from the unified frameworks of the finite element procedures. The adopted parallel Finite Element (FE) Domain Decomposition (DD) procedures should fully take advantages of multiple processing capabilities offered by most modern high performance computing platforms for efficient parallel computation. To achieve this objective. the formulation needs to integrate efficient sparse (and dense) assembly techniques, hybrid (or mixed) direct and iterative equation solvers, proper pre-conditioned strategies, unrolling strategies, and effective processors' communicating schemes. Finally, the numerical performance of the developed parallel finite element procedures will be evaluated by solving series of structural, and acoustic (symmetrical and un-symmetrical) problems (in different computing platforms). Comparisons with existing "commercialized" and/or "public domain" software are also included, whenever possible.

An iterative phase-space explicit discontinuous Galerkin method for stellar radiative transfer in extended atmospheres

NASA Astrophysics Data System (ADS)

de Almeida, Valmor F.

2017-07-01

A phase-space discontinuous Galerkin (PSDG) method is presented for the solution of stellar radiative transfer problems. It allows for greater adaptivity than competing methods without sacrificing generality. The method is extensively tested on a spherically symmetric, static, inverse-power-law scattering atmosphere. Results for different sizes of atmospheres and intensities of scattering agreed with asymptotic values. The exponentially decaying behavior of the radiative field in the diffusive-transparent transition region, and the forward peaking behavior at the surface of extended atmospheres were accurately captured. The integrodifferential equation of radiation transfer is solved iteratively by alternating between the radiative pressure equation and the original equation with the integral term treated as an energy density source term. In each iteration, the equations are solved via an explicit, flux-conserving, discontinuous Galerkin method. Finite elements are ordered in wave fronts perpendicular to the characteristic curves so that elemental linear algebraic systems are solved quickly by sweeping the phase space element by element. Two implementations of a diffusive boundary condition at the origin are demonstrated wherein the finite discontinuity in the radiation intensity is accurately captured by the proposed method. This allows for a consistent mechanism to preserve photon luminosity. The method was proved to be robust and fast, and a case is made for the adequacy of parallel processing. In addition to classical two-dimensional plots, results of normalized radiation intensity were mapped onto a log-polar surface exhibiting all distinguishing features of the problem studied.

Full-wave Moment Tensor and Tomographic Inversions Based on 3D Strain Green Tensor

DTIC Science & Technology

2010-01-31

propagation in three-dimensional (3D) earth, linearizes the inverse problem by iteratively updating the earth model , and provides an accurate way to...self-consistent FD-SGT databases constructed from finite-difference simulations of wave propagation in full-wave tomographic models can be used to...determine the moment tensors within minutes after a seismic event, making it possible for real time monitoring using 3D models . 15. SUBJECT TERMS

A Block Iterative Finite Element Model for Nonlinear Leaky Aquifer Systems

NASA Astrophysics Data System (ADS)

Gambolati, Giuseppe; Teatini, Pietro

1996-01-01

A new quasi three-dimensional finite element model of groundwater flow is developed for highly compressible multiaquifer systems where aquitard permeability and elastic storage are dependent on hydraulic drawdown. The model is solved by a block iterative strategy, which is naturally suggested by the geological structure of the porous medium and can be shown to be mathematically equivalent to a block Gauss-Seidel procedure. As such it can be generalized into a block overrelaxation procedure and greatly accelerated by the use of the optimum overrelaxation factor. Results for both linear and nonlinear multiaquifer systems emphasize the excellent computational performance of the model and indicate that convergence in leaky systems can be improved up to as much as one order of magnitude.

Rotation and neoclassical ripple transport in ITER

DOE PAGES

Paul, Elizabeth Joy; Landreman, Matt; Poli, Francesca M.; ...

2017-07-13

Neoclassical transport in the presence of non-axisymmetric magnetic fields causes a toroidal torque known as neoclassical toroidal viscosity (NTV). The toroidal symmetry of ITER will be broken by the finite number of toroidal field coils and by test blanket modules (TBMs). The addition of ferritic inserts (FIs) will decrease the magnitude of the toroidal field ripple. 3D magnetic equilibria in the presence of toroidal field ripple and ferromagnetic structures are calculated for an ITER steady-state scenario using the Variational Moments Equilibrium Code (VMEC). Furthermore, neoclassical transport quantities in the presence of these error fields are calculated using the Stellarator Fokker-Planckmore » Iterative Neoclassical Conservative Solver (SFINCS).« less

Rotation and neoclassical ripple transport in ITER

DOE Office of Scientific and Technical Information (OSTI.GOV)

Paul, Elizabeth Joy; Landreman, Matt; Poli, Francesca M.

Neoclassical transport in the presence of non-axisymmetric magnetic fields causes a toroidal torque known as neoclassical toroidal viscosity (NTV). The toroidal symmetry of ITER will be broken by the finite number of toroidal field coils and by test blanket modules (TBMs). The addition of ferritic inserts (FIs) will decrease the magnitude of the toroidal field ripple. 3D magnetic equilibria in the presence of toroidal field ripple and ferromagnetic structures are calculated for an ITER steady-state scenario using the Variational Moments Equilibrium Code (VMEC). Furthermore, neoclassical transport quantities in the presence of these error fields are calculated using the Stellarator Fokker-Planckmore » Iterative Neoclassical Conservative Solver (SFINCS).« less

Energy and technology review: Engineering modeling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cabayan, H.S.; Goudreau, G.L.; Ziolkowski, R.W.

1986-10-01

This report presents information concerning: Modeling Canonical Problems in Electromagnetic Coupling Through Apertures; Finite-Element Codes for Computing Electrostatic Fields; Finite-Element Modeling of Electromagnetic Phenomena; Modeling Microwave-Pulse Compression in a Resonant Cavity; Lagrangian Finite-Element Analysis of Penetration Mechanics; Crashworthiness Engineering; Computer Modeling of Metal-Forming Processes; Thermal-Mechanical Modeling of Tungsten Arc Welding; Modeling Air Breakdown Induced by Electromagnetic Fields; Iterative Techniques for Solving Boltzmann's Equations for p-Type Semiconductors; Semiconductor Modeling; and Improved Numerical-Solution Techniques in Large-Scale Stress Analysis.

An improved 3D MoF method based on analytical partial derivatives

NASA Astrophysics Data System (ADS)

Chen, Xiang; Zhang, Xiong

2016-12-01

MoF (Moment of Fluid) method is one of the most accurate approaches among various surface reconstruction algorithms. As other second order methods, MoF method needs to solve an implicit optimization problem to obtain the optimal approximate surface. Therefore, the partial derivatives of the objective function have to be involved during the iteration for efficiency and accuracy. However, to the best of our knowledge, the derivatives are currently estimated numerically by finite difference approximation because it is very difficult to obtain the analytical derivatives of the object function for an implicit optimization problem. Employing numerical derivatives in an iteration not only increase the computational cost, but also deteriorate the convergence rate and robustness of the iteration due to their numerical error. In this paper, the analytical first order partial derivatives of the objective function are deduced for 3D problems. The analytical derivatives can be calculated accurately, so they are incorporated into the MoF method to improve its accuracy, efficiency and robustness. Numerical studies show that by using the analytical derivatives the iterations are converged in all mixed cells with the efficiency improvement of 3 to 4 times.

Finite-beta equilibria for Wendelstein 7-X configurations using the Princeton Iterative Equilibrium Solver code

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arndt, S.; Merkel, P.; Monticello, D.A.

Fixed- and free-boundary equilibria for Wendelstein 7-X (W7-X) [W. Lotz {ital et al.}, {ital Plasma Physics and Controlled Nuclear Fusion Research 1990} (Proc. 13th Int. Conf. Washington, DC, 1990), (International Atomic Energy Agency, Vienna, 1991), Vol. 2, p. 603] configurations are calculated using the Princeton Iterative Equilibrium Solver (PIES) [A. H. Reiman {ital et al.}, Comput. Phys. Commun., {bold 43}, 157 (1986)] to deal with magnetic islands and stochastic regions. Usually, these W7-X configurations require a large number of iterations for PIES convergence. Here, two methods have been successfully tested in an attempt to decrease the number of iterations neededmore » for convergence. First, periodic sequences of different blending parameters are used. Second, the initial guess is vastly improved by using results of the Variational Moments Equilibrium Code (VMEC) [S. P. Hirshmann {ital et al.}, Phys. Fluids {bold 26}, 3553 (1983)]. Use of these two methods have allowed verification of the Hamada condition and tendency of {open_quotes}self-healing{close_quotes} of islands has been observed. {copyright} {ital 1999 American Institute of Physics.}« less

Fast Fourier transform-based solution of 2D and 3D magnetization problems in type-II superconductivity

NASA Astrophysics Data System (ADS)

Prigozhin, Leonid; Sokolovsky, Vladimir

2018-05-01

We consider the fast Fourier transform (FFT) based numerical method for thin film magnetization problems (Vestgården and Johansen 2012 Supercond. Sci. Technol. 25 104001), compare it with the finite element methods, and evaluate its accuracy. Proposed modifications of this method implementation ensure stable convergence of iterations and enhance its efficiency. A new method, also based on the FFT, is developed for 3D bulk magnetization problems. This method is based on a magnetic field formulation, different from the popular h-formulation of eddy current problems typically employed with the edge finite elements. The method is simple, easy to implement, and can be used with a general current–voltage relation; its efficiency is illustrated by numerical simulations.

Analysis of aircraft tires via semianalytic finite elements

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Kim, Kyun O.; Tanner, John A.

1990-01-01

A computational procedure is presented for the geometrically nonlinear analysis of aircraft tires. The tire was modeled by using a two-dimensional laminated anisotropic shell theory with the effects of variation in material and geometric parameters included. The four key elements of the procedure are: (1) semianalytic finite elements in which the shell variables are represented by Fourier series in the circumferential direction and piecewise polynomials in the meridional direction; (2) a mixed formulation with the fundamental unknowns consisting of strain parameters, stress-resultant parameters, and generalized displacements; (3) multilevel operator splitting to effect successive simplifications, and to uncouple the equations associated with different Fourier harmonics; and (4) multilevel iterative procedures and reduction techniques to generate the response of the shell.

A Newton method for the magnetohydrodynamic equilibrium equations

NASA Astrophysics Data System (ADS)

Oliver, Hilary James

We have developed and implemented a (J, B) space Newton method to solve the full nonlinear three dimensional magnetohydrodynamic equilibrium equations in toroidal geometry. Various cases have been run successfully, demonstrating significant improvement over Picard iteration, including a 3D stellarator equilibrium at β = 2%. The algorithm first solves the equilibrium force balance equation for the current density J, given a guess for the magnetic field B. This step is taken from the Picard-iterative PIES 3D equilibrium code. Next, we apply Newton's method to Ampere's Law by expansion of the functional J(B), which is defined by the first step. An analytic calculation in magnetic coordinates, of how the Pfirsch-Schlüter currents vary in the plasma in response to a small change in the magnetic field, yields the Newton gradient term (analogous to ∇f . δx in Newton's method for f(x) = 0). The algorithm is computationally feasible because we do this analytically, and because the gradient term is flux surface local when expressed in terms of a vector potential in an Ar=0 gauge. The equations are discretized by a hybrid spectral/offset grid finite difference technique, and leading order radial dependence is factored from Fourier coefficients to improve finite- difference accuracy near the polar-like origin. After calculating the Newton gradient term we transfer the equation from the magnetic grid to a fixed background grid, which greatly improves the code's performance.

A Block Preconditioned Conjugate Gradient-type Iterative Solver for Linear Systems in Thermal Reservoir Simulation

NASA Astrophysics Data System (ADS)

Betté, Srinivas; Diaz, Julio C.; Jines, William R.; Steihaug, Trond

1986-11-01

A preconditioned residual-norm-reducing iterative solver is described. Based on a truncated form of the generalized-conjugate-gradient method for nonsymmetric systems of linear equations, the iterative scheme is very effective for linear systems generated in reservoir simulation of thermal oil recovery processes. As a consequence of employing an adaptive implicit finite-difference scheme to solve the model equations, the number of variables per cell-block varies dynamically over the grid. The data structure allows for 5- and 9-point operators in the areal model, 5-point in the cross-sectional model, and 7- and 11-point operators in the three-dimensional model. Block-diagonal-scaling of the linear system, done prior to iteration, is found to have a significant effect on the rate of convergence. Block-incomplete-LU-decomposition (BILU) and block-symmetric-Gauss-Seidel (BSGS) methods, which result in no fill-in, are used as preconditioning procedures. A full factorization is done on the well terms, and the cells are ordered in a manner which minimizes the fill-in in the well-column due to this factorization. The convergence criterion for the linear (inner) iteration is linked to that of the nonlinear (Newton) iteration, thereby enhancing the efficiency of the computation. The algorithm, with both BILU and BSGS preconditioners, is evaluated in the context of a variety of thermal simulation problems. The solver is robust and can be used with little or no user intervention.

Finite Difference Time Marching in the Frequency Domain: A Parabolic Formulation for the Convective Wave Equation

NASA Technical Reports Server (NTRS)

Baumeister, K. J.; Kreider, K. L.

1996-01-01

An explicit finite difference iteration scheme is developed to study harmonic sound propagation in ducts. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Finite Difference Time Marching in the Frequency Domain: A Parabolic Formulation for Aircraft Acoustic Nacelle Design

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Kreider, Kevin L.

1996-01-01

An explicit finite difference iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Modal Test/Analysis Correlation of Space Station Structures Using Nonlinear Sensitivity

NASA Technical Reports Server (NTRS)

Gupta, Viney K.; Newell, James F.; Berke, Laszlo; Armand, Sasan

1992-01-01

The modal correlation problem is formulated as a constrained optimization problem for validation of finite element models (FEM's). For large-scale structural applications, a pragmatic procedure for substructuring, model verification, and system integration is described to achieve effective modal correlation. The space station substructure FEM's are reduced using Lanczos vectors and integrated into a system FEM using Craig-Bampton component modal synthesis. The optimization code is interfaced with MSC/NASTRAN to solve the problem of modal test/analysis correlation; that is, the problem of validating FEM's for launch and on-orbit coupled loads analysis against experimentally observed frequencies and mode shapes. An iterative perturbation algorithm is derived and implemented to update nonlinear sensitivity (derivatives of eigenvalues and eigenvectors) during optimizer iterations, which reduced the number of finite element analyses.

Modal test/analysis correlation of Space Station structures using nonlinear sensitivity

NASA Technical Reports Server (NTRS)

Gupta, Viney K.; Newell, James F.; Berke, Laszlo; Armand, Sasan

1992-01-01

The modal correlation problem is formulated as a constrained optimization problem for validation of finite element models (FEM's). For large-scale structural applications, a pragmatic procedure for substructuring, model verification, and system integration is described to achieve effective modal correlations. The space station substructure FEM's are reduced using Lanczos vectors and integrated into a system FEM using Craig-Bampton component modal synthesis. The optimization code is interfaced with MSC/NASTRAN to solve the problem of modal test/analysis correlation; that is, the problem of validating FEM's for launch and on-orbit coupled loads analysis against experimentally observed frequencies and mode shapes. An iterative perturbation algorithm is derived and implemented to update nonlinear sensitivity (derivatives of eigenvalues and eigenvectors) during optimizer iterations, which reduced the number of finite element analyses.

Numerical solution of quadratic matrix equations for free vibration analysis of structures

NASA Technical Reports Server (NTRS)

Gupta, K. K.

1975-01-01

This paper is concerned with the efficient and accurate solution of the eigenvalue problem represented by quadratic matrix equations. Such matrix forms are obtained in connection with the free vibration analysis of structures, discretized by finite 'dynamic' elements, resulting in frequency-dependent stiffness and inertia matrices. The paper presents a new numerical solution procedure of the quadratic matrix equations, based on a combined Sturm sequence and inverse iteration technique enabling economical and accurate determination of a few required eigenvalues and associated vectors. An alternative procedure based on a simultaneous iteration procedure is also described when only the first few modes are the usual requirement. The employment of finite dynamic elements in conjunction with the presently developed eigenvalue routines results in a most significant economy in the dynamic analysis of structures.

The development of a three-dimensional partially elliptic flow computer program for combustor research

NASA Technical Reports Server (NTRS)

Pan, Y. S.

1978-01-01

A three dimensional, partially elliptic, computer program was developed. Without requiring three dimensional computer storage locations for all flow variables, the partially elliptic program is capable of predicting three dimensional combustor flow fields with large downstream effects. The program requires only slight increase of computer storage over the parabolic flow program from which it was developed. A finite difference formulation for a three dimensional, fully elliptic, turbulent, reacting, flow field was derived. Because of the negligible diffusion effects in the main flow direction in a supersonic combustor, the set of finite-difference equations can be reduced to a partially elliptic form. Only the pressure field was governed by an elliptic equation and requires three dimensional storage; all other dependent variables are governed by parabolic equations. A numerical procedure which combines a marching integration scheme with an iterative scheme for solving the elliptic pressure was adopted.

Automated quadrilateral surface discretization method and apparatus usable to generate mesh in a finite element analysis system

DOEpatents

Blacker, Teddy D.

1994-01-01

An automatic quadrilateral surface discretization method and apparatus is provided for automatically discretizing a geometric region without decomposing the region. The automated quadrilateral surface discretization method and apparatus automatically generates a mesh of all quadrilateral elements which is particularly useful in finite element analysis. The generated mesh of all quadrilateral elements is boundary sensitive, orientation insensitive and has few irregular nodes on the boundary. A permanent boundary of the geometric region is input and rows are iteratively layered toward the interior of the geometric region. Also, an exterior permanent boundary and an interior permanent boundary for a geometric region may be input and the rows are iteratively layered inward from the exterior boundary in a first counter clockwise direction while the rows are iteratively layered from the interior permanent boundary toward the exterior of the region in a second clockwise direction. As a result, a high quality mesh for an arbitrary geometry may be generated with a technique that is robust and fast for complex geometric regions and extreme mesh gradations.

Finite element analysis of heat load of tungsten relevant to ITER conditions

NASA Astrophysics Data System (ADS)

Zinovev, A.; Terentyev, D.; Delannay, L.

2017-12-01

A computational procedure is proposed in order to predict the initiation of intergranular cracks in tungsten with ITER specification microstructure (i.e. characterised by elongated micrometre-sized grains). Damage is caused by a cyclic heat load, which emerges from plasma instabilities during operation of thermonuclear devices. First, a macroscopic thermo-mechanical simulation is performed in order to obtain temperature- and strain field in the material. The strain path is recorded at a selected point of interest of the macroscopic specimen, and is then applied at the microscopic level to a finite element mesh of a polycrystal. In the microscopic simulation, the stress state at the grain boundaries serves as the marker of cracking initiation. The simulated heat load cycle is a representative of edge-localized modes, which are anticipated during normal operations of ITER. Normal stresses at the grain boundary interfaces were shown to strongly depend on the direction of grain orientation with respect to the heat flux direction and to attain higher values if the flux is perpendicular to the elongated grains, where it apparently promotes crack initiation.

Lecture Notes on Multigrid Methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vassilevski, P S

The Lecture Notes are primarily based on a sequence of lectures given by the author while been a Fulbright scholar at 'St. Kliment Ohridski' University of Sofia, Sofia, Bulgaria during the winter semester of 2009-2010 academic year. The notes are somewhat expanded version of the actual one semester class he taught there. The material covered is slightly modified and adapted version of similar topics covered in the author's monograph 'Multilevel Block-Factorization Preconditioners' published in 2008 by Springer. The author tried to keep the notes as self-contained as possible. That is why the lecture notes begin with some basic introductory matrix-vectormore » linear algebra, numerical PDEs (finite element) facts emphasizing the relations between functions in finite dimensional spaces and their coefficient vectors and respective norms. Then, some additional facts on the implementation of finite elements based on relation tables using the popular compressed sparse row (CSR) format are given. Also, typical condition number estimates of stiffness and mass matrices, the global matrix assembly from local element matrices are given as well. Finally, some basic introductory facts about stationary iterative methods, such as Gauss-Seidel and its symmetrized version are presented. The introductory material ends up with the smoothing property of the classical iterative methods and the main definition of two-grid iterative methods. From here on, the second part of the notes begins which deals with the various aspects of the principal TG and the numerous versions of the MG cycles. At the end, in part III, we briefly introduce algebraic versions of MG referred to as AMG, focusing on classes of AMG specialized for finite element matrices.« less

An iterative phase-space explicit discontinuous Galerkin method for stellar radiative transfer in extended atmospheres

DOE Office of Scientific and Technical Information (OSTI.GOV)

de Almeida, Valmor F.

In this work, a phase-space discontinuous Galerkin (PSDG) method is presented for the solution of stellar radiative transfer problems. It allows for greater adaptivity than competing methods without sacrificing generality. The method is extensively tested on a spherically symmetric, static, inverse-power-law scattering atmosphere. Results for different sizes of atmospheres and intensities of scattering agreed with asymptotic values. The exponentially decaying behavior of the radiative field in the diffusive-transparent transition region, and the forward peaking behavior at the surface of extended atmospheres were accurately captured. The integrodifferential equation of radiation transfer is solved iteratively by alternating between the radiative pressure equationmore » and the original equation with the integral term treated as an energy density source term. In each iteration, the equations are solved via an explicit, flux-conserving, discontinuous Galerkin method. Finite elements are ordered in wave fronts perpendicular to the characteristic curves so that elemental linear algebraic systems are solved quickly by sweeping the phase space element by element. Two implementations of a diffusive boundary condition at the origin are demonstrated wherein the finite discontinuity in the radiation intensity is accurately captured by the proposed method. This allows for a consistent mechanism to preserve photon luminosity. The method was proved to be robust and fast, and a case is made for the adequacy of parallel processing. In addition to classical two-dimensional plots, results of normalized radiation intensity were mapped onto a log-polar surface exhibiting all distinguishing features of the problem studied.« less

An iterative phase-space explicit discontinuous Galerkin method for stellar radiative transfer in extended atmospheres

DOE PAGES

de Almeida, Valmor F.

2017-04-19

In this work, a phase-space discontinuous Galerkin (PSDG) method is presented for the solution of stellar radiative transfer problems. It allows for greater adaptivity than competing methods without sacrificing generality. The method is extensively tested on a spherically symmetric, static, inverse-power-law scattering atmosphere. Results for different sizes of atmospheres and intensities of scattering agreed with asymptotic values. The exponentially decaying behavior of the radiative field in the diffusive-transparent transition region, and the forward peaking behavior at the surface of extended atmospheres were accurately captured. The integrodifferential equation of radiation transfer is solved iteratively by alternating between the radiative pressure equationmore » and the original equation with the integral term treated as an energy density source term. In each iteration, the equations are solved via an explicit, flux-conserving, discontinuous Galerkin method. Finite elements are ordered in wave fronts perpendicular to the characteristic curves so that elemental linear algebraic systems are solved quickly by sweeping the phase space element by element. Two implementations of a diffusive boundary condition at the origin are demonstrated wherein the finite discontinuity in the radiation intensity is accurately captured by the proposed method. This allows for a consistent mechanism to preserve photon luminosity. The method was proved to be robust and fast, and a case is made for the adequacy of parallel processing. In addition to classical two-dimensional plots, results of normalized radiation intensity were mapped onto a log-polar surface exhibiting all distinguishing features of the problem studied.« less

Finite elements: Theory and application

NASA Technical Reports Server (NTRS)

Dwoyer, D. L. (Editor); Hussaini, M. Y. (Editor); Voigt, R. G. (Editor)

1988-01-01

Recent advances in FEM techniques and applications are discussed in reviews and reports presented at the ICASE/LaRC workshop held in Hampton, VA in July 1986. Topics addressed include FEM approaches for partial differential equations, mixed FEMs, singular FEMs, FEMs for hyperbolic systems, iterative methods for elliptic finite-element equations on general meshes, mathematical aspects of FEMS for incompressible viscous flows, and gradient weighted moving finite elements in two dimensions. Consideration is given to adaptive flux-corrected FEM transport techniques for CFD, mixed and singular finite elements and the field BEM, p and h-p versions of the FEM, transient analysis methods in computational dynamics, and FEMs for integrated flow/thermal/structural analysis.

The MHOST finite element program: 3-D inelastic analysis methods for hot section components. Volume 3: Systems' manual

NASA Technical Reports Server (NTRS)

Nakazawa, Shohei

1989-01-01

The internal structure is discussed of the MHOST finite element program designed for 3-D inelastic analysis of gas turbine hot section components. The computer code is the first implementation of the mixed iterative solution strategy for improved efficiency and accuracy over the conventional finite element method. The control structure of the program is covered along with the data storage scheme and the memory allocation procedure and the file handling facilities including the read and/or write sequences.

Fourier analysis of finite element preconditioned collocation schemes

NASA Technical Reports Server (NTRS)

Deville, Michel O.; Mund, Ernest H.

1990-01-01

The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.

Numerical solution of a coupled pair of elliptic equations from solid state electronics

NASA Technical Reports Server (NTRS)

Phillips, T. N.

1983-01-01

Iterative methods are considered for the solution of a coupled pair of second order elliptic partial differential equations which arise in the field of solid state electronics. A finite difference scheme is used which retains the conservative form of the differential equations. Numerical solutions are obtained in two ways, by multigrid and dynamic alternating direction implicit methods. Numerical results are presented which show the multigrid method to be an efficient way of solving this problem.

Computer model of one-dimensional equilibrium controlled sorption processes

USGS Publications Warehouse

Grove, D.B.; Stollenwerk, K.G.

1984-01-01

A numerical solution to the one-dimensional solute-transport equation with equilibrium-controlled sorption and a first-order irreversible-rate reaction is presented. The computer code is written in FORTRAN language, with a variety of options for input and output for user ease. Sorption reactions include Langmuir, Freundlich, and ion-exchange, with or without equal valance. General equations describing transport and reaction processes are solved by finite-difference methods, with nonlinearities accounted for by iteration. Complete documentation of the code, with examples, is included. (USGS)

Lattice dynamics and thermal conductivity of lithium fluoride via first-principles calculations

NASA Astrophysics Data System (ADS)

Liang, Ting; Chen, Wen-Qi; Hu, Cui-E.; Chen, Xiang-Rong; Chen, Qi-Feng

2018-04-01

The lattice thermal conductivity of lithium fluoride (LiF) is accurately computed from a first-principles approach based on an iterative solution of the Boltzmann transport equation. Real-space finite-difference supercell approach is employed to generate the second- and third-order interatomic force constants. The related physical quantities of LiF are calculated by the second- and third- order potential interactions at 30 K-1000 K. The calculated lattice thermal conductivity 13.89 W/(m K) for LiF at room temperature agrees well with the experimental value, demonstrating that the parameter-free approach can furnish precise descriptions of the lattice thermal conductivity for this material. Besides, the Born effective charges, dielectric constants and phonon spectrum of LiF accord well with the existing data. The lattice thermal conductivities for the iterative solution of BTE are also presented.

Simulation of fluid-structure interaction in micropumps by coupling of two commercial finite element programs

NASA Astrophysics Data System (ADS)

Klein, Andreas; Gerlach, Gerald

1998-09-01

This paper deals with the simulation of the fluid-structure interaction phenomena in micropumps. The proposed solution approach is based on external coupling of two different solvers, which are considered here as `black boxes'. Therefore, no specific intervention is necessary into the program code, and solvers can be exchanged arbitrarily. For the realization of the external iteration loop, two algorithms are considered: the relaxation-based Gauss-Seidel method and the computationally more extensive Newton method. It is demonstrated in terms of a simplified test case, that for rather weak coupling, the Gauss-Seidel method is sufficient. However, by simply changing the considered fluid from air to water, the two physical domains become strongly coupled, and the Gauss-Seidel method fails to converge in this case. The Newton iteration scheme must be used instead.

Scalable algorithms for three-field mixed finite element coupled poromechanics

NASA Astrophysics Data System (ADS)

Castelletto, Nicola; White, Joshua A.; Ferronato, Massimiliano

2016-12-01

We introduce a class of block preconditioners for accelerating the iterative solution of coupled poromechanics equations based on a three-field formulation. The use of a displacement/velocity/pressure mixed finite-element method combined with a first order backward difference formula for the approximation of time derivatives produces a sequence of linear systems with a 3 × 3 unsymmetric and indefinite block matrix. The preconditioners are obtained by approximating the two-level Schur complement with the aid of physically-based arguments that can be also generalized in a purely algebraic approach. A theoretical and experimental analysis is presented that provides evidence of the robustness, efficiency and scalability of the proposed algorithm. The performance is also assessed for a real-world challenging consolidation experiment of a shallow formation.

Mass Efficiency Considerations for Thermally Insulated Structural Skin of an Aerospace Vehicle

NASA Technical Reports Server (NTRS)

Blosser, Max L.

2012-01-01

An approximate equation was derived to predict the mass of insulation required to limit the maximum temperature reached by an insulated structure subjected to a transient heating pulse. In the course of the derivation two figures of merit were identified. One figure of merit correlates to the effectiveness of the heat capacity of the underlying structural material in reducing the amount of required insulation. The second figure of merit provides an indicator of the mass efficiency of the insulator material. An iterative, one dimensional finite element analysis was used to size the external insulation required to protect the structure at a single location on the Space Shuttle Orbiter and a reusable launch vehicle. Required insulation masses were calculated for a range of different materials for both structure and insulator. The required insulation masses calculated using the approximate equation were shown to typically agree with finite element results within 10 to 20 percent over the range of parameters studied. Finite element results closely followed the trends indicated by both figures of merit.

Domain decomposition methods for the parallel computation of reacting flows

NASA Technical Reports Server (NTRS)

Keyes, David E.

1988-01-01

Domain decomposition is a natural route to parallel computing for partial differential equation solvers. Subdomains of which the original domain of definition is comprised are assigned to independent processors at the price of periodic coordination between processors to compute global parameters and maintain the requisite degree of continuity of the solution at the subdomain interfaces. In the domain-decomposed solution of steady multidimensional systems of PDEs by finite difference methods using a pseudo-transient version of Newton iteration, the only portion of the computation which generally stands in the way of efficient parallelization is the solution of the large, sparse linear systems arising at each Newton step. For some Jacobian matrices drawn from an actual two-dimensional reacting flow problem, comparisons are made between relaxation-based linear solvers and also preconditioned iterative methods of Conjugate Gradient and Chebyshev type, focusing attention on both iteration count and global inner product count. The generalized minimum residual method with block-ILU preconditioning is judged the best serial method among those considered, and parallel numerical experiments on the Encore Multimax demonstrate for it approximately 10-fold speedup on 16 processors.

Analytical study of temperature distribution in a rectangular porous fin considering both insulated and convective tip

NASA Astrophysics Data System (ADS)

Deshamukhya, Tuhin; Bhanja, Dipankar; Nath, Sujit; Maji, Ambarish; Choubey, Gautam

2017-07-01

The following study is concerned with determination of temperature distribution of porous fins under convective and insulated tip conditions. The authors have made an effort to study the effect of various important parameters involved in the transfer of heat through porous fins as well as the temperature distribution along the fin length subjected to both convective as well as insulated ends. The non-linear equation obtained has been solved by Adomian Decomposition method and validated with a numerical scheme called Finite Difference method by using a central difference scheme and Gauss Siedel Iterative method.

Finite element procedures for coupled linear analysis of heat transfer, fluid and solid mechanics

NASA Technical Reports Server (NTRS)

Sutjahjo, Edhi; Chamis, Christos C.

1993-01-01

Coupled finite element formulations for fluid mechanics, heat transfer, and solid mechanics are derived from the conservation laws for energy, mass, and momentum. To model the physics of interactions among the participating disciplines, the linearized equations are coupled by combining domain and boundary coupling procedures. Iterative numerical solution strategy is presented to solve the equations, with the partitioning of temporal discretization implemented.

Finite element analysis of wrinkling membranes

NASA Technical Reports Server (NTRS)

Miller, R. K.; Hedgepeth, J. M.; Weingarten, V. I.; Das, P.; Kahyai, S.

1984-01-01

The development of a nonlinear numerical algorithm for the analysis of stresses and displacements in partly wrinkled flat membranes, and its implementation on the SAP VII finite-element code are described. A comparison of numerical results with exact solutions of two benchmark problems reveals excellent agreement, with good convergence of the required iterative procedure. An exact solution of a problem involving axisymmetric deformations of a partly wrinkled shallow curved membrane is also reported.

Iterative Addition of Kinetic Effects to Cold Plasma RF Wave Solvers

NASA Astrophysics Data System (ADS)

Green, David; Berry, Lee; RF-SciDAC Collaboration

2017-10-01

The hot nature of fusion plasmas requires a wave vector dependent conductivity tensor for accurate calculation of wave heating and current drive. Traditional methods for calculating the linear, kinetic full-wave plasma response rely on a spectral method such that the wave vector dependent conductivity fits naturally within the numerical method. These methods have seen much success for application to the well-confined core plasma of tokamaks. However, quantitative prediction of high power RF antenna designs for fusion applications has meant a requirement of resolving the geometric details of the antenna and other plasma facing surfaces for which the Fourier spectral method is ill-suited. An approach to enabling the addition of kinetic effects to the more versatile finite-difference and finite-element cold-plasma full-wave solvers was presented by where an operator-split iterative method was outlined. Here we expand on this approach, examine convergence and present a simplified kinetic current estimator for rapidly updating the right-hand side of the wave equation with kinetic corrections. This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725.

On the electromagnetic scattering from infinite rectangular grids with finite conductivity

NASA Technical Reports Server (NTRS)

Christodoulou, C. G.; Kauffman, J. F.

1986-01-01

A variety of methods can be used in constructing solutions to the problem of mesh scattering. However, each of these methods has certain drawbacks. The present paper is concerned with a new technique which is valid for all spacings. The new method involved, called the fast Fourier transform-conjugate gradient method (FFT-CGM), represents an iterative technique which employs the conjugate gradient method to improve upon each iterate, utilizing the fast Fourier transform. The FFT-CGM method provides a new accurate model which can be extended and applied to the more difficult problems of woven mesh surfaces. The formulation of the FFT-conjugate gradient method for aperture fields and current densities for a planar periodic structure is considered along with singular operators, the formulation of the FFT-CG method for thin wires with finite conductivity, and reflection coefficients.

The U.S. Geological Survey Modular Ground-Water Model - PCGN: A Preconditioned Conjugate Gradient Solver with Improved Nonlinear Control

USGS Publications Warehouse

Naff, Richard L.; Banta, Edward R.

2008-01-01

The preconditioned conjugate gradient with improved nonlinear control (PCGN) package provides addi-tional means by which the solution of nonlinear ground-water flow problems can be controlled as compared to existing solver packages for MODFLOW. Picard iteration is used to solve nonlinear ground-water flow equations by iteratively solving a linear approximation of the nonlinear equations. The linear solution is provided by means of the preconditioned conjugate gradient algorithm where preconditioning is provided by the modi-fied incomplete Cholesky algorithm. The incomplete Cholesky scheme incorporates two levels of fill, 0 and 1, in which the pivots can be modified so that the row sums of the preconditioning matrix and the original matrix are approximately equal. A relaxation factor is used to implement the modified pivots, which determines the degree of modification allowed. The effects of fill level and degree of pivot modification are briefly explored by means of a synthetic, heterogeneous finite-difference matrix; results are reported in the final section of this report. The preconditioned conjugate gradient method is coupled with Picard iteration so as to efficiently solve the nonlinear equations associated with many ground-water flow problems. The description of this coupling of the linear solver with Picard iteration is a primary concern of this document.

A new least-squares transport equation compatible with voids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hansen, J. B.; Morel, J. E.

2013-07-01

We define a new least-squares transport equation that is applicable in voids, can be solved using source iteration with diffusion-synthetic acceleration, and requires only the solution of an independent set of second-order self-adjoint equations for each direction during each source iteration. We derive the equation, discretize it using the S{sub n} method in conjunction with a linear-continuous finite-element method in space, and computationally demonstrate various of its properties. (authors)

Adaptive and iterative methods for simulations of nanopores with the PNP-Stokes equations

NASA Astrophysics Data System (ADS)

Mitscha-Baude, Gregor; Buttinger-Kreuzhuber, Andreas; Tulzer, Gerhard; Heitzinger, Clemens

2017-06-01

We present a 3D finite element solver for the nonlinear Poisson-Nernst-Planck (PNP) equations for electrodiffusion, coupled to the Stokes system of fluid dynamics. The model serves as a building block for the simulation of macromolecule dynamics inside nanopore sensors. The source code is released online at http://github.com/mitschabaude/nanopores. We add to existing numerical approaches by deploying goal-oriented adaptive mesh refinement. To reduce the computation overhead of mesh adaptivity, our error estimator uses the much cheaper Poisson-Boltzmann equation as a simplified model, which is justified on heuristic grounds but shown to work well in practice. To address the nonlinearity in the full PNP-Stokes system, three different linearization schemes are proposed and investigated, with two segregated iterative approaches both outperforming a naive application of Newton's method. Numerical experiments are reported on a real-world nanopore sensor geometry. We also investigate two different models for the interaction of target molecules with the nanopore sensor through the PNP-Stokes equations. In one model, the molecule is of finite size and is explicitly built into the geometry; while in the other, the molecule is located at a single point and only modeled implicitly - after solution of the system - which is computationally favorable. We compare the resulting force profiles of the electric and velocity fields acting on the molecule, and conclude that the point-size model fails to capture important physical effects such as the dependence of charge selectivity of the sensor on the molecule radius.

On the implementation of an accurate and efficient solver for convection-diffusion equations

NASA Astrophysics Data System (ADS)

Wu, Chin-Tien

In this dissertation, we examine several different aspects of computing the numerical solution of the convection-diffusion equation. The solution of this equation often exhibits sharp gradients due to Dirichlet outflow boundaries or discontinuities in boundary conditions. Because of the singular-perturbed nature of the equation, numerical solutions often have severe oscillations when grid sizes are not small enough to resolve sharp gradients. To overcome such difficulties, the streamline diffusion discretization method can be used to obtain an accurate approximate solution in regions where the solution is smooth. To increase accuracy of the solution in the regions containing layers, adaptive mesh refinement and mesh movement based on a posteriori error estimations can be employed. An error-adapted mesh refinement strategy based on a posteriori error estimations is also proposed to resolve layers. For solving the sparse linear systems that arise from discretization, goemetric multigrid (MG) and algebraic multigrid (AMG) are compared. In addition, both methods are also used as preconditioners for Krylov subspace methods. We derive some convergence results for MG with line Gauss-Seidel smoothers and bilinear interpolation. Finally, while considering adaptive mesh refinement as an integral part of the solution process, it is natural to set a stopping tolerance for the iterative linear solvers on each mesh stage so that the difference between the approximate solution obtained from iterative methods and the finite element solution is bounded by an a posteriori error bound. Here, we present two stopping criteria. The first is based on a residual-type a posteriori error estimator developed by Verfurth. The second is based on an a posteriori error estimator, using local solutions, developed by Kay and Silvester. Our numerical results show the refined mesh obtained from the iterative solution which satisfies the second criteria is similar to the refined mesh obtained from the finite element solution.

An Evaluation of an Algorithm for Linear Inequalities and Its Applications

NASA Technical Reports Server (NTRS)

Jurgensen, J.

1973-01-01

An algorithm is presented for obtaining a solution alpha to a set of inequalities (A alpha) 0 where A is an N x m-matrix and alpha is an m-vector. If the set of inequalities is consistant, then the algorithm is guaranteed to arrive at a solution in a finite number of steps. Also, if in the iteration, a negative vector is obtained, then the initial set of inequalities is inconsistant, and the iteration is terminated.

Anatomically Realistic Three-Dimensional Meshes of the Pelvic Floor & Anal Canal for Finite Element Analysis

PubMed Central

Noakes, Kimberley F.; Bissett, Ian P.; Pullan, Andrew J.; Cheng, Leo K.

2014-01-01

Three anatomically realistic meshes, suitable for finite element analysis, of the pelvic floor and anal canal regions have been developed to provide a framework with which to examine the mechanics, via finite element analysis of normal function within the pelvic floor. Two cadaver-based meshes were produced using the Visible Human Project (male and female) cryosection data sets, and a third mesh was produced based on MR image data from a live subject. The Visible Man (VM) mesh included 10 different pelvic structures while the Visible Woman and MRI meshes contained 14 and 13 structures respectively. Each image set was digitized and then finite element meshes were created using an iterative fitting procedure with smoothing constraints calculated from ‘L’-curves. These weights produced accurate geometric meshes of each pelvic structure with average Root Mean Square (RMS) fitting errors of less than 1.15 mm. The Visible Human cadaveric data provided high resolution images, however, the cadaveric meshes lacked the normal dynamic form of living tissue and suffered from artifacts related to postmortem changes. The lower resolution MRI mesh was able to accurately portray structure of the living subject and paves the way for dynamic, functional modeling. PMID:18317929

Adaptive finite element modelling of three-dimensional magnetotelluric fields in general anisotropic media

NASA Astrophysics Data System (ADS)

Liu, Ying; Xu, Zhenhuan; Li, Yuguo

2018-04-01

We present a goal-oriented adaptive finite element (FE) modelling algorithm for 3-D magnetotelluric fields in generally anisotropic conductivity media. The model consists of a background layered structure, containing anisotropic blocks. Each block and layer might be anisotropic by assigning to them 3 × 3 conductivity tensors. The second-order partial differential equations are solved using the adaptive finite element method (FEM). The computational domain is subdivided into unstructured tetrahedral elements, which allow for complex geometries including bathymetry and dipping interfaces. The grid refinement process is guided by a global posteriori error estimator and is performed iteratively. The system of linear FE equations for electric field E is solved with a direct solver MUMPS. Then the magnetic field H can be found, in which the required derivatives are computed numerically using cubic spline interpolation. The 3-D FE algorithm has been validated by comparisons with both the 3-D finite-difference solution and 2-D FE results. Two model types are used to demonstrate the effects of anisotropy upon 3-D magnetotelluric responses: horizontal and dipping anisotropy. Finally, a 3D sea hill model is modelled to study the effect of oblique interfaces and the dipping anisotropy.

Effect of abutment angulation on the strain on the bone around an implant in the anterior maxilla: a finite element study.

PubMed

Saab, Xavier E; Griggs, Jason A; Powers, John M; Engelmeier, Robert L

2007-02-01

Angled abutments are often used to restore dental implants placed in the anterior maxilla due to esthetic or spatial needs. The effect of abutment angulation on bone strain is unknown. The purpose of the current study was to measure and compare the strain distribution on the bone around an implant in the anterior maxilla using 2 different abutments by means of finite element analysis. Two-dimensional finite element models were designed using software (ANSYS) for 2 situations: (1) an implant with a straight abutment in the anterior maxilla, and (2) an implant with an angled abutment in the anterior maxilla. The implant used was 4x13 mm (MicroThread). The maxillary bone was modeled as type 3 bone with a cortical layer thickness of 0.5 mm. Oblique loads of 178 N were applied on the cingulum area of both models. Seven consecutive iterations of mesh refinement were performed in each model to observe the convergence of the results. The greatest strain was found on the cancellous bone, adjacent to the 3 most apical microthreads on the palatal side of the implant where tensile forces were created. The same strain distribution was observed around both the straight and angled abutments. After several iterations, the results converged to a value for the maximum first principal strain on the bone of both models, which was independent of element size. Most of the deformation occurred in the cancellous bone and ranged between 1000 and 3500 microstrain. Small areas of cancellous bone experienced strain above the physiologic limit (4000 microstrain). The model predicted a 15% higher maximum bone strain for the straight abutment compared with the angled abutment. The results converged after several iterations of mesh refinement, which confirmed the lack of dependence of the maximum strain at the implant-bone interface on mesh density. Most of the strain produced on the cancellous and cortical bone was within the range that has been reported to increase bone mass and mineralization.

Polarimetric signatures of a coniferous forest canopy based on vector radiative transfer theory

NASA Technical Reports Server (NTRS)

Karam, M. A.; Fung, A. K.; Amar, F.; Mougin, E.; Lopes, A.; Beaudoin, A.

1992-01-01

Complete polarization signatures of a coniferous forest canopy are studied by the iterative solution of the vector radiative transfer equations up to the second order. The forest canopy constituents (leaves, branches, stems, and trunk) are embedded in a multi-layered medium over a rough interface. The branches, stems and trunk scatterers are modeled as finite randomly oriented cylinders. The leaves are modeled as randomly oriented needles. For a plane wave exciting the canopy, the average Mueller matrix is formulated in terms of the iterative solution of the radiative transfer solution and used to determine the linearly polarized backscattering coefficients, the co-polarized and cross-polarized power returns, and the phase difference statistics. Numerical results are presented to investigate the effect of transmitting and receiving antenna configurations on the polarimetric signature of a pine forest. Comparison is made with measurements.

A k-space method for large-scale models of wave propagation in tissue.

PubMed

Mast, T D; Souriau, L P; Liu, D L; Tabei, M; Nachman, A I; Waag, R C

2001-03-01

Large-scale simulation of ultrasonic pulse propagation in inhomogeneous tissue is important for the study of ultrasound-tissue interaction as well as for development of new imaging methods. Typical scales of interest span hundreds of wavelengths; most current two-dimensional methods, such as finite-difference and finite-element methods, are unable to compute propagation on this scale with the efficiency needed for imaging studies. Furthermore, for most available methods of simulating ultrasonic propagation, large-scale, three-dimensional computations of ultrasonic scattering are infeasible. Some of these difficulties have been overcome by previous pseudospectral and k-space methods, which allow substantial portions of the necessary computations to be executed using fast Fourier transforms. This paper presents a simplified derivation of the k-space method for a medium of variable sound speed and density; the derivation clearly shows the relationship of this k-space method to both past k-space methods and pseudospectral methods. In the present method, the spatial differential equations are solved by a simple Fourier transform method, and temporal iteration is performed using a k-t space propagator. The temporal iteration procedure is shown to be exact for homogeneous media, unconditionally stable for "slow" (c(x) < or = c0) media, and highly accurate for general weakly scattering media. The applicability of the k-space method to large-scale soft tissue modeling is shown by simulating two-dimensional propagation of an incident plane wave through several tissue-mimicking cylinders as well as a model chest wall cross section. A three-dimensional implementation of the k-space method is also employed for the example problem of propagation through a tissue-mimicking sphere. Numerical results indicate that the k-space method is accurate for large-scale soft tissue computations with much greater efficiency than that of an analogous leapfrog pseudospectral method or a 2-4 finite difference time-domain method. However, numerical results also indicate that the k-space method is less accurate than the finite-difference method for a high contrast scatterer with bone-like properties, although qualitative results can still be obtained by the k-space method with high efficiency. Possible extensions to the method, including representation of absorption effects, absorbing boundary conditions, elastic-wave propagation, and acoustic nonlinearity, are discussed.

Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation

NASA Technical Reports Server (NTRS)

Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E.; Melvin, Robin G.; Young, David P.

1996-01-01

We study parallel two-level overlapping Schwarz algorithms for solving nonlinear finite element problems, in particular, for the full potential equation of aerodynamics discretized in two dimensions with bilinear elements. The overall algorithm, Newton-Krylov-Schwarz (NKS), employs an inexact finite-difference Newton method and a Krylov space iterative method, with a two-level overlapping Schwarz method as a preconditioner. We demonstrate that NKS, combined with a density upwinding continuation strategy for problems with weak shocks, is robust and, economical for this class of mixed elliptic-hyperbolic nonlinear partial differential equations, with proper specification of several parameters. We study upwinding parameters, inner convergence tolerance, coarse grid density, subdomain overlap, and the level of fill-in in the incomplete factorization, and report their effect on numerical convergence rate, overall execution time, and parallel efficiency on a distributed-memory parallel computer.

Methods for the calculation of axial wave numbers in lined ducts with mean flow

NASA Technical Reports Server (NTRS)

Eversman, W.

1981-01-01

A survey is made of the methods available for the calculation of axial wave numbers in lined ducts. Rectangular and circular ducts with both uniform and non-uniform flow are considered as are ducts with peripherally varying liners. A historical perspective is provided by a discussion of the classical methods for computing attenuation when no mean flow is present. When flow is present these techniques become either impractical or impossible. A number of direct eigenvalue determination schemes which have been used when flow is present are discussed. Methods described are extensions of the classical no-flow technique, perturbation methods based on the no-flow technique, direct integration methods for solution of the eigenvalue equation, an integration-iteration method based on the governing differential equation for acoustic transmission, Galerkin methods, finite difference methods, and finite element methods.

On nonlinear finite element analysis in single-, multi- and parallel-processors

NASA Technical Reports Server (NTRS)

Utku, S.; Melosh, R.; Islam, M.; Salama, M.

1982-01-01

Numerical solution of nonlinear equilibrium problems of structures by means of Newton-Raphson type iterations is reviewed. Each step of the iteration is shown to correspond to the solution of a linear problem, therefore the feasibility of the finite element method for nonlinear analysis is established. Organization and flow of data for various types of digital computers, such as single-processor/single-level memory, single-processor/two-level-memory, vector-processor/two-level-memory, and parallel-processors, with and without sub-structuring (i.e. partitioning) are given. The effect of the relative costs of computation, memory and data transfer on substructuring is shown. The idea of assigning comparable size substructures to parallel processors is exploited. Under Cholesky type factorization schemes, the efficiency of parallel processing is shown to decrease due to the occasional shared data, just as that due to the shared facilities.

A numerical formulation and algorithm for limit and shakedown analysis of large-scale elastoplastic structures

NASA Astrophysics Data System (ADS)

Peng, Heng; Liu, Yinghua; Chen, Haofeng

2018-05-01

In this paper, a novel direct method called the stress compensation method (SCM) is proposed for limit and shakedown analysis of large-scale elastoplastic structures. Without needing to solve the specific mathematical programming problem, the SCM is a two-level iterative procedure based on a sequence of linear elastic finite element solutions where the global stiffness matrix is decomposed only once. In the inner loop, the static admissible residual stress field for shakedown analysis is constructed. In the outer loop, a series of decreasing load multipliers are updated to approach to the shakedown limit multiplier by using an efficient and robust iteration control technique, where the static shakedown theorem is adopted. Three numerical examples up to about 140,000 finite element nodes confirm the applicability and efficiency of this method for two-dimensional and three-dimensional elastoplastic structures, with detailed discussions on the convergence and the accuracy of the proposed algorithm.

WIND: Computer program for calculation of three dimensional potential compressible flow about wind turbine rotor blades

NASA Technical Reports Server (NTRS)

Dulikravich, D. S.

1980-01-01

A computer program is presented which numerically solves an exact, full potential equation (FPE) for three dimensional, steady, inviscid flow through an isolated wind turbine rotor. The program automatically generates a three dimensional, boundary conforming grid and iteratively solves the FPE while fully accounting for both the rotating cascade and Coriolis effects. The numerical techniques incorporated involve rotated, type dependent finite differencing, a finite volume method, artificial viscosity in conservative form, and a successive line overrelaxation combined with the sequential grid refinement procedure to accelerate the iterative convergence rate. Consequently, the WIND program is capable of accurately analyzing incompressible and compressible flows, including those that are locally transonic and terminated by weak shocks. The program can also be used to analyze the flow around isolated aircraft propellers and helicopter rotors in hover as long as the total relative Mach number of the oncoming flow is subsonic.

Adaptive dynamic programming for finite-horizon optimal control of discrete-time nonlinear systems with ε-error bound.

PubMed

Wang, Fei-Yue; Jin, Ning; Liu, Derong; Wei, Qinglai

2011-01-01

In this paper, we study the finite-horizon optimal control problem for discrete-time nonlinear systems using the adaptive dynamic programming (ADP) approach. The idea is to use an iterative ADP algorithm to obtain the optimal control law which makes the performance index function close to the greatest lower bound of all performance indices within an ε-error bound. The optimal number of control steps can also be obtained by the proposed ADP algorithms. A convergence analysis of the proposed ADP algorithms in terms of performance index function and control policy is made. In order to facilitate the implementation of the iterative ADP algorithms, neural networks are used for approximating the performance index function, computing the optimal control policy, and modeling the nonlinear system. Finally, two simulation examples are employed to illustrate the applicability of the proposed method.

Adaptive eigenspace method for inverse scattering problems in the frequency domain

NASA Astrophysics Data System (ADS)

Grote, Marcus J.; Kray, Marie; Nahum, Uri

2017-02-01

A nonlinear optimization method is proposed for the solution of inverse scattering problems in the frequency domain, when the scattered field is governed by the Helmholtz equation. The time-harmonic inverse medium problem is formulated as a PDE-constrained optimization problem and solved by an inexact truncated Newton-type iteration. Instead of a grid-based discrete representation, the unknown wave speed is projected to a particular finite-dimensional basis of eigenfunctions, which is iteratively adapted during the optimization. Truncating the adaptive eigenspace (AE) basis at a (small and slowly increasing) finite number of eigenfunctions effectively introduces regularization into the inversion and thus avoids the need for standard Tikhonov-type regularization. Both analytical and numerical evidence underpins the accuracy of the AE representation. Numerical experiments demonstrate the efficiency and robustness to missing or noisy data of the resulting adaptive eigenspace inversion method.

Exact exchange potential evaluated from occupied Kohn-Sham and Hartree-Fock solutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cinal, M.; Holas, A.

2011-06-15

The reported algorithm determines the exact exchange potential v{sub x} in an iterative way using energy shifts (ESs) and orbital shifts (OSs) obtained with finite-difference formulas from the solutions (occupied orbitals and their energies) of the Hartree-Fock-like equation and the Kohn-Sham-like equation, the former used for the initial approximation to v{sub x} and the latter for increments of ES and OS due to subsequent changes of v{sub x}. Thus, the need for solution of the differential equations for OSs, used by Kuemmel and Perdew [Phys. Rev. Lett. 90, 043004 (2003)], is bypassed. The iterated exchange potential, expressed in terms ofmore » ESs and OSs, is improved by modifying ESs at odd iteration steps and OSs at even steps. The modification formulas are related to the optimized-effective-potential equation (satisfied at convergence) written as the condition of vanishing density shift (DS). They are obtained, respectively, by enforcing its satisfaction through corrections to approximate OSs and by determining the optimal ESs that minimize the DS norm. The proposed method, successfully tested for several closed-(sub)shell atoms, from Be to Kr, within the density functional theory exchange-only approximation, proves highly efficient. The calculations using the pseudospectral method for representing orbitals give iterative sequences of approximate exchange potentials (starting with the Krieger-Li-Iafrate approximation) that rapidly approach the exact v{sub x} so that, for Ne, Ar, and Zn, the corresponding DS norm becomes less than 10{sup -6} after 13, 13, and 9 iteration steps for a given electron density. In self-consistent density calculations, orbital energies of 10{sup -4} hartree accuracy are obtained for these atoms after, respectively, 9, 12, and 12 density iteration steps, each involving just two steps of v{sub x} iteration, while the accuracy limit of 10{sup -6} to 10{sup -7} hartree is reached after 20 density iterations.« less

Exact exchange potential evaluated from occupied Kohn-Sham and Hartree-Fock solutions

NASA Astrophysics Data System (ADS)

Cinal, M.; Holas, A.

2011-06-01

The reported algorithm determines the exact exchange potential vx in an iterative way using energy shifts (ESs) and orbital shifts (OSs) obtained with finite-difference formulas from the solutions (occupied orbitals and their energies) of the Hartree-Fock-like equation and the Kohn-Sham-like equation, the former used for the initial approximation to vx and the latter for increments of ES and OS due to subsequent changes of vx. Thus, the need for solution of the differential equations for OSs, used by Kümmel and Perdew [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.90.043004 90, 043004 (2003)], is bypassed. The iterated exchange potential, expressed in terms of ESs and OSs, is improved by modifying ESs at odd iteration steps and OSs at even steps. The modification formulas are related to the optimized-effective-potential equation (satisfied at convergence) written as the condition of vanishing density shift (DS). They are obtained, respectively, by enforcing its satisfaction through corrections to approximate OSs and by determining the optimal ESs that minimize the DS norm. The proposed method, successfully tested for several closed-(sub)shell atoms, from Be to Kr, within the density functional theory exchange-only approximation, proves highly efficient. The calculations using the pseudospectral method for representing orbitals give iterative sequences of approximate exchange potentials (starting with the Krieger-Li-Iafrate approximation) that rapidly approach the exact vx so that, for Ne, Ar, and Zn, the corresponding DS norm becomes less than 10-6 after 13, 13, and 9 iteration steps for a given electron density. In self-consistent density calculations, orbital energies of 10-4 hartree accuracy are obtained for these atoms after, respectively, 9, 12, and 12 density iteration steps, each involving just two steps of vx iteration, while the accuracy limit of 10-6 to 10-7 hartree is reached after 20 density iterations.

Elasto-Plastic Behavior of Aluminum Foams Subjected to Compression Loading

NASA Astrophysics Data System (ADS)

Silva, H. M.; Carvalho, C. D.; Peixinho, N. R.

2017-05-01

The non-linear behavior of uniform-size cellular foams made of aluminum is investigated when subjected to compressive loads while comparing numerical results obtained in the Finite Element Method software (FEM) ANSYS workbench and ANSYS Mechanical APDL (ANSYS Parametric Design Language). The numerical model is built on AUTODESK INVENTOR, being imported into ANSYS and solved by the Newton-Raphson iterative method. The most similar conditions were used in ANSYS mechanical and ANSYS workbench, as possible. The obtained numerical results and the differences between the two programs are presented and discussed

Hierarchical Parallelism in Finite Difference Analysis of Heat Conduction

NASA Technical Reports Server (NTRS)

Padovan, Joseph; Krishna, Lala; Gute, Douglas

1997-01-01

Based on the concept of hierarchical parallelism, this research effort resulted in highly efficient parallel solution strategies for very large scale heat conduction problems. Overall, the method of hierarchical parallelism involves the partitioning of thermal models into several substructured levels wherein an optimal balance into various associated bandwidths is achieved. The details are described in this report. Overall, the report is organized into two parts. Part 1 describes the parallel modelling methodology and associated multilevel direct, iterative and mixed solution schemes. Part 2 establishes both the formal and computational properties of the scheme.

Preconditioning the Helmholtz Equation for Rigid Ducts

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Kreider, Kevin L.

1998-01-01

An innovative hyperbolic preconditioning technique is developed for the numerical solution of the Helmholtz equation which governs acoustic propagation in ducts. Two pseudo-time parameters are used to produce an explicit iterative finite difference scheme. This scheme eliminates the large matrix storage requirements normally associated with numerical solutions to the Helmholtz equation. The solution procedure is very fast when compared to other transient and steady methods. Optimization and an error analysis of the preconditioning factors are present. For validation, the method is applied to sound propagation in a 2D semi-infinite hard wall duct.

Divergence correction schemes in finite difference method for 3D tensor CSAMT in axial anisotropic media

NASA Astrophysics Data System (ADS)

Wang, Kunpeng; Tan, Handong; Zhang, Zhiyong; Li, Zhiqiang; Cao, Meng

2017-05-01

Resistivity anisotropy and full-tensor controlled-source audio-frequency magnetotellurics (CSAMT) have gradually become hot research topics. However, much of the current anisotropy research for tensor CSAMT only focuses on the one-dimensional (1D) solution. As the subsurface is rarely 1D, it is necessary to study three-dimensional (3D) model response. The staggered-grid finite difference method is an effective simulation method for 3D electromagnetic forward modelling. Previous studies have suggested using the divergence correction to constrain the iterative process when using a staggered-grid finite difference model so as to accelerate the 3D forward speed and enhance the computational accuracy. However, the traditional divergence correction method was developed assuming an isotropic medium. This paper improves the traditional isotropic divergence correction method and derivation process to meet the tensor CSAMT requirements for anisotropy using the volume integral of the divergence equation. This method is more intuitive, enabling a simple derivation of a discrete equation and then calculation of coefficients related to the anisotropic divergence correction equation. We validate the result of our 3D computational results by comparing them to the results computed using an anisotropic, controlled-source 2.5D program. The 3D resistivity anisotropy model allows us to evaluate the consequences of using the divergence correction at different frequencies and for two orthogonal finite length sources. Our results show that the divergence correction plays an important role in 3D tensor CSAMT resistivity anisotropy research and offers a solid foundation for inversion of CSAMT data collected over an anisotropic body.

Multitasking 3-D forward modeling using high-order finite difference methods on the Cray X-MP/416

DOE Office of Scientific and Technical Information (OSTI.GOV)

Terki-Hassaine, O.; Leiss, E.L.

1988-01-01

The CRAY X-MP/416 was used to multitask 3-D forward modeling by the high-order finite difference method. Flowtrace analysis reveals that the most expensive operation in the unitasked program is a matrix vector multiplication. The in-core and out-of-core versions of a reentrant subroutine can perform any fraction of the matrix vector multiplication independently, a pattern compatible with multitasking. The matrix vector multiplication routine can be distributed over two to four processors. The rest of the program utilizes the microtasking feature that lets the system treat independent iterations of DO-loops as subtasks to be performed by any available processor. The availability ofmore » the Solid-State Storage Device (SSD) meant the I/O wait time was virtually zero. A performance study determined a theoretical speedup, taking into account the multitasking overhead. Multitasking programs utilizing both macrotasking and microtasking features obtained actual speedups that were approximately 80% of the ideal speedup.« less

Security of quantum key distribution with iterative sifting

NASA Astrophysics Data System (ADS)

Tamaki, Kiyoshi; Lo, Hoi-Kwong; Mizutani, Akihiro; Kato, Go; Lim, Charles Ci Wen; Azuma, Koji; Curty, Marcos

2018-01-01

Several quantum key distribution (QKD) protocols employ iterative sifting. After each quantum transmission round, Alice and Bob disclose part of their setting information (including their basis choices) for the detected signals. This quantum phase then ends when the basis dependent termination conditions are met, i.e., the numbers of detected signals per basis exceed certain pre-agreed threshold values. Recently, however, Pfister et al (2016 New J. Phys. 18 053001) showed that the basis dependent termination condition makes QKD insecure, especially in the finite key regime, and they suggested to disclose all the setting information after finishing the quantum phase. However, this protocol has two main drawbacks: it requires that Alice possesses a large memory, and she also needs to have some a priori knowledge about the transmission rate of the quantum channel. Here we solve these two problems by introducing a basis-independent termination condition to the iterative sifting in the finite key regime. The use of this condition, in combination with Azuma’s inequality, provides a precise estimation on the amount of privacy amplification that needs to be applied, thus leading to the security of QKD protocols, including the loss-tolerant protocol (Tamaki et al 2014 Phys. Rev. A 90 052314), with iterative sifting. Our analysis indicates that to announce the basis information after each quantum transmission round does not compromise the key generation rate of the loss-tolerant protocol. Our result allows the implementation of wider classes of classical post-processing techniques in QKD with quantified security.

The impact of finite-area inhomogeneities on resistive and Hall measurement

NASA Astrophysics Data System (ADS)

Koon, Daniel

2013-03-01

I derive an iterative expression for the electric potential in an otherwise homogeneous thin specimen as the result of a finite-area inhomogeneity in either the direct conductance, the Hall conductance, or both. This expression extends to the finite-area regime the calculation of the effect of such inhomogeneities on the measurement error in the sheet resistance and Hall sheet resistance. I then test these results on the exactly-solvable case of a circular inhomogeneity equally distant from the four electrodes of either a square four-point-probe array on an infinitely large conducting specimen or a circular van der Pauw specimen with symmetrically-placed electrodes.

Implementing a Matrix-free Analytical Jacobian to Handle Nonlinearities in Models of 3D Lithospheric Deformation

NASA Astrophysics Data System (ADS)

Kaus, B.; Popov, A.

2015-12-01

The analytical expression for the Jacobian is a key component to achieve fast and robust convergence of the nonlinear Newton-Raphson iterative solver. Accomplishing this task in practice often requires a significant algebraic effort. Therefore it is quite common to use a cheap alternative instead, for example by approximating the Jacobian with a finite difference estimation. Despite its simplicity it is a relatively fragile and unreliable technique that is sensitive to the scaling of the residual and unknowns, as well as to the perturbation parameter selection. Unfortunately no universal rule can be applied to provide both a robust scaling and a perturbation. The approach we use here is to derive the analytical Jacobian for the coupled set of momentum, mass, and energy conservation equations together with the elasto-visco-plastic rheology and a marker in cell/staggered finite difference method. The software project LaMEM (Lithosphere and Mantle Evolution Model) is primarily developed for the thermo-mechanically coupled modeling of the 3D lithospheric deformation. The code is based on a staggered grid finite difference discretization in space, and uses customized scalable solvers form PETSc library to efficiently run on the massively parallel machines (such as IBM Blue Gene/Q). Currently LaMEM relies on the Jacobian-Free Newton-Krylov (JFNK) nonlinear solver, which approximates the Jacobian-vector product using a simple finite difference formula. This approach never requires an assembled Jacobian matrix and uses only the residual computation routine. We use an approximate Jacobian (Picard) matrix to precondition the Krylov solver with the Galerkin geometric multigrid. Because of the inherent problems of the finite difference Jacobian estimation, this approach doesn't always result in stable convergence. In this work we present and discuss a matrix-free technique in which the Jacobian-vector product is replaced by analytically-derived expressions and compare results with those obtained with a finite difference approximation of the Jacobian. This project is funded by ERC Starting Grant 258830 and computer facilities were provided by Jülich supercomputer center (Germany).

Iterative Frequency Domain Decision Feedback Equalization and Decoding for Underwater Acoustic Communications

NASA Astrophysics Data System (ADS)

Zhao, Liang; Ge, Jian-Hua

2012-12-01

Single-carrier (SC) transmission with frequency-domain equalization (FDE) is today recognized as an attractive alternative to orthogonal frequency-division multiplexing (OFDM) for communication application with the inter-symbol interference (ISI) caused by multi-path propagation, especially in shallow water channel. In this paper, we investigate an iterative receiver based on minimum mean square error (MMSE) decision feedback equalizer (DFE) with symbol rate and fractional rate samplings in the frequency domain (FD) and serially concatenated trellis coded modulation (SCTCM) decoder. Based on sound speed profiles (SSP) measured in the lake and finite-element ray tracking (Bellhop) method, the shallow water channel is constructed to evaluate the performance of the proposed iterative receiver. Performance results show that the proposed iterative receiver can significantly improve the performance and obtain better data transmission than FD linear and adaptive decision feedback equalizers, especially in adopting fractional rate sampling.

Discrete-Time Stable Generalized Self-Learning Optimal Control With Approximation Errors.

PubMed

Wei, Qinglai; Li, Benkai; Song, Ruizhuo

2018-04-01

In this paper, a generalized policy iteration (GPI) algorithm with approximation errors is developed for solving infinite horizon optimal control problems for nonlinear systems. The developed stable GPI algorithm provides a general structure of discrete-time iterative adaptive dynamic programming algorithms, by which most of the discrete-time reinforcement learning algorithms can be described using the GPI structure. It is for the first time that approximation errors are explicitly considered in the GPI algorithm. The properties of the stable GPI algorithm with approximation errors are analyzed. The admissibility of the approximate iterative control law can be guaranteed if the approximation errors satisfy the admissibility criteria. The convergence of the developed algorithm is established, which shows that the iterative value function is convergent to a finite neighborhood of the optimal performance index function, if the approximate errors satisfy the convergence criterion. Finally, numerical examples and comparisons are presented.

Error bounds of adaptive dynamic programming algorithms for solving undiscounted optimal control problems.

PubMed

Liu, Derong; Li, Hongliang; Wang, Ding

2015-06-01

In this paper, we establish error bounds of adaptive dynamic programming algorithms for solving undiscounted infinite-horizon optimal control problems of discrete-time deterministic nonlinear systems. We consider approximation errors in the update equations of both value function and control policy. We utilize a new assumption instead of the contraction assumption in discounted optimal control problems. We establish the error bounds for approximate value iteration based on a new error condition. Furthermore, we also establish the error bounds for approximate policy iteration and approximate optimistic policy iteration algorithms. It is shown that the iterative approximate value function can converge to a finite neighborhood of the optimal value function under some conditions. To implement the developed algorithms, critic and action neural networks are used to approximate the value function and control policy, respectively. Finally, a simulation example is given to demonstrate the effectiveness of the developed algorithms.

TH-AB-BRA-09: Stability Analysis of a Novel Dose Calculation Algorithm for MRI Guided Radiotherapy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zelyak, O; Fallone, B; Cross Cancer Institute, Edmonton, AB

2016-06-15

Purpose: To determine the iterative deterministic solution stability of the Linear Boltzmann Transport Equation (LBTE) in the presence of magnetic fields. Methods: The LBTE with magnetic fields under investigation is derived using a discrete ordinates approach. The stability analysis is performed using analytical and numerical methods. Analytically, the spectral Fourier analysis is used to obtain the convergence rate of the source iteration procedures based on finding the largest eigenvalue of the iterative operator. This eigenvalue is a function of relevant physical parameters, such as magnetic field strength and material properties, and provides essential information about the domain of applicability requiredmore » for clinically optimal parameter selection and maximum speed of convergence. The analytical results are reinforced by numerical simulations performed using the same discrete ordinates method in angle, and a discontinuous finite element spatial approach. Results: The spectral radius for the source iteration technique of the time independent transport equation with isotropic and anisotropic scattering centers inside infinite 3D medium is equal to the ratio of differential and total cross sections. The result is confirmed numerically by solving LBTE and is in full agreement with previously published results. The addition of magnetic field reveals that the convergence becomes dependent on the strength of magnetic field, the energy group discretization, and the order of anisotropic expansion. Conclusion: The source iteration technique for solving the LBTE with magnetic fields with the discrete ordinates method leads to divergent solutions in the limiting cases of small energy discretizations and high magnetic field strengths. Future investigations into non-stationary Krylov subspace techniques as an iterative solver will be performed as this has been shown to produce greater stability than source iteration. Furthermore, a stability analysis of a discontinuous finite element space-angle approach (which has been shown to provide the greatest stability) will also be investigated. Dr. B Gino Fallone is a co-founder and CEO of MagnetTx Oncology Solutions (under discussions to license Alberta bi-planar linac MR for commercialization)« less

Fully coupled simulation of multiple hydraulic fractures to propagate simultaneously from a perforated horizontal wellbore

NASA Astrophysics Data System (ADS)

Zeng, Qinglei; Liu, Zhanli; Wang, Tao; Gao, Yue; Zhuang, Zhuo

2018-02-01

In hydraulic fracturing process in shale rock, multiple fractures perpendicular to a horizontal wellbore are usually driven to propagate simultaneously by the pumping operation. In this paper, a numerical method is developed for the propagation of multiple hydraulic fractures (HFs) by fully coupling the deformation and fracturing of solid formation, fluid flow in fractures, fluid partitioning through a horizontal wellbore and perforation entry loss effect. The extended finite element method (XFEM) is adopted to model arbitrary growth of the fractures. Newton's iteration is proposed to solve these fully coupled nonlinear equations, which is more efficient comparing to the widely adopted fixed-point iteration in the literatures and avoids the need to impose fluid pressure boundary condition when solving flow equations. A secant iterative method based on the stress intensity factor (SIF) is proposed to capture different propagation velocities of multiple fractures. The numerical results are compared with theoretical solutions in literatures to verify the accuracy of the method. The simultaneous propagation of multiple HFs is simulated by the newly proposed algorithm. The coupled influences of propagation regime, stress interaction, wellbore pressure loss and perforation entry loss on simultaneous propagation of multiple HFs are investigated.

A finite element analysis modeling tool for solid oxide fuel cell development: coupled electrochemistry, thermal and flow analysis in MARC®

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khaleel, Mohammad A.; Lin, Zijing; Singh, Prabhakar

2004-05-03

A 3D simulation tool for modeling solid oxide fuel cells is described. The tool combines the versatility and efficiency of a commercial finite element analysis code, MARC{reg_sign}, with an in-house developed robust and flexible electrochemical (EC) module. Based upon characteristic parameters obtained experimentally and assigned by the user, the EC module calculates the current density distribution, heat generation, and fuel and oxidant species concentration, taking the temperature profile provided by MARC{reg_sign} and operating conditions such as the fuel and oxidant flow rate and the total stack output voltage or current as the input. MARC{reg_sign} performs flow and thermal analyses basedmore » on the initial and boundary thermal and flow conditions and the heat generation calculated by the EC module. The main coupling between MARC{reg_sign} and EC is for MARC{reg_sign} to supply the temperature field to EC and for EC to give the heat generation profile to MARC{reg_sign}. The loosely coupled, iterative scheme is advantageous in terms of memory requirement, numerical stability and computational efficiency. The coupling is iterated to self-consistency for a steady-state solution. Sample results for steady states as well as the startup process for stacks with different flow designs are presented to illustrate the modeling capability and numerical performance characteristic of the simulation tool.« less

Numerical simulation of axisymmetric turbulent flow in combustors and diffusors. Ph.D. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Yung, Chain Nan

1988-01-01

A method for predicting turbulent flow in combustors and diffusers is developed. The Navier-Stokes equations, incorporating a turbulence kappa-epsilon model equation, were solved in a nonorthogonal curvilinear coordinate system. The solution applied the finite volume method to discretize the differential equations and utilized the SIMPLE algorithm iteratively to solve the differenced equations. A zonal grid method, wherein the flow field was divided into several subsections, was developed. This approach permitted different computational schemes to be used in the various zones. In addition, grid generation was made a more simple task. However, treatment of the zonal boundaries required special handling. Boundary overlap and interpolating techniques were used and an adjustment of the flow variables was required to assure conservation of mass, momentum and energy fluxes. The numerical accuracy was assessed using different finite differencing methods, i.e., hybrid, quadratic upwind and skew upwind, to represent the convection terms. Flows in different geometries of combustors and diffusers were simulated and results compared with experimental data and good agreement was obtained.

A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems, Part 1: Model Description and User's Manual

USGS Publications Warehouse

Torak, L.J.

1993-01-01

A MODular, Finite-Element digital-computer program (MODFE) was developed to simulate steady or unsteady-state, two-dimensional or axisymmetric ground-water flow. Geometric- and hydrologic-aquifer characteristics in two spatial dimensions are represented by triangular finite elements and linear basis functions; one-dimensional finite elements and linear basis functions represent time. Finite-element matrix equations are solved by the direct symmetric-Doolittle method or the iterative modified, incomplete-Cholesky, conjugate-gradient method. Physical processes that can be represented by the model include (1) confined flow, unconfined flow (using the Dupuit approximation), or a combination of both; (2) leakage through either rigid or elastic confining beds; (3) specified recharge or discharge at points, along lines, and over areas; (4) flow across specified-flow, specified-head, or bead-dependent boundaries; (5) decrease of aquifer thickness to zero under extreme water-table decline and increase of aquifer thickness from zero as the water table rises; and (6) head-dependent fluxes from springs, drainage wells, leakage across riverbeds or confining beds combined with aquifer dewatering, and evapotranspiration. The report describes procedures for applying MODFE to ground-water-flow problems, simulation capabilities, and data preparation. Guidelines for designing the finite-element mesh and for node numbering and determining band widths are given. Tables are given that reference simulation capabilities to specific versions of MODFE. Examples of data input and model output for different versions of MODFE are provided.

A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems; Part 1, Model description and user's manual

USGS Publications Warehouse

Torak, Lynn J.

1992-01-01

A MODular, Finite-Element digital-computer program (MODFE) was developed to simulate steady or unsteady-state, two-dimensional or axisymmetric ground-water flow. Geometric- and hydrologic-aquifer characteristics in two spatial dimensions are represented by triangular finite elements and linear basis functions; one-dimensional finite elements and linear basis functions represent time. Finite-element matrix equations are solved by the direct symmetric-Doolittle method or the iterative modified, incomplete-Cholesky, conjugate-gradient method. Physical processes that can be represented by the model include (1) confined flow, unconfined flow (using the Dupuit approximation), or a combination of both; (2) leakage through either rigid or elastic confining beds; (3) specified recharge or discharge at points, along lines, and over areas; (4) flow across specified-flow, specified-head, or head-dependent boundaries; (5) decrease of aquifer thickness to zero under extreme water-table decline and increase of aquifer thickness from zero as the water table rises; and (6) head-dependent fluxes from springs, drainage wells, leakage across riverbeds or confining beds combined with aquifer dewatering, and evapotranspiration.The report describes procedures for applying MODFE to ground-water-flow problems, simulation capabilities, and data preparation. Guidelines for designing the finite-element mesh and for node numbering and determining band widths are given. Tables are given that reference simulation capabilities to specific versions of MODFE. Examples of data input and model output for different versions of MODFE are provided.

Existence and amplitude bounds for irrotational water waves in finite depth

NASA Astrophysics Data System (ADS)

Kogelbauer, Florian

2017-12-01

We prove the existence of solutions to the irrotational water-wave problem in finite depth and derive an explicit upper bound on the amplitude of the nonlinear solutions in terms of the wavenumber, the total hydraulic head, the wave speed and the relative mass flux. Our approach relies upon a reformulation of the water-wave problem as a one-dimensional pseudo-differential equation and the Newton-Kantorovich iteration for Banach spaces. This article is part of the theme issue 'Nonlinear water waves'.

Strong Convergence for a Finite Family of Generalized Asymptotically Nonexpansive Mappings

NASA Astrophysics Data System (ADS)

Ma, Zhi-Hong; Chen, Ru-Dond

The purpose of this paper is to show the convergence theorems for generalized asymptotically nonexpansive mappings and asymptotically nonexpansive mappings in Banach spaces by using a new iteration which is a natural generalization of the implicit iteration. In the meantime, we give the necessary and sufficient conditions of the strong convergence to approximate a common fixed point and modify some flaw in the results of Thakur [11]. As one will see, the results presented in this paper are an extension of the corresponding results [8,11].

Modeling of frequency-domain scalar wave equation with the average-derivative optimal scheme based on a multigrid-preconditioned iterative solver

NASA Astrophysics Data System (ADS)

Cao, Jian; Chen, Jing-Bo; Dai, Meng-Xue

2018-01-01

An efficient finite-difference frequency-domain modeling of seismic wave propagation relies on the discrete schemes and appropriate solving methods. The average-derivative optimal scheme for the scalar wave modeling is advantageous in terms of the storage saving for the system of linear equations and the flexibility for arbitrary directional sampling intervals. However, using a LU-decomposition-based direct solver to solve its resulting system of linear equations is very costly for both memory and computational requirements. To address this issue, we consider establishing a multigrid-preconditioned BI-CGSTAB iterative solver fit for the average-derivative optimal scheme. The choice of preconditioning matrix and its corresponding multigrid components is made with the help of Fourier spectral analysis and local mode analysis, respectively, which is important for the convergence. Furthermore, we find that for the computation with unequal directional sampling interval, the anisotropic smoothing in the multigrid precondition may affect the convergence rate of this iterative solver. Successful numerical applications of this iterative solver for the homogenous and heterogeneous models in 2D and 3D are presented where the significant reduction of computer memory and the improvement of computational efficiency are demonstrated by comparison with the direct solver. In the numerical experiments, we also show that the unequal directional sampling interval will weaken the advantage of this multigrid-preconditioned iterative solver in the computing speed or, even worse, could reduce its accuracy in some cases, which implies the need for a reasonable control of directional sampling interval in the discretization.

A boundary element alternating method for two-dimensional mixed-mode fracture problems

NASA Technical Reports Server (NTRS)

Raju, I. S.; Krishnamurthy, T.

1992-01-01

A boundary element alternating method, denoted herein as BEAM, is presented for two dimensional fracture problems. This is an iterative method which alternates between two solutions. An analytical solution for arbitrary polynomial normal and tangential pressure distributions applied to the crack faces of an embedded crack in an infinite plate is used as the fundamental solution in the alternating method. A boundary element method for an uncracked finite plate is the second solution. For problems of edge cracks a technique of utilizing finite elements with BEAM is presented to overcome the inherent singularity in boundary element stress calculation near the boundaries. Several computational aspects that make the algorithm efficient are presented. Finally, the BEAM is applied to a variety of two dimensional crack problems with different configurations and loadings to assess the validity of the method. The method gives accurate stress intensity factors with minimal computing effort.

Modeling and analysis of the space shuttle nose-gear tire with semianalytic finite elements

NASA Technical Reports Server (NTRS)

Kim, Kyun O.; Noor, Ahmed K.; Tanner, John A.

1990-01-01

A computational procedure is presented for the geometrically nonlinear analysis of aircraft tires. The Space Shuttle Orbiter nose gear tire was modeled by using a two-dimensional laminated anisotropic shell theory with the effects of variation in material and geometric parameters included. The four key elements of the procedure are: (1) semianalytic finite elements in which the shell variables are represented by Fourier series in the circumferential direction and piecewise polynominals in the meridional direction; (2) a mixed formulation with the fundamental unknowns consisting of strain parameters, stress-resultant parameters, and generalized displacements; (3) multilevel operator splitting to effect successive simplifications, and to uncouple the equations associated with different Fourier harmonics; and (4) multilevel iterative procedures and reduction techniques to generate the response of the shell. Numerical results of the Space Shuttle Orbiter nose gear tire model are compared with experimental measurements of the tire subjected to inflation loading.

A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance

NASA Astrophysics Data System (ADS)

Witte, J. H.; Reisinger, C.

2010-09-01

We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately, many intuitive (e.g. finite difference based) discretisations can be shown to converge. However, especially when using fully implicit time stepping schemes with their desireable stability properties, one is still faced with the considerable task of solving the resulting nonlinear discrete system. In this paper, we introduce a penalty method which approximates the nonlinear discrete system to an order of O(1/ρ), where ρ>0 is the penalty parameter, and we show that an iterative scheme can be used to solve the penalised discrete problem in finitely many steps. We include a number of examples from mathematical finance for which the described approach yields a rigorous numerical scheme and present numerical results.

A simplified method for elastic-plastic-creep structural analysis

NASA Technical Reports Server (NTRS)

Kaufman, A.

1984-01-01

A simplified inelastic analysis computer program (ANSYPM) was developed for predicting the stress-strain history at the critical location of a thermomechanically cycled structure from an elastic solution. The program uses an iterative and incremental procedure to estimate the plastic strains from the material stress-strain properties and a plasticity hardening model. Creep effects are calculated on the basis of stress relaxation at constant strain, creep at constant stress or a combination of stress relaxation and creep accumulation. The simplified method was exercised on a number of problems involving uniaxial and multiaxial loading, isothermal and nonisothermal conditions, dwell times at various points in the cycles, different materials and kinematic hardening. Good agreement was found between these analytical results and nonlinear finite element solutions for these problems. The simplified analysis program used less than 1 percent of the CPU time required for a nonlinear finite element analysis.

A simplified method for elastic-plastic-creep structural analysis

NASA Technical Reports Server (NTRS)

Kaufman, A.

1985-01-01

A simplified inelastic analysis computer program (ANSYPM) was developed for predicting the stress-strain history at the critical location of a thermomechanically cycled structure from an elastic solution. The program uses an iterative and incremental procedure to estimate the plastic strains from the material stress-strain properties and a plasticity hardening model. Creep effects are calculated on the basis of stress relaxation at constant strain, creep at constant stress or a combination of stress relaxation and creep accumulation. The simplified method was exercised on a number of problems involving uniaxial and multiaxial loading, isothermal and nonisothermal conditions, dwell times at various points in the cycles, different materials and kinematic hardening. Good agreement was found between these analytical results and nonlinear finite element solutions for these problems. The simplified analysis program used less than 1 percent of the CPU time required for a nonlinear finite element analysis.

Partitioning strategy for efficient nonlinear finite element dynamic analysis on multiprocessor computers

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Peters, Jeanne M.

1989-01-01

A computational procedure is presented for the nonlinear dynamic analysis of unsymmetric structures on vector multiprocessor systems. The procedure is based on a novel hierarchical partitioning strategy in which the response of the unsymmetric and antisymmetric response vectors (modes), each obtained by using only a fraction of the degrees of freedom of the original finite element model. The three key elements of the procedure which result in high degree of concurrency throughout the solution process are: (1) mixed (or primitive variable) formulation with independent shape functions for the different fields; (2) operator splitting or restructuring of the discrete equations at each time step to delineate the symmetric and antisymmetric vectors constituting the response; and (3) two level iterative process for generating the response of the structure. An assessment is made of the effectiveness of the procedure on the CRAY X-MP/4 computers.

3D modelling of non-linear visco-elasto-plastic crustal and lithospheric processes using LaMEM

NASA Astrophysics Data System (ADS)

Popov, Anton; Kaus, Boris

2016-04-01

LaMEM (Lithosphere and Mantle Evolution Model) is a three-dimensional thermo-mechanical numerical code to simulate crustal and lithospheric deformation. The code is based on a staggered finite difference (FDSTAG) discretization in space, which is a stable and very efficient technique to solve the (nearly) incompressible Stokes equations that does not suffer from spurious pressure modes or artificial compressibility (a typical feature of low-order finite element techniques). Higher order finite element methods are more accurate than FDSTAG methods under idealized test cases where the jump in viscosity is exactly aligned with the boundaries of the elements. Yet, geodynamically more realistic cases involve evolving subduction zones, nonlinear rheologies or localized plastic shear bands. In these cases, the viscosity pattern evolves spontaneously during a simulation or even during nonlinear iterations, and the advantages of higher order methods disappear and they all converge with approximately first order accuracy, similar to that of FDSTAG [1]. Yet, since FDSTAG methods have considerably less degrees of freedom than quadratic finite element methods, they require about an order of magnitude less memory for the same number of nodes in 3D which also implies that every matrix-vector multiplication is significantly faster. LaMEM is build on top of the PETSc library and uses the particle-in-cell technique to track material properties, history variables which makes it straightforward to incorporate effects like phase changes or chemistry. An internal free surface is present, together with (simple) erosion and sedimentation processes, and a number of methods are available to import complex geometries into the code (e.g, http://geomio.bitbucket.org). Customized Galerkin coupled geometric multigrid preconditioners are implemented which resulted in a good parallel scalability of the code (we have tested LaMEM on 458'752 cores [2]). Yet, the drawback of using FDSTAG discretizations is that the Jacobian, which is a key component for fast and robust convergence of Newton-Raphson nonlinear iterative solvers, is more difficult to implement than in FE codes and actually results in a larger stencil. Rather than discretizing it explicitly, we therefore developed a matrix-free analytical Jacobian implementation for the coupled sets of momentum, mass, and energy conservation equations, combined with visco-elasto-plastic rheologies. Tests show that for simple nonlinear viscous rheologies there is little advantage of the MF approach over the standard MFFD PETSc approach, but that iterations converge slightly faster if plasticity is present. Results also show that the Newton solver usually converges in a quadratic manner even for pressure-dependent Drucker-Prager rheologies and without harmonic viscosity averaging of plastic and viscous rheologies. Yet, if the timestep is too large (and the model becomes effectively viscoplastic), or if the shear band pattern changes dramatically, stagnation of iterations might occur. This can be remedied with an appropriate regularization, which we discuss. LaMEM is available as open source software. [1] Thielmann, M., May, D.A., and Kaus, B., 2014, Discretization Errors in the Hybrid Finite Element Particle-in-cell Method: Pure and Applied Geophysics,, doi: 10.1007/s00024-014-0808-9. [2] Kaus B.J.P., Popov A.A., Baumann T.S., Püsök A.E., Bauville A., Fernandez N., Collignon M. (2015) Forward and inverse modelling of lithospheric deformation on geological timescales. NIC Symposium 2016 - Proceedings. NIC Series. Vol. 48.

On the use of finite difference matrix-vector products in Newton-Krylov solvers for implicit climate dynamics with spectral elements

DOE PAGES

Woodward, Carol S.; Gardner, David J.; Evans, Katherine J.

2015-01-01

Efficient solutions of global climate models require effectively handling disparate length and time scales. Implicit solution approaches allow time integration of the physical system with a step size governed by accuracy of the processes of interest rather than by stability of the fastest time scales present. Implicit approaches, however, require the solution of nonlinear systems within each time step. Usually, a Newton's method is applied to solve these systems. Each iteration of the Newton's method, in turn, requires the solution of a linear model of the nonlinear system. This model employs the Jacobian of the problem-defining nonlinear residual, but thismore » Jacobian can be costly to form. If a Krylov linear solver is used for the solution of the linear system, the action of the Jacobian matrix on a given vector is required. In the case of spectral element methods, the Jacobian is not calculated but only implemented through matrix-vector products. The matrix-vector multiply can also be approximated by a finite difference approximation which may introduce inaccuracy in the overall nonlinear solver. In this paper, we review the advantages and disadvantages of finite difference approximations of these matrix-vector products for climate dynamics within the spectral element shallow water dynamical core of the Community Atmosphere Model.« less

Three-dimensional forward modeling of DC resistivity using the aggregation-based algebraic multigrid method

NASA Astrophysics Data System (ADS)

Chen, Hui; Deng, Ju-Zhi; Yin, Min; Yin, Chang-Chun; Tang, Wen-Wu

2017-03-01

To speed up three-dimensional (3D) DC resistivity modeling, we present a new multigrid method, the aggregation-based algebraic multigrid method (AGMG). We first discretize the differential equation of the secondary potential field with mixed boundary conditions by using a seven-point finite-difference method to obtain a large sparse system of linear equations. Then, we introduce the theory behind the pairwise aggregation algorithms for AGMG and use the conjugate-gradient method with the V-cycle AGMG preconditioner (AGMG-CG) to solve the linear equations. We use typical geoelectrical models to test the proposed AGMG-CG method and compare the results with analytical solutions and the 3DDCXH algorithm for 3D DC modeling (3DDCXH). In addition, we apply the AGMG-CG method to different grid sizes and geoelectrical models and compare it to different iterative methods, such as ILU-BICGSTAB, ILU-GCR, and SSOR-CG. The AGMG-CG method yields nearly linearly decreasing errors, whereas the number of iterations increases slowly with increasing grid size. The AGMG-CG method is precise and converges fast, and thus can improve the computational efficiency in forward modeling of three-dimensional DC resistivity.

Parallel Ellipsoidal Perfectly Matched Layers for Acoustic Helmholtz Problems on Exterior Domains

DOE PAGES

Bunting, Gregory; Prakash, Arun; Walsh, Timothy; ...

2018-01-26

Exterior acoustic problems occur in a wide range of applications, making the finite element analysis of such problems a common practice in the engineering community. Various methods for truncating infinite exterior domains have been developed, including absorbing boundary conditions, infinite elements, and more recently, perfectly matched layers (PML). PML are gaining popularity due to their generality, ease of implementation, and effectiveness as an absorbing boundary condition. PML formulations have been developed in Cartesian, cylindrical, and spherical geometries, but not ellipsoidal. In addition, the parallel solution of PML formulations with iterative solvers for the solution of the Helmholtz equation, and howmore » this compares with more traditional strategies such as infinite elements, has not been adequately investigated. In this study, we present a parallel, ellipsoidal PML formulation for acoustic Helmholtz problems. To faciliate the meshing process, the ellipsoidal PML layer is generated with an on-the-fly mesh extrusion. Though the complex stretching is defined along ellipsoidal contours, we modify the Jacobian to include an additional mapping back to Cartesian coordinates in the weak formulation of the finite element equations. This allows the equations to be solved in Cartesian coordinates, which is more compatible with existing finite element software, but without the necessity of dealing with corners in the PML formulation. Herein we also compare the conditioning and performance of the PML Helmholtz problem with infinite element approach that is based on high order basis functions. On a set of representative exterior acoustic examples, we show that high order infinite element basis functions lead to an increasing number of Helmholtz solver iterations, whereas for PML the number of iterations remains constant for the same level of accuracy. Finally, this provides an additional advantage of PML over the infinite element approach.« less

Parallel Ellipsoidal Perfectly Matched Layers for Acoustic Helmholtz Problems on Exterior Domains

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bunting, Gregory; Prakash, Arun; Walsh, Timothy

Exterior acoustic problems occur in a wide range of applications, making the finite element analysis of such problems a common practice in the engineering community. Various methods for truncating infinite exterior domains have been developed, including absorbing boundary conditions, infinite elements, and more recently, perfectly matched layers (PML). PML are gaining popularity due to their generality, ease of implementation, and effectiveness as an absorbing boundary condition. PML formulations have been developed in Cartesian, cylindrical, and spherical geometries, but not ellipsoidal. In addition, the parallel solution of PML formulations with iterative solvers for the solution of the Helmholtz equation, and howmore » this compares with more traditional strategies such as infinite elements, has not been adequately investigated. In this study, we present a parallel, ellipsoidal PML formulation for acoustic Helmholtz problems. To faciliate the meshing process, the ellipsoidal PML layer is generated with an on-the-fly mesh extrusion. Though the complex stretching is defined along ellipsoidal contours, we modify the Jacobian to include an additional mapping back to Cartesian coordinates in the weak formulation of the finite element equations. This allows the equations to be solved in Cartesian coordinates, which is more compatible with existing finite element software, but without the necessity of dealing with corners in the PML formulation. Herein we also compare the conditioning and performance of the PML Helmholtz problem with infinite element approach that is based on high order basis functions. On a set of representative exterior acoustic examples, we show that high order infinite element basis functions lead to an increasing number of Helmholtz solver iterations, whereas for PML the number of iterations remains constant for the same level of accuracy. Finally, this provides an additional advantage of PML over the infinite element approach.« less

An empirical investigation of methods for nonsymmetric linear systems

NASA Technical Reports Server (NTRS)

Sherman, A. H.

1981-01-01

The present investigation is concerned with a comparison of methods for solving linear algebraic systems which arise from finite difference discretizations of the elliptic convection-diffusion equation in a planar region Omega with Dirichlet boundary conditions. Such linear systems are typically of the form Ax = b where A is an N x N sparse nonsymmetric matrix. In a discussion of discretizations, it is assumed that a regular rectilinear mesh of width h has been imposed on Omega. The discretizations considered include central differences, upstream differences, and modified upstream differences. Six methods for solving Ax = b are considered. Three variants of Gaussian elimination have been chosen as representatives of state-of-the-art software for direct methods under different assumptions about pivoting. Three iterative methods are also included.

TAP 1: A Finite Element Program for Steady-State Thermal Analysis of Convectively Cooled Structures

NASA Technical Reports Server (NTRS)

Thornton, E. A.

1976-01-01

The program has a finite element library of six elements: two conduction/convection elements to model heat transfer in a solid, two convection elements to model heat transfer in a fluid, and two integrated conduction/convection elements to represent combined heat transfer in tubular and plate/fin fluid passages. Nonlinear thermal analysis due to temperature dependent thermal parameters is performed using the Newton-Raphson iteration method. Program output includes nodal temperatures and element heat fluxes. Pressure drops in fluid passages may be computed as an option. A companion plotting program for displaying the finite element model and predicted temperature distributions is presented. User instructions and sample problems are presented in appendixes.

Finite element concepts in computational aerodynamics

NASA Technical Reports Server (NTRS)

Baker, A. J.

1978-01-01

Finite element theory was employed to establish an implicit numerical solution algorithm for the time averaged unsteady Navier-Stokes equations. Both the multidimensional and a time-split form of the algorithm were considered, the latter of particular interest for problem specification on a regular mesh. A Newton matrix iteration procedure is outlined for solving the resultant nonlinear algebraic equation systems. Multidimensional discretization procedures are discussed with emphasis on automated generation of specific nonuniform solution grids and accounting of curved surfaces. The time-split algorithm was evaluated with regards to accuracy and convergence properties for hyperbolic equations on rectangular coordinates. An overall assessment of the viability of the finite element concept for computational aerodynamics is made.

Méthode du second membre modifié pour la gestion de rapports de viscosité importants dans le problème de Stokes bifluide

NASA Astrophysics Data System (ADS)

Bui, Thi Thu Cuc; Frey, Pascal; Maury, Bertrand

2008-06-01

In this Note, we present a method to solve numerically the Stokes equation for the incompressible flow between two immiscible fluids presenting very different viscosities. The resolution of the finite element systems of equations is performed using Uzawa's method. The stiffness matrix conditioning problems related to the very important viscosity ratios are circumvented using an new iterative scheme. A numerical example is proposed to show the efficiency of this approach. To cite this article: T.T.C. Bui et al., C. R. Mecanique 336 (2008).

Boundary formulations for sensitivity analysis without matrix derivatives

NASA Technical Reports Server (NTRS)

Kane, J. H.; Guru Prasad, K.

1993-01-01

A new hybrid approach to continuum structural shape sensitivity analysis employing boundary element analysis (BEA) is presented. The approach uses iterative reanalysis to obviate the need to factor perturbed matrices in the determination of surface displacement and traction sensitivities via a univariate perturbation/finite difference (UPFD) step. The UPFD approach makes it possible to immediately reuse existing subroutines for computation of BEA matrix coefficients in the design sensitivity analysis process. The reanalysis technique computes economical response of univariately perturbed models without factoring perturbed matrices. The approach provides substantial computational economy without the burden of a large-scale reprogramming effort.

Analysis of airfoil leading edge separation bubbles

NASA Technical Reports Server (NTRS)

Carter, J. E.; Vatsa, V. N.

1982-01-01

A local inviscid-viscous interaction technique was developed for the analysis of low speed airfoil leading edge transitional separation bubbles. In this analysis an inverse boundary layer finite difference analysis is solved iteratively with a Cauchy integral representation of the inviscid flow which is assumed to be a linear perturbation to a known global viscous airfoil analysis. Favorable comparisons with data indicate the overall validity of the present localized interaction approach. In addition numerical tests were performed to test the sensitivity of the computed results to the mesh size, limits on the Cauchy integral, and the location of the transition region.

Measurement of gas diffusion coefficient in liquid-saturated porous media using magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Song, Yongchen; Hao, Min; Zhao, Yuechao; Zhang, Liang

2014-12-01

In this study, the dual-chamber pressure decay method and magnetic resonance imaging (MRI) were used to dynamically visualize the gas diffusion process in liquid-saturated porous media, and the relationship of concentration-distance for gas diffusing into liquid-saturated porous media at different times were obtained by MR images quantitative analysis. A non-iterative finite volume method was successfully applied to calculate the local gas diffusion coefficient in liquid-saturated porous media. The results agreed very well with the conventional pressure decay method, thus it demonstrates that the method was feasible of determining the local diffusion coefficient of gas in liquid-saturated porous media at different times during diffusion process.

FDM study of ion exchange diffusion equation in glass

NASA Astrophysics Data System (ADS)

Zhou, Zigang; Yang, Yongjia; Wang, Qiang; Sun, Guangchun

2009-05-01

Ion-exchange technique in glass was developed to fabricate gradient refractive index optical devices. In this paper, the Finite Difference Method(FDM), which is used for the solution of ion-diffusion equation, is reported. This method transforms continual diffusion equation to separate difference equation. It unitizes the matrix of MATLAB program to solve the iteration process. The collation results under square boundary condition show that it gets a more accurate numerical solution. Compared to experiment data, the relative error is less than 0.2%. Furthermore, it has simply operation and kinds of output solutions. This method can provide better results for border-proliferation of the hexagonal and the channel devices too.

The calculation of steady non-linear transonic flow over finite wings with linear theory aerodynamics

NASA Technical Reports Server (NTRS)

Cunningham, A. M., Jr.

1976-01-01

The feasibility of calculating steady mean flow solutions for nonlinear transonic flow over finite wings with a linear theory aerodynamic computer program is studied. The methodology is based on independent solutions for upper and lower surface pressures that are coupled through the external flow fields. Two approaches for coupling the solutions are investigated which include the diaphragm and the edge singularity method. The final method is a combination of both where a line source along the wing leading edge is used to account for blunt nose airfoil effects; and the upper and lower surface flow fields are coupled through a diaphragm in the plane of the wing. An iterative solution is used to arrive at the nonuniform flow solution for both nonlifting and lifting cases. Final results for a swept tapered wing in subcritical flow show that the method converges in three iterations and gives excellent agreement with experiment at alpha = 0 deg and 2 deg. Recommendations are made for development of a procedure for routine application.

Solution of large nonlinear quasistatic structural mechanics problems on distributed-memory multiprocessor computers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blanford, M.

1997-12-31

Most commercially-available quasistatic finite element programs assemble element stiffnesses into a global stiffness matrix, then use a direct linear equation solver to obtain nodal displacements. However, for large problems (greater than a few hundred thousand degrees of freedom), the memory size and computation time required for this approach becomes prohibitive. Moreover, direct solution does not lend itself to the parallel processing needed for today`s multiprocessor systems. This talk gives an overview of the iterative solution strategy of JAS3D, the nonlinear large-deformation quasistatic finite element program. Because its architecture is derived from an explicit transient-dynamics code, it does not ever assemblemore » a global stiffness matrix. The author describes the approach he used to implement the solver on multiprocessor computers, and shows examples of problems run on hundreds of processors and more than a million degrees of freedom. Finally, he describes some of the work he is presently doing to address the challenges of iterative convergence for ill-conditioned problems.« less

Simulating transient dynamics of the time-dependent time fractional Fokker-Planck systems

NASA Astrophysics Data System (ADS)

Kang, Yan-Mei

2016-09-01

For a physically realistic type of time-dependent time fractional Fokker-Planck (FP) equation, derived as the continuous limit of the continuous time random walk with time-modulated Boltzmann jumping weight, a semi-analytic iteration scheme based on the truncated (generalized) Fourier series is presented to simulate the resultant transient dynamics when the external time modulation is a piece-wise constant signal. At first, the iteration scheme is demonstrated with a simple time-dependent time fractional FP equation on finite interval with two absorbing boundaries, and then it is generalized to the more general time-dependent Smoluchowski-type time fractional Fokker-Planck equation. The numerical examples verify the efficiency and accuracy of the iteration method, and some novel dynamical phenomena including polarized motion orientations and periodic response death are discussed.

A combined registration and finite element analysis method for fast estimation of intraoperative brain shift; phantom and animal model study.

PubMed

Mohammadi, Amrollah; Ahmadian, Alireza; Rabbani, Shahram; Fattahi, Ehsan; Shirani, Shapour

2017-12-01

Finite element models for estimation of intraoperative brain shift suffer from huge computational cost. In these models, image registration and finite element analysis are two time-consuming processes. The proposed method is an improved version of our previously developed Finite Element Drift (FED) registration algorithm. In this work the registration process is combined with the finite element analysis. In the Combined FED (CFED), the deformation of whole brain mesh is iteratively calculated by geometrical extension of a local load vector which is computed by FED. While the processing time of the FED-based method including registration and finite element analysis was about 70 s, the computation time of the CFED was about 3.2 s. The computational cost of CFED is almost 50% less than similar state of the art brain shift estimators based on finite element models. The proposed combination of registration and structural analysis can make the calculation of brain deformation much faster. Copyright © 2016 John Wiley & Sons, Ltd.

Efficient design of nanoplasmonic waveguide devices using the space mapping algorithm.

PubMed

Dastmalchi, Pouya; Veronis, Georgios

2013-12-30

We show that the space mapping algorithm, originally developed for microwave circuit optimization, can enable the efficient design of nanoplasmonic waveguide devices which satisfy a set of desired specifications. Space mapping utilizes a physics-based coarse model to approximate a fine model accurately describing a device. Here the fine model is a full-wave finite-difference frequency-domain (FDFD) simulation of the device, while the coarse model is based on transmission line theory. We demonstrate that simply optimizing the transmission line model of the device is not enough to obtain a device which satisfies all the required design specifications. On the other hand, when the iterative space mapping algorithm is used, it converges fast to a design which meets all the specifications. In addition, full-wave FDFD simulations of only a few candidate structures are required before the iterative process is terminated. Use of the space mapping algorithm therefore results in large reductions in the required computation time when compared to any direct optimization method of the fine FDFD model.

Distributed weighted least-squares estimation with fast convergence for large-scale systems.

PubMed

Marelli, Damián Edgardo; Fu, Minyue

2015-01-01

In this paper we study a distributed weighted least-squares estimation problem for a large-scale system consisting of a network of interconnected sub-systems. Each sub-system is concerned with a subset of the unknown parameters and has a measurement linear in the unknown parameters with additive noise. The distributed estimation task is for each sub-system to compute the globally optimal estimate of its own parameters using its own measurement and information shared with the network through neighborhood communication. We first provide a fully distributed iterative algorithm to asymptotically compute the global optimal estimate. The convergence rate of the algorithm will be maximized using a scaling parameter and a preconditioning method. This algorithm works for a general network. For a network without loops, we also provide a different iterative algorithm to compute the global optimal estimate which converges in a finite number of steps. We include numerical experiments to illustrate the performances of the proposed methods.

Distributed weighted least-squares estimation with fast convergence for large-scale systems☆

PubMed Central

Marelli, Damián Edgardo; Fu, Minyue

2015-01-01

In this paper we study a distributed weighted least-squares estimation problem for a large-scale system consisting of a network of interconnected sub-systems. Each sub-system is concerned with a subset of the unknown parameters and has a measurement linear in the unknown parameters with additive noise. The distributed estimation task is for each sub-system to compute the globally optimal estimate of its own parameters using its own measurement and information shared with the network through neighborhood communication. We first provide a fully distributed iterative algorithm to asymptotically compute the global optimal estimate. The convergence rate of the algorithm will be maximized using a scaling parameter and a preconditioning method. This algorithm works for a general network. For a network without loops, we also provide a different iterative algorithm to compute the global optimal estimate which converges in a finite number of steps. We include numerical experiments to illustrate the performances of the proposed methods. PMID:25641976

Multichannel blind iterative image restoration.

PubMed

Sroubek, Filip; Flusser, Jan

2003-01-01

Blind image deconvolution is required in many applications of microscopy imaging, remote sensing, and astronomical imaging. Unfortunately in a single-channel framework, serious conceptual and numerical problems are often encountered. Very recently, an eigenvector-based method (EVAM) was proposed for a multichannel framework which determines perfectly convolution masks in a noise-free environment if channel disparity, called co-primeness, is satisfied. We propose a novel iterative algorithm based on recent anisotropic denoising techniques of total variation and a Mumford-Shah functional with the EVAM restoration condition included. A linearization scheme of half-quadratic regularization together with a cell-centered finite difference discretization scheme is used in the algorithm and provides a unified approach to the solution of total variation or Mumford-Shah. The algorithm performs well even on very noisy images and does not require an exact estimation of mask orders. We demonstrate capabilities of the algorithm on synthetic data. Finally, the algorithm is applied to defocused images taken with a digital camera and to data from astronomical ground-based observations of the Sun.

3-D Analysis of Flanged Joints Through Various Preload Methods Using ANSYS

NASA Astrophysics Data System (ADS)

Murugan, Jeyaraj Paul; Kurian, Thomas; Jayaprakash, Janardhan; Sreedharapanickar, Somanath

2015-10-01

Flanged joints are being employed in aerospace solid rocket motor hardware for the integration of various systems or subsystems. Hence, the design of flanged joints is very important in ensuring the integrity of motor while functioning. As these joints are subjected to higher loads due to internal pressure acting inside the motor chamber, an appropriate preload is required to be applied in this joint before subjecting it to the external load. Preload, also known as clamp load, is applied on the fastener and helps to hold the mating flanges together. Generally preload is simulated as a thermal load and the exact preload is obtained through number of iterations. Infact, more iterations are required when considering the material nonlinearity of the bolt. This way of simulation will take more computational time for generating the required preload. Now a days most commercial software packages use pretension elements for simulating the preload. This element does not require iterations for inducing the preload and it can be solved with single iteration. This approach takes less computational time and thus one can study the characteristics of the joint easily by varying the preload. When the structure contains more number of joints with different sizes of fasteners, pretension elements can be used compared to thermal load approach for simulating each size of fastener. This paper covers the details of analyses carried out simulating the preload through various options viz., preload through thermal, initial state command and pretension element etc. using ANSYS finite element package.

Finite elements and the method of conjugate gradients on a concurrent processor

NASA Technical Reports Server (NTRS)

Lyzenga, G. A.; Raefsky, A.; Hager, G. H.

1985-01-01

An algorithm for the iterative solution of finite element problems on a concurrent processor is presented. The method of conjugate gradients is used to solve the system of matrix equations, which is distributed among the processors of a MIMD computer according to an element-based spatial decomposition. This algorithm is implemented in a two-dimensional elastostatics program on the Caltech Hypercube concurrent processor. The results of tests on up to 32 processors show nearly linear concurrent speedup, with efficiencies over 90 percent for sufficiently large problems.

Finite elements and the method of conjugate gradients on a concurrent processor

NASA Technical Reports Server (NTRS)

Lyzenga, G. A.; Raefsky, A.; Hager, B. H.

1984-01-01

An algorithm for the iterative solution of finite element problems on a concurrent processor is presented. The method of conjugate gradients is used to solve the system of matrix equations, which is distributed among the processors of a MIMD computer according to an element-based spatial decomposition. This algorithm is implemented in a two-dimensional elastostatics program on the Caltech Hypercube concurrent processor. The results of tests on up to 32 processors show nearly linear concurrent speedup, with efficiencies over 90% for sufficiently large problems.

New discretization and solution techniques for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

Gunzburger, M. D.; Nicolaides, R. A.; Liu, C. H.

1983-01-01

Several topics arising in the finite element solution of the incompressible Navier-Stokes equations are considered. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. The role of artificial viscosity in viscous flow calculations is studied, emphasizing work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some modifications are mentioned.

Computational simulation of laser heat processing of materials

NASA Astrophysics Data System (ADS)

Shankar, Vijaya; Gnanamuthu, Daniel

1987-04-01

A computational model simulating the laser heat treatment of AISI 4140 steel plates with a CW CO2 laser beam has been developed on the basis of the three-dimensional, time-dependent heat equation (subject to the appropriate boundary conditions). The solution method is based on Newton iteration applied to a triple-approximate factorized form of the equation. The method is implicit and time-accurate; the maintenance of time-accuracy in the numerical formulation is noted to be critical for the simulation of finite length workpieces with a finite laser beam dwell time.

Finite element analysis of periodic transonic flow problems

NASA Technical Reports Server (NTRS)

Fix, G. J.

1978-01-01

Flow about an oscillating thin airfoil in a transonic stream was considered. It was assumed that the flow field can be decomposed into a mean flow plus a periodic perturbation. On the surface of the airfoil the usual Neumman conditions are imposed. Two computer programs were written, both using linear basis functions over triangles for the finite element space. The first program uses a banded Gaussian elimination solver to solve the matrix problem, while the second uses an iterative technique, namely SOR. The only results obtained are for an oscillating flat plate.

Integrable mappings and the notion of anticonfinement

NASA Astrophysics Data System (ADS)

Mase, T.; Willox, R.; Ramani, A.; Grammaticos, B.

2018-06-01

We examine the notion of anticonfinement and the role it has to play in the singularity analysis of discrete systems. A singularity is said to be anticonfined if singular values continue to arise indefinitely for the forward and backward iterations of a mapping, with only a finite number of iterates taking regular values in between. We show through several concrete examples that the behaviour of some anticonfined singularities is strongly related to the integrability properties of the discrete mappings in which they arise, and we explain how to use this information to decide on the integrability or non-integrability of the mapping.

Non-oscillatory and non-diffusive solution of convection problems by the iteratively reweighted least-squares finite element method

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan

1993-01-01

A comparative description is presented for the least-squares FEM (LSFEM) for 2D steady-state pure convection problems. In addition to exhibiting better control of the streamline derivative than the streamline upwinding Petrov-Galerkin method, numerical convergence rates are obtained which show the LSFEM to be virtually optimal. The LSFEM is used as a framework for an iteratively reweighted LSFEM yielding nonoscillatory and nondiffusive solutions for problems with contact discontinuities; this method is shown to convect contact discontinuities without error when using triangular and bilinear elements.

Finite mixture models for the computation of isotope ratios in mixed isotopic samples

NASA Astrophysics Data System (ADS)

Koffler, Daniel; Laaha, Gregor; Leisch, Friedrich; Kappel, Stefanie; Prohaska, Thomas

2013-04-01

Finite mixture models have been used for more than 100 years, but have seen a real boost in popularity over the last two decades due to the tremendous increase in available computing power. The areas of application of mixture models range from biology and medicine to physics, economics and marketing. These models can be applied to data where observations originate from various groups and where group affiliations are not known, as is the case for multiple isotope ratios present in mixed isotopic samples. Recently, the potential of finite mixture models for the computation of 235U/238U isotope ratios from transient signals measured in individual (sub-)µm-sized particles by laser ablation - multi-collector - inductively coupled plasma mass spectrometry (LA-MC-ICPMS) was demonstrated by Kappel et al. [1]. The particles, which were deposited on the same substrate, were certified with respect to their isotopic compositions. Here, we focus on the statistical model and its application to isotope data in ecogeochemistry. Commonly applied evaluation approaches for mixed isotopic samples are time-consuming and are dependent on the judgement of the analyst. Thus, isotopic compositions may be overlooked due to the presence of more dominant constituents. Evaluation using finite mixture models can be accomplished unsupervised and automatically. The models try to fit several linear models (regression lines) to subgroups of data taking the respective slope as estimation for the isotope ratio. The finite mixture models are parameterised by: • The number of different ratios. • Number of points belonging to each ratio-group. • The ratios (i.e. slopes) of each group. Fitting of the parameters is done by maximising the log-likelihood function using an iterative expectation-maximisation (EM) algorithm. In each iteration step, groups of size smaller than a control parameter are dropped; thereby the number of different ratios is determined. The analyst only influences some control parameters of the algorithm, i.e. the maximum count of ratios, the minimum relative group-size of data points belonging to each ratio has to be defined. Computation of the models can be done with statistical software. In this study Leisch and Grün's flexmix package [2] for the statistical open-source software R was applied. A code example is available in the electronic supplementary material of Kappel et al. [1]. In order to demonstrate the usefulness of finite mixture models in fields dealing with the computation of multiple isotope ratios in mixed samples, a transparent example based on simulated data is presented and problems regarding small group-sizes are illustrated. In addition, the application of finite mixture models to isotope ratio data measured in uranium oxide particles is shown. The results indicate that finite mixture models perform well in computing isotope ratios relative to traditional estimation procedures and can be recommended for more objective and straightforward calculation of isotope ratios in geochemistry than it is current practice. [1] S. Kappel, S. Boulyga, L. Dorta, D. Günther, B. Hattendorf, D. Koffler, G. Laaha, F. Leisch and T. Prohaska: Evaluation Strategies for Isotope Ratio Measurements of Single Particles by LA-MC-ICPMS, Analytical and Bioanalytical Chemistry, 2013, accepted for publication on 2012-12-18 (doi: 10.1007/s00216-012-6674-3) [2] B. Grün and F. Leisch: Fitting finite mixtures of generalized linear regressions in R. Computational Statistics & Data Analysis, 51(11), 5247-5252, 2007. (doi:10.1016/j.csda.2006.08.014)

Vectorized and multitasked solution of the few-group neutron diffusion equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zee, S.K.; Turinsky, P.J.; Shayer, Z.

1989-03-01

A numerical algorithm with parallelism was used to solve the two-group, multidimensional neutron diffusion equations on computers characterized by shared memory, vector pipeline, and multi-CPU architecture features. Specifically, solutions were obtained on the Cray X/MP-48, the IBM-3090 with vector facilities, and the FPS-164. The material-centered mesh finite difference method approximation and outer-inner iteration method were employed. Parallelism was introduced in the inner iterations using the cyclic line successive overrelaxation iterative method and solving in parallel across lines. The outer iterations were completed using the Chebyshev semi-iterative method that allows parallelism to be introduced in both space and energy groups. Formore » the three-dimensional model, power, soluble boron, and transient fission product feedbacks were included. Concentrating on the pressurized water reactor (PWR), the thermal-hydraulic calculation of moderator density assumed single-phase flow and a closed flow channel, allowing parallelism to be introduced in the solution across the radial plane. Using a pinwise detail, quarter-core model of a typical PWR in cycle 1, for the two-dimensional model without feedback the measured million floating point operations per second (MFLOPS)/vector speedups were 83/11.7. 18/2.2, and 2.4/5.6 on the Cray, IBM, and FPS without multitasking, respectively. Lower performance was observed with a coarser mesh, i.e., shorter vector length, due to vector pipeline start-up. For an 18 x 18 x 30 (x-y-z) three-dimensional model with feedback of the same core, MFLOPS/vector speedups of --61/6.7 and an execution time of 0.8 CPU seconds on the Cray without multitasking were measured. Finally, using two CPUs and the vector pipelines of the Cray, a multitasking efficiency of 81% was noted for the three-dimensional model.« less

An analysis for high Reynolds number inviscid/viscid interactions in cascades

NASA Technical Reports Server (NTRS)

Barnett, Mark; Verdon, Joseph M.; Ayer, Timothy C.

1993-01-01

An efficient steady analysis for predicting strong inviscid/viscid interaction phenomena such as viscous-layer separation, shock/boundary-layer interaction, and trailing-edge/near-wake interaction in turbomachinery blade passages is needed as part of a comprehensive analytical blade design prediction system. Such an analysis is described. It uses an inviscid/viscid interaction approach, in which the flow in the outer inviscid region is assumed to be potential, and that in the inner or viscous-layer region is governed by Prandtl's equations. The inviscid solution is determined using an implicit, least-squares, finite-difference approximation, the viscous-layer solution using an inverse, finite-difference, space-marching method which is applied along the blade surfaces and wake streamlines. The inviscid and viscid solutions are coupled using a semi-inverse global iteration procedure, which permits the prediction of boundary-layer separation and other strong-interaction phenomena. Results are presented for three cascades, with a range of inlet flow conditions considered for one of them, including conditions leading to large-scale flow separations. Comparisons with Navier-Stokes solutions and experimental data are also given.

Computational investigation of large-scale vortex interaction with flexible bodies

NASA Astrophysics Data System (ADS)

Connell, Benjamin; Yue, Dick K. P.

2003-11-01

The interaction of large-scale vortices with flexible bodies is examined with particular interest paid to the energy and momentum budgets of the system. Finite difference direct numerical simulation of the Navier-Stokes equations on a moving curvilinear grid is coupled with a finite difference structural solver of both a linear membrane under tension and linear Euler-Bernoulli beam. The hydrodynamics and structural dynamics are solved simultaneously using an iterative procedure with the external structural forcing calculated from the hydrodynamics at the surface and the flow-field velocity boundary condition given by the structural motion. We focus on an investigation into the canonical problem of a vortex-dipole impinging on a flexible membrane. It is discovered that the structural properties of the membrane direct the interaction in terms of the flow evolution and the energy budget. Pressure gradients associated with resonant membrane response are shown to sustain the oscillatory motion of the vortex pair. Understanding how the key mechanisms in vortex-body interactions are guided by the structural properties of the body is a prerequisite to exploiting these mechanisms.

Finite-difference model to simulate the areal flow of saltwater and fresh water separated by an interface

USGS Publications Warehouse

Mercer, James W.; Larson, S.P.; Faust, Charles R.

1980-01-01

Model documentation is presented for a two-dimensional (areal) model capable of simulating ground-water flow of salt water and fresh water separated by an interface. The partial differential equations are integrated over the thicknesses of fresh water and salt water resulting in two equations describing the flow characteristics in the areal domain. These equations are approximated using finite-difference techniques and the resulting algebraic equations are solved for the dependent variables, fresh water head and salt water head. An iterative solution method was found to be most appropriate. The program is designed to simulate time-dependent problems such as those associated with the development of coastal aquifers, and can treat water-table conditions or confined conditions with steady-state leakage of fresh water. The program will generally be most applicable to the analysis of regional aquifer problems in which the zone between salt water and fresh water can be considered a surface (sharp interface). Example problems and a listing of the computer code are included. (USGS).

An adaptive moving finite volume scheme for modeling flood inundation over dry and complex topography

NASA Astrophysics Data System (ADS)

Zhou, Feng; Chen, Guoxian; Huang, Yuefei; Yang, Jerry Zhijian; Feng, Hui

2013-04-01

A new geometrical conservative interpolation on unstructured meshes is developed for preserving still water equilibrium and positivity of water depth at each iteration of mesh movement, leading to an adaptive moving finite volume (AMFV) scheme for modeling flood inundation over dry and complex topography. Unlike traditional schemes involving position-fixed meshes, the iteration process of the AFMV scheme moves a fewer number of the meshes adaptively in response to flow variables calculated in prior solutions and then simulates their posterior values on the new meshes. At each time step of the simulation, the AMFV scheme consists of three parts: an adaptive mesh movement to shift the vertices position, a geometrical conservative interpolation to remap the flow variables by summing the total mass over old meshes to avoid the generation of spurious waves, and a partial differential equations(PDEs) discretization to update the flow variables for a new time step. Five different test cases are presented to verify the computational advantages of the proposed scheme over nonadaptive methods. The results reveal three attractive features: (i) the AMFV scheme could preserve still water equilibrium and positivity of water depth within both mesh movement and PDE discretization steps; (ii) it improved the shock-capturing capability for handling topographic source terms and wet-dry interfaces by moving triangular meshes to approximate the spatial distribution of time-variant flood processes; (iii) it was able to solve the shallow water equations with a relatively higher accuracy and spatial-resolution with a lower computational cost.

A new ghost-node method for linking different models and initial investigations of heterogeneity and nonmatching grids

USGS Publications Warehouse

Dickinson, J.E.; James, S.C.; Mehl, S.; Hill, M.C.; Leake, S.A.; Zyvoloski, G.A.; Faunt, C.C.; Eddebbarh, A.-A.

2007-01-01

A flexible, robust method for linking parent (regional-scale) and child (local-scale) grids of locally refined models that use different numerical methods is developed based on a new, iterative ghost-node method. Tests are presented for two-dimensional and three-dimensional pumped systems that are homogeneous or that have simple heterogeneity. The parent and child grids are simulated using the block-centered finite-difference MODFLOW and control-volume finite-element FEHM models, respectively. The models are solved iteratively through head-dependent (child model) and specified-flow (parent model) boundary conditions. Boundary conditions for models with nonmatching grids or zones of different hydraulic conductivity are derived and tested against heads and flows from analytical or globally-refined models. Results indicate that for homogeneous two- and three-dimensional models with matched grids (integer number of child cells per parent cell), the new method is nearly as accurate as the coupling of two MODFLOW models using the shared-node method and, surprisingly, errors are slightly lower for nonmatching grids (noninteger number of child cells per parent cell). For heterogeneous three-dimensional systems, this paper compares two methods for each of the two sets of boundary conditions: external heads at head-dependent boundary conditions for the child model are calculated using bilinear interpolation or a Darcy-weighted interpolation; specified-flow boundary conditions for the parent model are calculated using model-grid or hydrogeologic-unit hydraulic conductivities. Results suggest that significantly more accurate heads and flows are produced when both Darcy-weighted interpolation and hydrogeologic-unit hydraulic conductivities are used, while the other methods produce larger errors at the boundary between the regional and local models. The tests suggest that, if posed correctly, the ghost-node method performs well. Additional testing is needed for highly heterogeneous systems. ?? 2007 Elsevier Ltd. All rights reserved.

Establishing the biomechanical properties of the pelvic soft tissues through an inverse finite element analysis using magnetic resonance imaging.

PubMed

Silva, M E T; Brandão, S; Parente, M P L; Mascarenhas, T; Natal Jorge, R M

2016-04-01

The mechanical characteristics of the female pelvic floor are relevant when explaining pelvic dysfunction. The decreased elasticity of the tissue often causes inability to maintain urethral position, also leading to vaginal and rectal descend when coughing or defecating as a response to an increase in the internal abdominal pressure. These conditions can be associated with changes in the mechanical properties of the supportive structures-namely, the pelvic floor muscles-including impairment. In this work, we used an inverse finite element analysis to calculate the material constants for the passive mechanical behavior of the pelvic floor muscles. The numerical model of the pelvic floor muscles and bones was built from magnetic resonance axial images acquired at rest. Muscle deformation, simulating the Valsalva maneuver with a pressure of 4 KPa, was compared with the muscle displacement obtained through additional dynamic magnetic resonance imaging. The difference in displacement was of 0.15 mm in the antero-posterior direction and 3.69 mm in the supero-inferior direction, equating to a percentage error of 7.0% and 16.9%, respectively. We obtained the shortest difference in the displacements using an iterative process that reached the material constants for the Mooney-Rivlin constitutive model (c10=11.8 KPa and c20=5.53 E-02 KPa). For each iteration, the orthogonal distance between each node from the group of nodes which defined the puborectal muscle in the numerical model versus dynamic magnetic resonance imaging was computed. With the methodology used in this work, it was possible to obtain in vivo biomechanical properties of the pelvic floor muscles for a specific subject using input information acquired non-invasively. © IMechE 2016.

On the primary variable switching technique for simulating unsaturated-saturated flows

NASA Astrophysics Data System (ADS)

Diersch, H.-J. G.; Perrochet, P.

Primary variable switching appears as a promising numerical technique for variably saturated flows. While the standard pressure-based form of the Richards equation can suffer from poor mass balance accuracy, the mixed form with its improved conservative properties can possess convergence difficulties for dry initial conditions. On the other hand, variable switching can overcome most of the stated numerical problems. The paper deals with variable switching for finite elements in two and three dimensions. The technique is incorporated in both an adaptive error-controlled predictor-corrector one-step Newton (PCOSN) iteration strategy and a target-based full Newton (TBFN) iteration scheme. Both schemes provide different behaviors with respect to accuracy and solution effort. Additionally, a simplified upstream weighting technique is used. Compared with conventional approaches the primary variable switching technique represents a fast and robust strategy for unsaturated problems with dry initial conditions. The impact of the primary variable switching technique is studied over a wide range of mostly 2D and partly difficult-to-solve problems (infiltration, drainage, perched water table, capillary barrier), where comparable results are available. It is shown that the TBFN iteration is an effective but error-prone procedure. TBFN sacrifices temporal accuracy in favor of accelerated convergence if aggressive time step sizes are chosen.

Material Assessment for ITER's Collective Thomson Scattering first mirror

DOE Office of Scientific and Technical Information (OSTI.GOV)

Santos, R.; Policarpo, H.; Goncalves, B.

2015-07-01

The International Thermonuclear Energy Reactor (ITER) Collective Thomson Scattering (CTS) system is a diagnostic instrument that measures plasma density and velocity through Thomson scattering of microwave radiation. Some of the key components of the CTS are quasi-optical mirrors that are used to produce astigmatic beam patterns, which have impact on the strength and spatial resolution of the diagnostic signal. The mirrors are exposed to neutron radiation, which may alter the quality of the signal received. In this work, three different materials (molybdenum (Mo), stainless steel 316 (SS-316) and tungsten (W)) are considered for the first mirror of the CTS. Themore » objective is to access which of the material studied are best suited for this mirror, considering different neutron radiation loads simulated scenarios defined by ITER, based on the resultant stresses and temperature distributions. For it, the neutron irradiation, and subsequent heat-load on the mirrors are simulated using the Monte Carlo N-Particle (MCNP) code. Based on the MCNP heat-load results, transient thermal-structural Finite Element Analysis (FEA) of the mirror over a 400 s discharge, with and without cooling on the rear side, are conducted using in commercial FEA software ANSYS. Results show that of the tested materials Mo and W are the most suitable material for this application. Even though, this study does not yet consider the variation of the material properties with temperature, it presents a quick initial satisfactory assessment that may be considered in subsequent and more complex analysis. (authors)« less

On multilevel RBF collocation to solve nonlinear PDEs arising from endogenous stochastic volatility models

NASA Astrophysics Data System (ADS)

Bastani, Ali Foroush; Dastgerdi, Maryam Vahid; Mighani, Abolfazl

2018-06-01

The main aim of this paper is the analytical and numerical study of a time-dependent second-order nonlinear partial differential equation (PDE) arising from the endogenous stochastic volatility model, introduced in [Bensoussan, A., Crouhy, M. and Galai, D., Stochastic equity volatility related to the leverage effect (I): equity volatility behavior. Applied Mathematical Finance, 1, 63-85, 1994]. As the first step, we derive a consistent set of initial and boundary conditions to complement the PDE, when the firm is financed by equity and debt. In the sequel, we propose a Newton-based iteration scheme for nonlinear parabolic PDEs which is an extension of a method for solving elliptic partial differential equations introduced in [Fasshauer, G. E., Newton iteration with multiquadrics for the solution of nonlinear PDEs. Computers and Mathematics with Applications, 43, 423-438, 2002]. The scheme is based on multilevel collocation using radial basis functions (RBFs) to solve the resulting locally linearized elliptic PDEs obtained at each level of the Newton iteration. We show the effectiveness of the resulting framework by solving a prototypical example from the field and compare the results with those obtained from three different techniques: (1) a finite difference discretization; (2) a naive RBF collocation and (3) a benchmark approximation, introduced for the first time in this paper. The numerical results confirm the robustness, higher convergence rate and good stability properties of the proposed scheme compared to other alternatives. We also comment on some possible research directions in this field.

Semi-discrete Galerkin solution of the compressible boundary-layer equations with viscous-inviscid interaction

NASA Technical Reports Server (NTRS)

Day, Brad A.; Meade, Andrew J., Jr.

1993-01-01

A semi-discrete Galerkin (SDG) method is under development to model attached, turbulent, and compressible boundary layers for transonic airfoil analysis problems. For the boundary-layer formulation the method models the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby providing high resolution near the wall and permitting the use of a uniform finite element grid which automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past RAE 2822 and NACA 0012 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack.

Finite element methods for the biomechanics of soft hydrated tissues: nonlinear analysis and adaptive control of meshes.

PubMed

Spilker, R L; de Almeida, E S; Donzelli, P S

1992-01-01

This chapter addresses computationally demanding numerical formulations in the biomechanics of soft tissues. The theory of mixtures can be used to represent soft hydrated tissues in the human musculoskeletal system as a two-phase continuum consisting of an incompressible solid phase (collagen and proteoglycan) and an incompressible fluid phase (interstitial water). We first consider the finite deformation of soft hydrated tissues in which the solid phase is represented as hyperelastic. A finite element formulation of the governing nonlinear biphasic equations is presented based on a mixed-penalty approach and derived using the weighted residual method. Fluid and solid phase deformation, velocity, and pressure are interpolated within each element, and the pressure variables within each element are eliminated at the element level. A system of nonlinear, first-order differential equations in the fluid and solid phase deformation and velocity is obtained. In order to solve these equations, the contributions of the hyperelastic solid phase are incrementally linearized, a finite difference rule is introduced for temporal discretization, and an iterative scheme is adopted to achieve equilibrium at the end of each time increment. We demonstrate the accuracy and adequacy of the procedure using a six-node, isoparametric axisymmetric element, and we present an example problem for which independent numerical solution is available. Next, we present an automated, adaptive environment for the simulation of soft tissue continua in which the finite element analysis is coupled with automatic mesh generation, error indicators, and projection methods. Mesh generation and updating, including both refinement and coarsening, for the two-dimensional examples examined in this study are performed using the finite quadtree approach. The adaptive analysis is based on an error indicator which is the L2 norm of the difference between the finite element solution and a projected finite element solution. Total stress, calculated as the sum of the solid and fluid phase stresses, is used in the error indicator. To allow the finite difference algorithm to proceed in time using an updated mesh, solution values must be transferred to the new nodal locations. This rezoning is accomplished using a projected field for the primary variables. The accuracy and effectiveness of this adaptive finite element analysis is demonstrated using a linear, two-dimensional, axisymmetric problem corresponding to the indentation of a thin sheet of soft tissue. The method is shown to effectively capture the steep gradients and to produce solutions in good agreement with independent, converged, numerical solutions.

A triangular thin shell finite element: Nonlinear analysis. [structural analysis

NASA Technical Reports Server (NTRS)

Thomas, G. R.; Gallagher, R. H.

1975-01-01

Aspects of the formulation of a triangular thin shell finite element which pertain to geometrically nonlinear (small strain, finite displacement) behavior are described. The procedure for solution of the resulting nonlinear algebraic equations combines a one-step incremental (tangent stiffness) approach with one iteration in the Newton-Raphson mode. A method is presented which permits a rational estimation of step size in this procedure. Limit points are calculated by means of a superposition scheme coupled to the incremental side of the solution procedure while bifurcation points are calculated through a process of interpolation of the determinants of the tangent-stiffness matrix. Numerical results are obtained for a flat plate and two curved shell problems and are compared with alternative solutions.

New Multigrid Method Including Elimination Algolithm Based on High-Order Vector Finite Elements in Three Dimensional Magnetostatic Field Analysis

NASA Astrophysics Data System (ADS)

Hano, Mitsuo; Hotta, Masashi

A new multigrid method based on high-order vector finite elements is proposed in this paper. Low level discretizations in this method are obtained by using low-order vector finite elements for the same mesh. Gauss-Seidel method is used as a smoother, and a linear equation of lowest level is solved by ICCG method. But it is often found that multigrid solutions do not converge into ICCG solutions. An elimination algolithm of constant term using a null space of the coefficient matrix is also described. In three dimensional magnetostatic field analysis, convergence time and number of iteration of this multigrid method are discussed with the convectional ICCG method.

Simulation of Aluminum Micro-mirrors for Space Applications at Cryogenic Temperatures

NASA Technical Reports Server (NTRS)

Kuhn, J. L.; Dutta, S. B.; Greenhouse, M. A.; Mott, D. B.

2000-01-01

Closed form and finite element models are developed to predict the device response of aluminum electrostatic torsion micro-mirrors fabricated on silicon substrate for space applications at operating temperatures of 30K. Initially, closed form expressions for electrostatic pressure arid mechanical restoring torque are used to predict the pull-in and release voltages at room temperature. Subsequently, a detailed mechanical finite element model is developed to predict stresses and vertical beam deflection induced by the electrostatic and thermal loads. An incremental and iterative solution method is used in conjunction with the nonlinear finite element model and closed form electrostatic equations to solve. the coupled electro-thermo-mechanical problem. The simulation results are compared with experimental measurements at room temperature of fabricated micro-mirror devices.

Hybrid preconditioning for iterative diagonalization of ill-conditioned generalized eigenvalue problems in electronic structure calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cai, Yunfeng, E-mail: yfcai@math.pku.edu.cn; Department of Computer Science, University of California, Davis 95616; Bai, Zhaojun, E-mail: bai@cs.ucdavis.edu

2013-12-15

The iterative diagonalization of a sequence of large ill-conditioned generalized eigenvalue problems is a computational bottleneck in quantum mechanical methods employing a nonorthogonal basis for ab initio electronic structure calculations. We propose a hybrid preconditioning scheme to effectively combine global and locally accelerated preconditioners for rapid iterative diagonalization of such eigenvalue problems. In partition-of-unity finite-element (PUFE) pseudopotential density-functional calculations, employing a nonorthogonal basis, we show that the hybrid preconditioned block steepest descent method is a cost-effective eigensolver, outperforming current state-of-the-art global preconditioning schemes, and comparably efficient for the ill-conditioned generalized eigenvalue problems produced by PUFE as the locally optimal blockmore » preconditioned conjugate-gradient method for the well-conditioned standard eigenvalue problems produced by planewave methods.« less

User's Guide for ENSAERO_FE Parallel Finite Element Solver

NASA Technical Reports Server (NTRS)

Eldred, Lloyd B.; Guruswamy, Guru P.

1999-01-01

A high fidelity parallel static structural analysis capability is created and interfaced to the multidisciplinary analysis package ENSAERO-MPI of Ames Research Center. This new module replaces ENSAERO's lower fidelity simple finite element and modal modules. Full aircraft structures may be more accurately modeled using the new finite element capability. Parallel computation is performed by breaking the full structure into multiple substructures. This approach is conceptually similar to ENSAERO's multizonal fluid analysis capability. The new substructure code is used to solve the structural finite element equations for each substructure in parallel. NASTRANKOSMIC is utilized as a front end for this code. Its full library of elements can be used to create an accurate and realistic aircraft model. It is used to create the stiffness matrices for each substructure. The new parallel code then uses an iterative preconditioned conjugate gradient method to solve the global structural equations for the substructure boundary nodes.

3D Tensorial Elastodynamics for Isotropic Media on Vertically Deformed Meshes

NASA Astrophysics Data System (ADS)

Shragge, J. C.

2017-12-01

Solutions of the 3D elastodynamic wave equation are sometimes required in industrial and academic applications of elastic reverse-time migration (E-RTM) and full waveform inversion (E-FWI) that involve vertically deformed meshes. Examples include incorporating irregular free-surface topography and handling internal boundaries (e.g., water bottom) directly into the computational meshes. In 3D E-RTM and E-FWI applications, the number of forward modeling simulations can number in the tens of thousands (per iteration), which necessitates the development of stable, accurate and efficient 3D elastodynamics solvers. For topographic scenarios, most finite-difference solution approaches use a change-of-variable strategy that has a number of associated computational challenges, including difficulties in handling of the free-surface boundary condition. In this study, I follow a tensorial approach and use a generalized family of analytic transforms to develop a set of analytic equations for 3D elastodynamics that directly incorporates vertical grid deformations. Importantly, this analytic approach allows for the specification of an analytic free-surface boundary condition appropriate for vertically deformed meshes. These equations are both straightforward and efficient to solve using a velocity-stress formulation with finite-difference (MFD) operators implemented on a fully staggered grid. Moreover, I demonstrate that the use of mimetic finite difference (MFD) methods allows stable, accurate, and efficient numerical solutions to be simulated for typical topographic scenarios. Examples demonstrate that high-quality elastic wavefields can be generated for topographic surfaces exhibiting significant topographic relief.

The semi-discrete Galerkin finite element modelling of compressible viscous flow past an airfoil

NASA Technical Reports Server (NTRS)

Meade, Andrew J., Jr.

1992-01-01

A method is developed to solve the two-dimensional, steady, compressible, turbulent boundary-layer equations and is coupled to an existing Euler solver for attached transonic airfoil analysis problems. The boundary-layer formulation utilizes the semi-discrete Galerkin (SDG) method to model the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby permitting the use of a uniform finite element grid which provides high resolution near the wall and automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes, through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past NACA 0012 and RAE 2822 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack. All results show good agreement with experiment, and the coupled code proved to be a computationally-efficient and accurate airfoil analysis tool.

Least-squares finite element solution of 3D incompressible Navier-Stokes problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Lin, Tsung-Liang; Povinelli, Louis A.

1992-01-01

Although significant progress has been made in the finite element solution of incompressible viscous flow problems. Development of more efficient methods is still needed before large-scale computation of 3D problems becomes feasible. This paper presents such a development. The most popular finite element method for the solution of incompressible Navier-Stokes equations is the classic Galerkin mixed method based on the velocity-pressure formulation. The mixed method requires the use of different elements to interpolate the velocity and the pressure in order to satisfy the Ladyzhenskaya-Babuska-Brezzi (LBB) condition for the existence of the solution. On the other hand, due to the lack of symmetry and positive definiteness of the linear equations arising from the mixed method, iterative methods for the solution of linear systems have been hard to come by. Therefore, direct Gaussian elimination has been considered the only viable method for solving the systems. But, for three-dimensional problems, the computer resources required by a direct method become prohibitively large. In order to overcome these difficulties, a least-squares finite element method (LSFEM) has been developed. This method is based on the first-order velocity-pressure-vorticity formulation. In this paper the LSFEM is extended for the solution of three-dimensional incompressible Navier-Stokes equations written in the following first-order quasi-linear velocity-pressure-vorticity formulation.

Numerical simulation of two-dimensional heat transfer in composite bodies with application to de-icing of aircraft components. Ph.D. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Chao, D. F. K.

1983-01-01

Transient, numerical simulations of the de-icing of composite aircraft components by electrothermal heating were performed for a two dimensional rectangular geometry. The implicit Crank-Nicolson formulation was used to insure stability of the finite-difference heat conduction equations and the phase change in the ice layer was simulated using the Enthalpy method. The Gauss-Seidel point iterative method was used to solve the system of difference equations. Numerical solutions illustrating de-icer performance for various composite aircraft structures and environmental conditions are presented. Comparisons are made with previous studies. The simulation can also be used to solve a variety of other heat conduction problems involving composite bodies.

Analysis of one dimension migration law from rainfall runoff on urban roof

NASA Astrophysics Data System (ADS)

Weiwei, Chen

2017-08-01

Research was taken on the hydrology and water quality process in the natural rain condition and water samples were collected and analyzed. The pollutant were included SS, COD and TN. Based on the mass balance principle, one dimension migration model was built for the rainfall runoff pollution in surface. The difference equation was developed according to the finite difference method, by applying the Newton iteration method for solving it. The simulated pollutant concentration process was in consistent with the measured value on model, and Nash-Sutcliffe coefficient was higher than 0.80. The model had better practicability, which provided evidence for effectively utilizing urban rainfall resource, non-point source pollution of making management technologies and measures, sponge city construction, and so on.

A modified dodge algorithm for the parabolized Navier-Stokes equations and compressible duct flows

NASA Technical Reports Server (NTRS)

Cooke, C. H.

1981-01-01

A revised version of a split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three-dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard successive overrelaxation iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition.

Numerical solutions of 2-D multi-stage rotor/stator unsteady flow interactions

NASA Astrophysics Data System (ADS)

Yang, R.-J.; Lin, S.-J.

1991-01-01

The Rai method of single-stage rotor/stator flow interaction is extended to handle multistage configurations. In this study, a two-dimensional Navier-Stokes multi-zone approach was used to investigate unsteady flow interactions within two multistage axial turbines. The governing equations are solved by an iterative, factored, implicit finite-difference, upwind algorithm. Numerical accuracy is checked by investigating the effect of time step size, the effect of subiteration in the Newton-Raphson technique, and the effect of full viscous versus thin-layer approximation. Computer results compared well with experimental data. Unsteady flow interactions, wake cutting, and the associated evolution of vortical entities are discussed.

Improved Boundary Conditions for Cell-centered Difference Schemes

NASA Technical Reports Server (NTRS)

VanderWijngaart, Rob F.; Klopfer, Goetz H.; Chancellor, Marisa K. (Technical Monitor)

1997-01-01

Cell-centered finite-volume (CCFV) schemes have certain attractive properties for the solution of the equations governing compressible fluid flow. Among others, they provide a natural vehicle for specifying flux conditions at the boundaries of the physical domain. Unfortunately, they lead to slow convergence for numerical programs utilizing them. In this report a method for investigating and improving the convergence of CCFV schemes is presented, which focuses on the effect of the numerical boundary conditions. The key to the method is the computation of the spectral radius of the iteration matrix of the entire demoralized system of equations, not just of the interior point scheme or the boundary conditions.

Single realization stochastic FDTD for weak scattering waves in biological random media.

PubMed

Tan, Tengmeng; Taflove, Allen; Backman, Vadim

2013-02-01

This paper introduces an iterative scheme to overcome the unresolved issues presented in S-FDTD (stochastic finite-difference time-domain) for obtaining ensemble average field values recently reported by Smith and Furse in an attempt to replace the brute force multiple-realization also known as Monte-Carlo approach with a single-realization scheme. Our formulation is particularly useful for studying light interactions with biological cells and tissues having sub-wavelength scale features. Numerical results demonstrate that such a small scale variation can be effectively modeled with a random medium problem which when simulated with the proposed S-FDTD indeed produces a very accurate result.

Single realization stochastic FDTD for weak scattering waves in biological random media

PubMed Central

Tan, Tengmeng; Taflove, Allen; Backman, Vadim

2015-01-01

This paper introduces an iterative scheme to overcome the unresolved issues presented in S-FDTD (stochastic finite-difference time-domain) for obtaining ensemble average field values recently reported by Smith and Furse in an attempt to replace the brute force multiple-realization also known as Monte-Carlo approach with a single-realization scheme. Our formulation is particularly useful for studying light interactions with biological cells and tissues having sub-wavelength scale features. Numerical results demonstrate that such a small scale variation can be effectively modeled with a random medium problem which when simulated with the proposed S-FDTD indeed produces a very accurate result. PMID:27158153

External Boundary Conditions for Three-Dimensional Problems of Computational Aerodynamics

NASA Technical Reports Server (NTRS)

Tsynkov, Semyon V.

1997-01-01

We consider an unbounded steady-state flow of viscous fluid over a three-dimensional finite body or configuration of bodies. For the purpose of solving this flow problem numerically, we discretize the governing equations (Navier-Stokes) on a finite-difference grid. The grid obviously cannot stretch from the body up to infinity, because the number of the discrete variables in that case would not be finite. Therefore, prior to the discretization we truncate the original unbounded flow domain by introducing some artificial computational boundary at a finite distance of the body. Typically, the artificial boundary is introduced in a natural way as the external boundary of the domain covered by the grid. The flow problem formulated only on the finite computational domain rather than on the original infinite domain is clearly subdefinite unless some artificial boundary conditions (ABC's) are specified at the external computational boundary. Similarly, the discretized flow problem is subdefinite (i.e., lacks equations with respect to unknowns) unless a special closing procedure is implemented at this artificial boundary. The closing procedure in the discrete case is called the ABC's as well. In this paper, we present an innovative approach to constructing highly accurate ABC's for three-dimensional flow computations. The approach extends our previous technique developed for the two-dimensional case; it employs the finite-difference counterparts to Calderon's pseudodifferential boundary projections calculated in the framework of the difference potentials method (DPM) by Ryaben'kii. The resulting ABC's appear spatially nonlocal but particularly easy to implement along with the existing solvers. The new boundary conditions have been successfully combined with the NASA-developed production code TLNS3D and used for the analysis of wing-shaped configurations in subsonic (including incompressible limit) and transonic flow regimes. As demonstrated by the computational experiments and comparisons with the standard (local) methods, the DPM-based ABC's allow one to greatly reduce the size of the computational domain while still maintaining high accuracy of the numerical solution. Moreover, they may provide for a noticeable increase of the convergence rate of multigrid iterations.

Coupled Modeling of Hydrodynamics and Sound in Coastal Ocean for Renewable Ocean Energy Development

DOE Office of Scientific and Technical Information (OSTI.GOV)

Long, Wen; Jung, Ki Won; Yang, Zhaoqing

An underwater sound model was developed to simulate sound propagation from marine and hydrokinetic energy (MHK) devices or offshore wind (OSW) energy platforms. Finite difference methods were developed to solve the 3D Helmholtz equation for sound propagation in the coastal environment. A 3D sparse matrix solver with complex coefficients was formed for solving the resulting acoustic pressure field. The Complex Shifted Laplacian Preconditioner (CSLP) method was applied to solve the matrix system iteratively with MPI parallelization using a high performance cluster. The sound model was then coupled with the Finite Volume Community Ocean Model (FVCOM) for simulating sound propagation generatedmore » by human activities, such as construction of OSW turbines or tidal stream turbine operations, in a range-dependent setting. As a proof of concept, initial validation of the solver is presented for two coastal wedge problems. This sound model can be useful for evaluating impacts on marine mammals due to deployment of MHK devices and OSW energy platforms.« less

A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations

NASA Astrophysics Data System (ADS)

Li, Meng; Gu, Xian-Ming; Huang, Chengming; Fei, Mingfa; Zhang, Guoyu

2018-04-01

In this paper, a fast linearized conservative finite element method is studied for solving the strongly coupled nonlinear fractional Schrödinger equations. We prove that the scheme preserves both the mass and energy, which are defined by virtue of some recursion relationships. Using the Sobolev inequalities and then employing the mathematical induction, the discrete scheme is proved to be unconditionally convergent in the sense of L2-norm and H α / 2-norm, which means that there are no any constraints on the grid ratios. Then, the prior bound of the discrete solution in L2-norm and L∞-norm are also obtained. Moreover, we propose an iterative algorithm, by which the coefficient matrix is independent of the time level, and thus it leads to Toeplitz-like linear systems that can be efficiently solved by Krylov subspace solvers with circulant preconditioners. This method can reduce the memory requirement of the proposed linearized finite element scheme from O (M2) to O (M) and the computational complexity from O (M3) to O (Mlog ⁡ M) in each iterative step, where M is the number of grid nodes. Finally, numerical results are carried out to verify the correction of the theoretical analysis, simulate the collision of two solitary waves, and show the utility of the fast numerical solution techniques.

Non-perturbative modelling of energetic particle effects on resistive wall mode: Anisotropy and finite orbit width

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Yueqiang, E-mail: yueqiang.liu@ccfe.ac.uk; Chapman, I. T.; Graves, J. P.

2014-05-15

A non-perturbative magnetohydrodynamic-kinetic hybrid formulation is developed and implemented into the MARS-K code [Liu et al., Phys. Plasmas 15, 112503 (2008)] that takes into account the anisotropy and asymmetry [Graves et al., Nature Commun. 3, 624 (2012)] of the equilibrium distribution of energetic particles (EPs) in particle pitch angle space, as well as first order finite orbit width (FOW) corrections for both passing and trapped EPs. Anisotropic models, which affect both the adiabatic and non-adiabatic drift kinetic energy contributions, are implemented for both neutral beam injection and ion cyclotron resonant heating induced EPs. The first order FOW correction does notmore » contribute to the precessional drift resonance of trapped particles, but generally remains finite for the bounce and transit resonance contributions, as well as for the adiabatic contributions from asymmetrically distributed passing particles. Numerical results for a 9MA steady state ITER plasma suggest that (i) both the anisotropy and FOW effects can be important for the resistive wall mode stability in ITER plasmas; and (ii) the non-perturbative approach predicts less kinetic stabilization of the mode, than the perturbative approach, in the presence of anisotropy and FOW effects for the EPs. The latter may partially be related to the modification of the eigenfunction of the mode by the drift kinetic effects.« less

Stochastic Galerkin methods for the steady-state Navier–Stokes equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sousedík, Bedřich, E-mail: sousedik@umbc.edu; Elman, Howard C., E-mail: elman@cs.umd.edu

2016-07-01

We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmarkmore » problems.« less

Thermal analysis of the in-vessel components of the ITER plasma-position reflectometry.

PubMed

Quental, P B; Policarpo, H; Luís, R; Varela, P

2016-11-01

The ITER plasma position reflectometry system measures the edge electron density profile of the plasma, providing real-time supplementary contribution to the magnetic measurements of the plasma-wall distance. Some of the system components will be in direct sight of the plasma and therefore subject to plasma and stray radiation, which may cause excessive temperatures and stresses. In this work, thermal finite element analysis of the antenna and adjacent waveguides is conducted with ANSYS V17 (ANSYS® Academic Research, Release 17.0, 2016). Results allow the identification of critical temperature points, and solutions are proposed to improve the thermal behavior of the system.

Thermal analysis of the in-vessel components of the ITER plasma-position reflectometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Quental, P. B., E-mail: pquental@ipfn.tecnico.ulisboa.pt; Policarpo, H.; Luís, R.

The ITER plasma position reflectometry system measures the edge electron density profile of the plasma, providing real-time supplementary contribution to the magnetic measurements of the plasma-wall distance. Some of the system components will be in direct sight of the plasma and therefore subject to plasma and stray radiation, which may cause excessive temperatures and stresses. In this work, thermal finite element analysis of the antenna and adjacent waveguides is conducted with ANSYS V17 (ANSYS® Academic Research, Release 17.0, 2016). Results allow the identification of critical temperature points, and solutions are proposed to improve the thermal behavior of the system.

Stochastic Galerkin methods for the steady-state Navier–Stokes equations

DOE PAGES

Sousedík, Bedřich; Elman, Howard C.

2016-04-12

We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmarkmore » problems.« less

Finite elements for the calculation of turbulent flows in three-dimensional complex geometries

NASA Astrophysics Data System (ADS)

Ruprecht, A.

A finite element program for the calculation of incompressible turbulent flows is presented. In order to reduce the required storage an iterative algorithm is used which solves the necessary equations sequentially. The state of turbulence is defined by the k-epsilon model. In addition to the standard k-epsilon model, the modification of Bardina et al., taking into account the rotation of the mean flow, is investigated. With this program, the flow in the draft tube of a Kaplan turbine is examined. Calculations are carried out for swirling and nonswirling entrance flow. The results are compared with measurements.

A finite element formulation for scattering from electrically large 2-dimensional structures

NASA Technical Reports Server (NTRS)

Ross, Daniel C.; Volakis, John L.

1992-01-01

A finite element formulation is given using the scattered field approach with a fictitious material absorber to truncate the mesh. The formulation includes the use of arbitrary approximation functions so that more accurate results can be achieved without any modification to the software. Additionally, non-polynomial approximation functions can be used, including complex approximation functions. The banded system that results is solved with an efficient sparse/banded iterative scheme and as a consequence, large structures can be analyzed. Results are given for simple cases to verify the formulation and also for large, complex geometries.

New discretization and solution techniques for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

Gunzburger, M. D.; Nicolaides, R. A.; Liu, C. H.

1983-01-01

This paper considers several topics arising in the finite element solution of the incompressible Navier-Stokes equations. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. Following this, the role of artificial viscosity in viscous flow calculations is studied, emphasizing recent work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some recent modifications are mentioned.

Marine Controlled-Source Electromagnetic 2D Inversion for synthetic models.

NASA Astrophysics Data System (ADS)

Liu, Y.; Li, Y.

2016-12-01

We present a 2D inverse algorithm for frequency domain marine controlled-source electromagnetic (CSEM) data, which is based on the regularized Gauss-Newton approach. As a forward solver, our parallel adaptive finite element forward modeling program is employed. It is a self-adaptive, goal-oriented grid refinement algorithm in which a finite element analysis is performed on a sequence of refined meshes. The mesh refinement process is guided by a dual error estimate weighting to bias refinement towards elements that affect the solution at the EM receiver locations. With the use of the direct solver (MUMPS), we can effectively compute the electromagnetic fields for multi-sources and parametric sensitivities. We also implement the parallel data domain decomposition approach of Key and Ovall (2011), with the goal of being able to compute accurate responses in parallel for complicated models and a full suite of data parameters typical of offshore CSEM surveys. All minimizations are carried out by using the Gauss-Newton algorithm and model perturbations at each iteration step are obtained by using the Inexact Conjugate Gradient iteration method. Synthetic test inversions are presented.

Parallel Finite Element Domain Decomposition for Structural/Acoustic Analysis

NASA Technical Reports Server (NTRS)

Nguyen, Duc T.; Tungkahotara, Siroj; Watson, Willie R.; Rajan, Subramaniam D.

2005-01-01

A domain decomposition (DD) formulation for solving sparse linear systems of equations resulting from finite element analysis is presented. The formulation incorporates mixed direct and iterative equation solving strategics and other novel algorithmic ideas that are optimized to take advantage of sparsity and exploit modern computer architecture, such as memory and parallel computing. The most time consuming part of the formulation is identified and the critical roles of direct sparse and iterative solvers within the framework of the formulation are discussed. Experiments on several computer platforms using several complex test matrices are conducted using software based on the formulation. Small-scale structural examples are used to validate thc steps in the formulation and large-scale (l,000,000+ unknowns) duct acoustic examples are used to evaluate the ORIGIN 2000 processors, and a duster of 6 PCs (running under the Windows environment). Statistics show that the formulation is efficient in both sequential and parallel computing environmental and that the formulation is significantly faster and consumes less memory than that based on one of the best available commercialized parallel sparse solvers.

Finite volume multigrid method of the planar contraction flow of a viscoelastic fluid

NASA Astrophysics Data System (ADS)

Moatssime, H. Al; Esselaoui, D.; Hakim, A.; Raghay, S.

2001-08-01

This paper reports on a numerical algorithm for the steady flow of viscoelastic fluid. The conservative and constitutive equations are solved using the finite volume method (FVM) with a hybrid scheme for the velocities and first-order upwind approximation for the viscoelastic stress. A non-uniform staggered grid system is used. The iterative SIMPLE algorithm is employed to relax the coupled momentum and continuity equations. The non-linear algebraic equations over the flow domain are solved iteratively by the symmetrical coupled Gauss-Seidel (SCGS) method. In both, the full approximation storage (FAS) multigrid algorithm is used. An Oldroyd-B fluid model was selected for the calculation. Results are reported for planar 4:1 abrupt contraction at various Weissenberg numbers. The solutions are found to be stable and smooth. The solutions show that at high Weissenberg number the domain must be long enough. The convergence of the method has been verified with grid refinement. All the calculations have been performed on a PC equipped with a Pentium III processor at 550 MHz. Copyright

Algebraic multigrid preconditioning within parallel finite-element solvers for 3-D electromagnetic modelling problems in geophysics

NASA Astrophysics Data System (ADS)

Koldan, Jelena; Puzyrev, Vladimir; de la Puente, Josep; Houzeaux, Guillaume; Cela, José María

2014-06-01

We present an elaborate preconditioning scheme for Krylov subspace methods which has been developed to improve the performance and reduce the execution time of parallel node-based finite-element (FE) solvers for 3-D electromagnetic (EM) numerical modelling in exploration geophysics. This new preconditioner is based on algebraic multigrid (AMG) that uses different basic relaxation methods, such as Jacobi, symmetric successive over-relaxation (SSOR) and Gauss-Seidel, as smoothers and the wave front algorithm to create groups, which are used for a coarse-level generation. We have implemented and tested this new preconditioner within our parallel nodal FE solver for 3-D forward problems in EM induction geophysics. We have performed series of experiments for several models with different conductivity structures and characteristics to test the performance of our AMG preconditioning technique when combined with biconjugate gradient stabilized method. The results have shown that, the more challenging the problem is in terms of conductivity contrasts, ratio between the sizes of grid elements and/or frequency, the more benefit is obtained by using this preconditioner. Compared to other preconditioning schemes, such as diagonal, SSOR and truncated approximate inverse, the AMG preconditioner greatly improves the convergence of the iterative solver for all tested models. Also, when it comes to cases in which other preconditioners succeed to converge to a desired precision, AMG is able to considerably reduce the total execution time of the forward-problem code-up to an order of magnitude. Furthermore, the tests have confirmed that our AMG scheme ensures grid-independent rate of convergence, as well as improvement in convergence regardless of how big local mesh refinements are. In addition, AMG is designed to be a black-box preconditioner, which makes it easy to use and combine with different iterative methods. Finally, it has proved to be very practical and efficient in the parallel context.

A singular finite element technique for calculating continuum damping of Alfvén eigenmodes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bowden, G. W.; Hole, M. J.

2015-02-15

Damping due to continuum resonances can be calculated using dissipation-less ideal magnetohydrodynamics provided that the poles due to these resonances are properly treated. We describe a singular finite element technique for calculating the continuum damping of Alfvén waves. A Frobenius expansion is used to determine appropriate finite element basis functions on an inner region surrounding a pole due to the continuum resonance. The location of the pole due to the continuum resonance and mode frequency is calculated iteratively using a Galerkin method. This method is used to find the complex frequency and mode structure of a toroidicity-induced Alfvén eigenmode inmore » a large aspect ratio circular tokamak and is shown to agree closely with a complex contour technique.« less

Design and Stress Analysis of Low-Noise Adjusted Bearing Contact Spiral Bevel Gears

NASA Technical Reports Server (NTRS)

Fuentes, A.; Litvin, F. L.; Mullins, B. R.; Woods, R.; Handschuh, R. F.; Lewicki, David G.

2002-01-01

An integrated computerized approach for design and stress analysis of low-noise spiral bevel gear drives with adjusted bearing contact is proposed. The procedure of computations is an iterative process that requires four separate procedures and provide: (a) a parabolic function of transmission errors that is able to reduce the effect of errors of alignment on noise and vibration, and (b) reduction of the shift of bearing contact caused by misalignment. Application of finite element analysis enables us to determine the contact and bending stresses and investigate the formation of the bearing contact. The design of finite element models and boundary conditions is automated and does not require intermediate CAD computer programs for application of general purpose computer program for finite element analysis.

Finite element-integral simulation of static and flight fan noise radiation from the JT15D turbofan engine

NASA Technical Reports Server (NTRS)

Baumeister, K. J.; Horowitz, S. J.

1982-01-01

An iterative finite element integral technique is used to predict the sound field radiated from the JT15D turbofan inlet. The sound field is divided into two regions: the sound field within and near the inlet which is computed using the finite element method and the radiation field beyond the inlet which is calculated using an integral solution technique. The velocity potential formulation of the acoustic wave equation was employed in the program. For some single mode JT15D data, the theory and experiment are in good agreement for the far field radiation pattern as well as suppressor attenuation. Also, the computer program is used to simulate flight effects that cannot be performed on a ground static test stand.

Dynamical mean field theory equations on nearly real frequency axis

NASA Astrophysics Data System (ADS)

Fathi, M. B.; Jafari, S. A.

2010-03-01

The iterated perturbation theory (IPT) equations of the dynamical mean field theory (DMFT) for the half-filled Hubbard model are solved on nearly real frequencies at various values of the Hubbard parameters, U, to investigate the nature of metal-insulator transition (MIT) at finite temperatures. This method avoids the instabilities associated with the infamous Padé analytic continuation and reveals fine structures across the MIT at finite temperatures, which cannot be captured by conventional methods for solving DMFT-IPT equations on Matsubara frequencies. Our method suggests that at finite temperatures, there is a crossover from a bad metal to a bad insulator in which the height of the quasi-particle (Kondo) peak decreases to a non-zero small bump, which gradually suppresses as one moves deeper into the bad insulating regime.

Numerical modeling of the radiative transfer in a turbid medium using the synthetic iteration.

PubMed

Budak, Vladimir P; Kaloshin, Gennady A; Shagalov, Oleg V; Zheltov, Victor S

2015-07-27

In this paper we propose the fast, but the accurate algorithm for numerical modeling of light fields in the turbid media slab. For the numerical solution of the radiative transfer equation (RTE) it is required its discretization based on the elimination of the solution anisotropic part and the replacement of the scattering integral by a finite sum. The solution regular part is determined numerically. A good choice of the method of the solution anisotropic part elimination determines the high convergence of the algorithm in the mean square metric. The method of synthetic iterations can be used to improve the convergence in the uniform metric. A significant increase in the solution accuracy with the use of synthetic iterations allows applying the two-stream approximation for the regular part determination. This approach permits to generalize the proposed method in the case of an arbitrary 3D geometry of the medium.

Parallel iterative solution for h and p approximations of the shallow water equations

USGS Publications Warehouse

Barragy, E.J.; Walters, R.A.

1998-01-01

A p finite element scheme and parallel iterative solver are introduced for a modified form of the shallow water equations. The governing equations are the three-dimensional shallow water equations. After a harmonic decomposition in time and rearrangement, the resulting equations are a complex Helmholz problem for surface elevation, and a complex momentum equation for the horizontal velocity. Both equations are nonlinear and the resulting system is solved using the Picard iteration combined with a preconditioned biconjugate gradient (PBCG) method for the linearized subproblems. A subdomain-based parallel preconditioner is developed which uses incomplete LU factorization with thresholding (ILUT) methods within subdomains, overlapping ILUT factorizations for subdomain boundaries and under-relaxed iteration for the resulting block system. The method builds on techniques successfully applied to linear elements by introducing ordering and condensation techniques to handle uniform p refinement. The combined methods show good performance for a range of p (element order), h (element size), and N (number of processors). Performance and scalability results are presented for a field scale problem where up to 512 processors are used. ?? 1998 Elsevier Science Ltd. All rights reserved.

Finite element solution of nonlinear eddy current problems with periodic excitation and its industrial applications☆

PubMed Central

Bíró, Oszkár; Koczka, Gergely; Preis, Kurt

2014-01-01

An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer. PMID:24829517

Finite element solution of nonlinear eddy current problems with periodic excitation and its industrial applications.

PubMed

Bíró, Oszkár; Koczka, Gergely; Preis, Kurt

2014-05-01

An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer.

Integrated modelling of steady-state scenarios and heating and current drive mixes for ITER

DOE Office of Scientific and Technical Information (OSTI.GOV)

Murakami, Masanori; Park, Jin Myung; Giruzzi, G.

2011-01-01

Recent progress on ITER steady-state (SS) scenario modelling by the ITPA-IOS group is reviewed. Code-to-code benchmarks as the IOS group's common activities for the two SS scenarios (weak shear scenario and internal transport barrier scenario) are discussed in terms of transport, kinetic profiles, and heating and current drive (CD) sources using various transport codes. Weak magnetic shear scenarios integrate the plasma core and edge by combining a theory-based transport model (GLF23) with scaled experimental boundary profiles. The edge profiles (at normalized radius rho = 0.8-1.0) are adopted from an edge-localized mode-averaged analysis of a DIII-D ITER demonstration discharge. A fullymore » noninductive SS scenario is achieved with fusion gain Q = 4.3, noninductive fraction f(NI) = 100%, bootstrap current fraction f(BS) = 63% and normalized beta beta(N) = 2.7 at plasma current I(p) = 8MA and toroidal field B(T) = 5.3 T using ITER day-1 heating and CD capability. Substantial uncertainties come from outside the radius of setting the boundary conditions (rho = 0.8). The present simulation assumed that beta(N)(rho) at the top of the pedestal (rho = 0.91) is about 25% above the peeling-ballooning threshold. ITER will have a challenge to achieve the boundary, considering different operating conditions (T(e)/T(i) approximate to 1 and density peaking). Overall, the experimentally scaled edge is an optimistic side of the prediction. A number of SS scenarios with different heating and CD mixes in a wide range of conditions were explored by exploiting the weak-shear steady-state solution procedure with the GLF23 transport model and the scaled experimental edge. The results are also presented in the operation space for DT neutron power versus stationary burn pulse duration with assumed poloidal flux availability at the beginning of stationary burn, indicating that the long pulse operation goal (3000s) at I(p) = 9 MA is possible. Source calculations in these simulations have been revised for electron cyclotron current drive including parallel momentum conservation effects and for neutral beam current drive with finite orbit and magnetic pitch effects.« less

Optimized System Identification

NASA Technical Reports Server (NTRS)

Juang, Jer-Nan; Longman, Richard W.

1999-01-01

In system identification, one usually cares most about finding a model whose outputs are as close as possible to the true system outputs when the same input is applied to both. However, most system identification algorithms do not minimize this output error. Often they minimize model equation error instead, as in typical least-squares fits using a finite-difference model, and it is seen here that this distinction is significant. Here, we develop a set of system identification algorithms that minimize output error for multi-input/multi-output and multi-input/single-output systems. This is done with sequential quadratic programming iterations on the nonlinear least-squares problems, with an eigendecomposition to handle indefinite second partials. This optimization minimizes a nonlinear function of many variables, and hence can converge to local minima. To handle this problem, we start the iterations from the OKID (Observer/Kalman Identification) algorithm result. Not only has OKID proved very effective in practice, it minimizes an output error of an observer which has the property that as the data set gets large, it converges to minimizing the criterion of interest here. Hence, it is a particularly good starting point for the nonlinear iterations here. Examples show that the methods developed here eliminate the bias that is often observed using any system identification methods of either over-estimating or under-estimating the damping of vibration modes in lightly damped structures.

Calculating massive 3-loop graphs for operator matrix elements by the method of hyperlogarithms

NASA Astrophysics Data System (ADS)

Ablinger, Jakob; Blümlein, Johannes; Raab, Clemens; Schneider, Carsten; Wißbrock, Fabian

2014-08-01

We calculate convergent 3-loop Feynman diagrams containing a single massive loop equipped with twist τ=2 local operator insertions corresponding to spin N. They contribute to the massive operator matrix elements in QCD describing the massive Wilson coefficients for deep-inelastic scattering at large virtualities. Diagrams of this kind can be computed using an extended version of the method of hyperlogarithms, originally being designed for massless Feynman diagrams without operators. The method is applied to Benz- and V-type graphs, belonging to the genuine 3-loop topologies. In case of the V-type graphs with five massive propagators, new types of nested sums and iterated integrals emerge. The sums are given in terms of finite binomially and inverse binomially weighted generalized cyclotomic sums, while the 1-dimensionally iterated integrals are based on a set of ∼30 square-root valued letters. We also derive the asymptotic representations of the nested sums and present the solution for N∈C. Integrals with a power-like divergence in N-space ∝aN,a∈R,a>1, for large values of N emerge. They still possess a representation in x-space, which is given in terms of root-valued iterated integrals in the present case. The method of hyperlogarithms is also used to calculate higher moments for crossed box graphs with different operator insertions.

Efficient numerical method for analyzing optical bistability in photonic crystal microcavities.

PubMed

Yuan, Lijun; Lu, Ya Yan

2013-05-20

Nonlinear optical effects can be enhanced by photonic crystal microcavities and be used to develop practical ultra-compact optical devices with low power requirements. The finite-difference time-domain method is the standard numerical method for simulating nonlinear optical devices, but it has limitations in terms of accuracy and efficiency. In this paper, a rigorous and efficient frequency-domain numerical method is developed for analyzing nonlinear optical devices where the nonlinear effect is concentrated in the microcavities. The method replaces the linear problem outside the microcavities by a rigorous and numerically computed boundary condition, then solves the nonlinear problem iteratively in a small region around the microcavities. Convergence of the iterative method is much easier to achieve since the size of the problem is significantly reduced. The method is presented for a specific two-dimensional photonic crystal waveguide-cavity system with a Kerr nonlinearity, using numerical methods that can take advantage of the geometric features of the structure. The method is able to calculate multiple solutions exhibiting the optical bistability phenomenon in the strongly nonlinear regime.

Energy deposition and thermal effects of runaway electrons in ITER-FEAT plasma facing components

NASA Astrophysics Data System (ADS)

Maddaluno, G.; Maruccia, G.; Merola, M.; Rollet, S.

2003-03-01

The profile of energy deposited by runaway electrons (RAEs) of 10 or 50 MeV in International Thermonuclear Experimental Reactor-Fusion Energy Advanced Tokamak (ITER-FEAT) plasma facing components (PFCs) and the subsequent temperature pattern have been calculated by using the Monte Carlo code FLUKA and the finite element heat conduction code ANSYS. The RAE energy deposition density was assumed to be 50 MJ/m 2 and both 10 and 100 ms deposition times were considered. Five different configurations of PFCs were investigated: primary first wall armoured with Be, with and without protecting CFC poloidal limiters, both port limiter first wall options (Be flat tile and CFC monoblock), divertor baffle first wall, armoured with W. The analysis has outlined that for all the configurations but one (port limiter with Be flat tile) the heat sink and the cooling tube beneath the armour are well protected for both RAE energies and for both energy deposition times. On the other hand large melting (W, Be) or sublimation (C) of the surface layer occurs, eventually affecting the PFCs lifetime.

An installed nacelle design code using a multiblock Euler solver. Volume 1: Theory document

NASA Technical Reports Server (NTRS)

Chen, H. C.

1992-01-01

An efficient multiblock Euler design code was developed for designing a nacelle installed on geometrically complex airplane configurations. This approach employed a design driver based on a direct iterative surface curvature method developed at LaRC. A general multiblock Euler flow solver was used for computing flow around complex geometries. The flow solver used a finite-volume formulation with explicit time-stepping to solve the Euler Equations. It used a multiblock version of the multigrid method to accelerate the convergence of the calculations. The design driver successively updated the surface geometry to reduce the difference between the computed and target pressure distributions. In the flow solver, the change in surface geometry was simulated by applying surface transpiration boundary conditions to avoid repeated grid generation during design iterations. Smoothness of the designed surface was ensured by alternate application of streamwise and circumferential smoothings. The capability and efficiency of the code was demonstrated through the design of both an isolated nacelle and an installed nacelle at various flow conditions. Information on the execution of the computer program is provided in volume 2.

Extended Kalman filtering for the detection of damage in linear mechanical structures

NASA Astrophysics Data System (ADS)

Liu, X.; Escamilla-Ambrosio, P. J.; Lieven, N. A. J.

2009-09-01

This paper addresses the problem of assessing the location and extent of damage in a vibrating structure by means of vibration measurements. Frequency domain identification methods (e.g. finite element model updating) have been widely used in this area while time domain methods such as the extended Kalman filter (EKF) method, are more sparsely represented. The difficulty of applying EKF in mechanical system damage identification and localisation lies in: the high computational cost, the dependence of estimation results on the initial estimation error covariance matrix P(0), the initial value of parameters to be estimated, and on the statistics of measurement noise R and process noise Q. To resolve these problems in the EKF, a multiple model adaptive estimator consisting of a bank of EKF in modal domain was designed, each filter in the bank is based on different P(0). The algorithm was iterated by using the weighted global iteration method. A fuzzy logic model was incorporated in each filter to estimate the variance of the measurement noise R. The application of the method is illustrated by simulated and real examples.

A new look at the robust control of discrete-time Markov jump linear systems

NASA Astrophysics Data System (ADS)

Todorov, M. G.; Fragoso, M. D.

2016-03-01

In this paper, we make a foray in the role played by a set of four operators on the study of robust H2 and mixed H2/H∞ control problems for discrete-time Markov jump linear systems. These operators appear in the study of mean square stability for this class of systems. By means of new linear matrix inequality (LMI) characterisations of controllers, which include slack variables that, to some extent, separate the robustness and performance objectives, we introduce four alternative approaches to the design of controllers which are robustly stabilising and at the same time provide a guaranteed level of H2 performance. Since each operator provides a different degree of conservatism, the results are unified in the form of an iterative LMI technique for designing robust H2 controllers, whose convergence is attained in a finite number of steps. The method yields a new way of computing mixed H2/H∞ controllers, whose conservatism decreases with iteration. Two numerical examples illustrate the applicability of the proposed results for the control of a small unmanned aerial vehicle, and for an underactuated robotic arm.

Theoretical and numerical evaluation of polarimeter using counter-circularly-polarized-probing-laser under the coupling between Faraday and Cotton-Mouton effect.

PubMed

Imazawa, Ryota; Kawano, Yasunori; Itami, Kiyoshi

2016-04-01

This study evaluated an effect of an coupling between the Faraday and Cotton-Mouton effect to a measurement signal of the Dodel-Kunz method which uses counter-circular-polarized probing-laser for measuring the Faraday effect. When the coupling is small (the Faraday effect is dominant and the characteristic eigenmodes are approximately circularly polarized), the measurement signal can be algebraically expressed and it is shown that the finite effect of the coupling is still significant. When the Faraday effect is not dominant, a numerical calculation is necessary. The numerical calculation under an ITER-like condition (Bt = 5.3 T, Ip = 15 MA, a = 2 m, ne = 10(20) m(-3) and λ = 119 μm) showed that difference between the pure Faraday rotation and the measurement signal of the Dodel-Kunz method was an order of one degree, which exceeds allowable error of ITER poloidal polarimeter. In conclusion, similar to other polarimeter techniques, the Dodel-Kunz method is not free from the coupling between the Faraday and Cotton-Mouton effect.

A comparative study of an ABC and an artificial absorber for truncating finite element meshes

NASA Technical Reports Server (NTRS)

Oezdemir, T.; Volakis, John L.

1993-01-01

The type of mesh termination used in the context of finite element formulations plays a major role on the efficiency and accuracy of the field solution. The performance of an absorbing boundary condition (ABC) and an artificial absorber (a new concept) for terminating the finite element mesh was evaluated. This analysis is done in connection with the problem of scattering by a finite slot array in a thick ground plane. The two approximate mesh truncation schemes are compared with the exact finite element-boundary integral (FEM-BI) method in terms of accuracy and efficiency. It is demonstrated that both approximate truncation schemes yield reasonably accurate results even when the mesh is extended only 0.3 wavelengths away from the array aperture. However, the artificial absorber termination method leads to a substantially more efficient solution. Moreover, it is shown that the FEM-BI method remains quite competitive with the FEM-artificial absorber method when the FFT is used for computing the matrix-vector products in the iterative solution algorithm. These conclusions are indeed surprising and of major importance in electromagnetic simulations based on the finite element method.

A hybrid numerical technique for predicting the aerodynamic and acoustic fields of advanced turboprops

NASA Technical Reports Server (NTRS)

Homicz, G. F.; Moselle, J. R.

1985-01-01

A hybrid numerical procedure is presented for the prediction of the aerodynamic and acoustic performance of advanced turboprops. A hybrid scheme is proposed which in principle leads to a consistent simultaneous prediction of both fields. In the inner flow a finite difference method, the Approximate-Factorization Alternating-Direction-Implicit (ADI) scheme, is used to solve the nonlinear Euler equations. In the outer flow the linearized acoustic equations are solved via a Boundary-Integral Equation (BIE) method. The two solutions are iteratively matched across a fictitious interface in the flow so as to maintain continuity. At convergence the resulting aerodynamic load prediction will automatically satisfy the appropriate free-field boundary conditions at the edge of the finite difference grid, while the acoustic predictions will reflect the back-reaction of the radiated field on the magnitude of the loading source terms, as well as refractive effects in the inner flow. The equations and logic needed to match the two solutions are developed and the computer program implementing the procedure is described. Unfortunately, no converged solutions were obtained, due to unexpectedly large running times. The reasons for this are discussed and several means to alleviate the situation are suggested.

Reprint of Solution of Ambrosio-Tortorelli model for image segmentation by generalized relaxation method

NASA Astrophysics Data System (ADS)

D'Ambra, Pasqua; Tartaglione, Gaetano

2015-04-01

Image segmentation addresses the problem to partition a given image into its constituent objects and then to identify the boundaries of the objects. This problem can be formulated in terms of a variational model aimed to find optimal approximations of a bounded function by piecewise-smooth functions, minimizing a given functional. The corresponding Euler-Lagrange equations are a set of two coupled elliptic partial differential equations with varying coefficients. Numerical solution of the above system often relies on alternating minimization techniques involving descent methods coupled with explicit or semi-implicit finite-difference discretization schemes, which are slowly convergent and poorly scalable with respect to image size. In this work we focus on generalized relaxation methods also coupled with multigrid linear solvers, when a finite-difference discretization is applied to the Euler-Lagrange equations of Ambrosio-Tortorelli model. We show that non-linear Gauss-Seidel, accelerated by inner linear iterations, is an effective method for large-scale image analysis as those arising from high-throughput screening platforms for stem cells targeted differentiation, where one of the main goal is segmentation of thousand of images to analyze cell colonies morphology.

Solution of Ambrosio-Tortorelli model for image segmentation by generalized relaxation method

NASA Astrophysics Data System (ADS)

D'Ambra, Pasqua; Tartaglione, Gaetano

2015-03-01

Image segmentation addresses the problem to partition a given image into its constituent objects and then to identify the boundaries of the objects. This problem can be formulated in terms of a variational model aimed to find optimal approximations of a bounded function by piecewise-smooth functions, minimizing a given functional. The corresponding Euler-Lagrange equations are a set of two coupled elliptic partial differential equations with varying coefficients. Numerical solution of the above system often relies on alternating minimization techniques involving descent methods coupled with explicit or semi-implicit finite-difference discretization schemes, which are slowly convergent and poorly scalable with respect to image size. In this work we focus on generalized relaxation methods also coupled with multigrid linear solvers, when a finite-difference discretization is applied to the Euler-Lagrange equations of Ambrosio-Tortorelli model. We show that non-linear Gauss-Seidel, accelerated by inner linear iterations, is an effective method for large-scale image analysis as those arising from high-throughput screening platforms for stem cells targeted differentiation, where one of the main goal is segmentation of thousand of images to analyze cell colonies morphology.

Computational modeling of chemo-electro-mechanical coupling: A novel implicit monolithic finite element approach

PubMed Central

Wong, J.; Göktepe, S.; Kuhl, E.

2014-01-01

Summary Computational modeling of the human heart allows us to predict how chemical, electrical, and mechanical fields interact throughout a cardiac cycle. Pharmacological treatment of cardiac disease has advanced significantly over the past decades, yet it remains unclear how the local biochemistry of an individual heart cell translates into global cardiac function. Here we propose a novel, unified strategy to simulate excitable biological systems across three biological scales. To discretize the governing chemical, electrical, and mechanical equations in space, we propose a monolithic finite element scheme. We apply a highly efficient and inherently modular global-local split, in which the deformation and the transmembrane potential are introduced globally as nodal degrees of freedom, while the chemical state variables are treated locally as internal variables. To ensure unconditional algorithmic stability, we apply an implicit backward Euler finite difference scheme to discretize the resulting system in time. To increase algorithmic robustness and guarantee optimal quadratic convergence, we suggest an incremental iterative Newton-Raphson scheme. The proposed algorithm allows us to simulate the interaction of chemical, electrical, and mechanical fields during a representative cardiac cycle on a patient-specific geometry, robust and stable, with calculation times on the order of four days on a standard desktop computer. PMID:23798328

Thermodynamic Modelling of Phase Transformation in a Multi-Component System

NASA Astrophysics Data System (ADS)

Vala, J.

2007-09-01

Diffusion in multi-component alloys can be characterized by the vacancy mechanism for substitutional components, by the existence of sources and sinks for vacancies and by the motion of atoms of interstitial components. The description of diffusive and massive phase transformation of a multi-component system is based on the thermodynamic extremal principle by Onsager; the finite thickness of the interface between both phases is respected. The resulting system of partial differential equations of evolution with integral terms for unknown mole fractions (and additional variables in case of non-ideal sources and sinks for vacancies), can be analyzed using the method of lines and the finite difference technique (or, alternatively, the finite element one) together with the semi-analytic and numerical integration formulae and with certain iteration procedure, making use of the spectral properties of linear operators. The original software code for the numerical evaluation of solutions of such systems, written in MATLAB, offers a chance to simulate various real processes of diffusional phase transformation. Some results for the (nearly) steady-state real processes in substitutional alloys have been published yet. The aim of this paper is to demonstrate that the same approach can handle both substitutional and interstitial components even in case of a general system of evolution.

A mixed finite-element method for solving the poroelastic Biot equations with electrokinetic coupling

NASA Astrophysics Data System (ADS)

Pain, C. C.; Saunders, J. H.; Worthington, M. H.; Singer, J. M.; Stuart-Bruges, W.; Mason, G.; Goddard, A.

2005-02-01

In this paper, a numerical method for solving the Biot poroelastic equations is developed. These equations comprise acoustic (typically water) and elastic (porous medium frame) equations, which are coupled mainly through fluid/solid drag terms. This wave solution is coupled to a simplified form of Maxwell's equations, which is solved for the streaming potential resulting from electrokinesis. The ultimate aim is to use the generated electrical signals to provide porosity, permeability and other information about the formation surrounding a borehole. The electrical signals are generated through electrokinesis by seismic waves causing movement of the fluid through pores or fractures of a porous medium. The focus of this paper is the numerical solution of the Biot equations in displacement form, which is achieved using a mixed finite-element formulation with a different finite-element representation for displacements and stresses. The mixed formulation is used in order to reduce spurious displacement modes and fluid shear waves in the numerical solutions. These equations are solved in the time domain using an implicit unconditionally stable time-stepping method using iterative solution methods amenable to solving large systems of equations. The resulting model is embodied in the MODELLING OF ACOUSTICS, POROELASTICS AND ELECTROKINETICS (MAPEK) computer model for electroseismic analysis.

Validation of non-rigid point-set registration methods using a porcine bladder pelvic phantom

NASA Astrophysics Data System (ADS)

Zakariaee, Roja; Hamarneh, Ghassan; Brown, Colin J.; Spadinger, Ingrid

2016-01-01

The problem of accurate dose accumulation in fractionated radiotherapy treatment for highly deformable organs, such as bladder, has garnered increasing interest over the past few years. However, more research is required in order to find a robust and efficient solution and to increase the accuracy over the current methods. The purpose of this study was to evaluate the feasibility and accuracy of utilizing non-rigid (affine or deformable) point-set registration in accumulating dose in bladder of different sizes and shapes. A pelvic phantom was built to house an ex vivo porcine bladder with fiducial landmarks adhered onto its surface. Four different volume fillings of the bladder were used (90, 180, 360 and 480 cc). The performance of MATLAB implementations of five different methods were compared, in aligning the bladder contour point-sets. The approaches evaluated were coherent point drift (CPD), gaussian mixture model, shape context, thin-plate spline robust point matching (TPS-RPM) and finite iterative closest point (ICP-finite). The evaluation metrics included registration runtime, target registration error (TRE), root-mean-square error (RMS) and Hausdorff distance (HD). The reference (source) dataset was alternated through all four points-sets, in order to study the effect of reference volume on the registration outcomes. While all deformable algorithms provided reasonable registration results, CPD provided the best TRE values (6.4 mm), and TPS-RPM yielded the best mean RMS and HD values (1.4 and 6.8 mm, respectively). ICP-finite was the fastest technique and TPS-RPM, the slowest.

Comparative studies for two different orientations of pebble bed in an HCCB blanket

NASA Astrophysics Data System (ADS)

Paritosh, CHAUDHURI; Chandan, DANANI; E, RAJENDRAKUMAR

2017-12-01

The Indian Test Blanket Module (TBM) program in ITER is one of the major steps in its fusion reactor program towards DEMO and the future fusion power reactor vision. Research and development (R&D) is focused on two types of breeding blanket concepts: lead-lithium ceramic breeder (LLCB) and helium-cooled ceramic breeder (HCCB) blanket systems for the DEMO reactor. As part of the ITER-TBM program, the LLCB concept will be tested in one-half of ITER port no. 2, whose materials and technologies will be tested during ITER operation. The HCCB concept is a variant of the solid breeder blanket, which is presently part of our domestic R&D program for DEMO relevant technology development. In the HCCB concept Li2TiO3 and beryllium are used as the tritium breeder and neutron multiplier, respectively, in the form of a packed bed having edge-on configuration with reduced activation ferritic martensitic steel as the structural material. In this paper two design schemes, mainly two different orientations of pebble beds, are discussed. In the current concept (case-1), the ceramic breeder beds are kept horizontal in the toroidal-radial direction. Due to gravity, the pebbles may settle down at the bottom and create a finite gap between the pebbles and the top cooling plate, which will affect the heat transfer between them. In the alternate design concept (case-2), the pebble bed is vertically (poloidal-radial) orientated where the side plates act as cooling plates instead of top and bottom plates. These two design variants are analyzed analytically and 2D thermal-hydraulic simulation studies are carried out with ANSYS, using the heat loads obtained from neutronic calculations. Based on the analysis the performance is compared and details of the thermal and radiative heat transfer studies are also discussed in this paper.

ITER structural design criteria and their extension to advanced reactor blankets*1

NASA Astrophysics Data System (ADS)

Majumdar, S.; Kalinin, G.

2000-12-01

Applications of the recent ITER structural design criteria (ISDC) are illustrated by two components. First, the low-temperature-design rules are applied to copper alloys that are particularly prone to irradiation embrittlement at relatively low fluences at certain temperatures. Allowable stresses are derived and the impact of the embrittlement on allowable surface heat flux of a simple first-wall/limiter design is demonstrated. Next, the high-temperature-design rules of ISDC are applied to evaporation of lithium and vapor extraction (EVOLVE), a blanket design concept currently being investigated under the US Advanced Power Extraction (APEX) program. A single tungsten first-wall tube is considered for thermal and stress analyses by finite-element method.

Finite element method framework for RF-based through-the-wall mapping

NASA Astrophysics Data System (ADS)

Campos, Rafael Saraiva; Lovisolo, Lisandro; de Campos, Marcello Luiz R.

2017-05-01

Radiofrequency (RF) Through-the-Wall Mapping (TWM) employs techniques originally applied in X-Ray Computerized Tomographic Imaging to map obstacles behind walls. It aims to provide valuable information for rescuing efforts in damaged buildings, as well as for military operations in urban scenarios. This work defines a Finite Element Method (FEM) based framework to allow fast and accurate simulations of the reconstruction of floors blueprints, using Ultra High-Frequency (UHF) signals at three different frequencies (500 MHz, 1 GHz and 2 GHz). To the best of our knowledge, this is the first use of FEM in a TWM scenario. This framework allows quick evaluation of different algorithms without the need to assemble a full test setup, which might not be available due to budgetary and time constraints. Using this, the present work evaluates a collection of reconstruction methods (Filtered Backprojection Reconstruction, Direct Fourier Reconstruction, Algebraic Reconstruction and Simultaneous Iterative Reconstruction) under a parallel-beam acquisition geometry for different spatial sampling rates, number of projections, antenna gains and operational frequencies. The use of multiple frequencies assesses the trade-off between higher resolution at shorter wavelengths and lower through-the-wall penetration. Considering all the drawbacks associated with such a complex problem, a robust and reliable computational setup based on a flexible method such as FEM can be very useful.

Memory-optimized shift operator alternating direction implicit finite difference time domain method for plasma

NASA Astrophysics Data System (ADS)

Song, Wanjun; Zhang, Hou

2017-11-01

Through introducing the alternating direction implicit (ADI) technique and the memory-optimized algorithm to the shift operator (SO) finite difference time domain (FDTD) method, the memory-optimized SO-ADI FDTD for nonmagnetized collisional plasma is proposed and the corresponding formulae of the proposed method for programming are deduced. In order to further the computational efficiency, the iteration method rather than Gauss elimination method is employed to solve the equation set in the derivation of the formulae. Complicated transformations and convolutions are avoided in the proposed method compared with the Z transforms (ZT) ADI FDTD method and the piecewise linear JE recursive convolution (PLJERC) ADI FDTD method. The numerical dispersion of the SO-ADI FDTD method with different plasma frequencies and electron collision frequencies is analyzed and the appropriate ratio of grid size to the minimum wavelength is given. The accuracy of the proposed method is validated by the reflection coefficient test on a nonmagnetized collisional plasma sheet. The testing results show that the proposed method is advantageous for improving computational efficiency and saving computer memory. The reflection coefficient of a perfect electric conductor (PEC) sheet covered by multilayer plasma and the RCS of the objects coated by plasma are calculated by the proposed method and the simulation results are analyzed.

Elasto-plastic flow in cracked bodies using a new finite element model. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Karabin, M. E., Jr.

1977-01-01

Cracked geometries were studied by finite element techniques with the aid of a new special element embedded at the crack tip. This model seeked to accurately represent the singular stresses and strains associated with the elasto-plastic flow process. The present model was not restricted to a material type and did not predetermine a singularity. Rather the singularity was treated as an unknown. For each step of the incremental process the nodal degrees of freedom and the unknown singularity were found through minimization of an energy-like functional. The singularity and nodal degrees of freedom were determined by means of an iterative process.

Finite-size effects and switching times for Moran process with mutation.

PubMed

DeVille, Lee; Galiardi, Meghan

2017-04-01

We consider the Moran process with two populations competing under an iterated Prisoner's Dilemma in the presence of mutation, and concentrate on the case where there are multiple evolutionarily stable strategies. We perform a complete bifurcation analysis of the deterministic system which arises in the infinite population size. We also study the Master equation and obtain asymptotics for the invariant distribution and metastable switching times for the stochastic process in the case of large but finite population. We also show that the stochastic system has asymmetries in the form of a skew for parameter values where the deterministic limit is symmetric.

Application of the conjugate-gradient method to ground-water models

USGS Publications Warehouse

Manteuffel, T.A.; Grove, D.B.; Konikow, Leonard F.

1984-01-01

The conjugate-gradient method can solve efficiently and accurately finite-difference approximations to the ground-water flow equation. An aquifer-simulation model using the conjugate-gradient method was applied to a problem of ground-water flow in an alluvial aquifer at the Rocky Mountain Arsenal, Denver, Colorado. For this application, the accuracy and efficiency of the conjugate-gradient method compared favorably with other available methods for steady-state flow. However, its efficiency relative to other available methods depends on the nature of the specific problem. The main advantage of the conjugate-gradient method is that it does not require the use of iteration parameters, thereby eliminating this partly subjective procedure. (USGS)

A solution to the Navier-Stokes equations based upon the Newton Kantorovich method

NASA Technical Reports Server (NTRS)

Davis, J. E.; Gabrielsen, R. E.; Mehta, U. B.

1977-01-01

An implicit finite difference scheme based on the Newton-Kantorovich technique was developed for the numerical solution of the nonsteady, incompressible, two-dimensional Navier-Stokes equations in conservation-law form. The algorithm was second-order-time accurate, noniterative with regard to the nonlinear terms in the vorticity transport equation except at the earliest few time steps, and spatially factored. Numerical results were obtained with the technique for a circular cylinder at Reynolds number 15. Results indicate that the technique is in excellent agreement with other numerical techniques for all geometries and Reynolds numbers investigated, and indicates a potential for significant reduction in computation time over current iterative techniques.

A Relaxation Method for Nonlocal and Non-Hermitian Operators

NASA Astrophysics Data System (ADS)

Lagaris, I. E.; Papageorgiou, D. G.; Braun, M.; Sofianos, S. A.

1996-06-01

We present a grid method to solve the time dependent Schrödinger equation (TDSE). It uses the Crank-Nicholson scheme to propagate the wavefunction forward in time and finite differences to approximate the derivative operators. The resulting sparse linear system is solved by the symmetric successive overrelaxation iterative technique. The method handles local and nonlocal interactions and Hamiltonians that correspond to either Hermitian or to non-Hermitian matrices with real eigenvalues. We test the method by solving the TDSE in the imaginary time domain, thus converting the time propagation to asymptotic relaxation. Benchmark problems solved are both in one and two dimensions, with local, nonlocal, Hermitian and non-Hermitian Hamiltonians.

A Pseudo-Temporal Multi-Grid Relaxation Scheme for Solving the Parabolized Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

White, J. A.; Morrison, J. H.

1999-01-01

A multi-grid, flux-difference-split, finite-volume code, VULCAN, is presented for solving the elliptic and parabolized form of the equations governing three-dimensional, turbulent, calorically perfect and non-equilibrium chemically reacting flows. The space marching algorithms developed to improve convergence rate and or reduce computational cost are emphasized. The algorithms presented are extensions to the class of implicit pseudo-time iterative, upwind space-marching schemes. A full approximate storage, full multi-grid scheme is also described which is used to accelerate the convergence of a Gauss-Seidel relaxation method. The multi-grid algorithm is shown to significantly improve convergence on high aspect ratio grids.

Inverse boundary-layer theory and comparison with experiment

NASA Technical Reports Server (NTRS)

Carter, J. E.

1978-01-01

Inverse boundary layer computational procedures, which permit nonsingular solutions at separation and reattachment, are presented. In the first technique, which is for incompressible flow, the displacement thickness is prescribed; in the second technique, for compressible flow, a perturbation mass flow is the prescribed condition. The pressure is deduced implicitly along with the solution in each of these techniques. Laminar and turbulent computations, which are typical of separated flow, are presented and comparisons are made with experimental data. In both inverse procedures, finite difference techniques are used along with Newton iteration. The resulting procedure is no more complicated than conventional boundary layer computations. These separated boundary layer techniques appear to be well suited for complete viscous-inviscid interaction computations.

Scattering and Emission from Inhomogeneous Vegetation Canopy and Alien Target by Using Three-Dimensional Vector Radiative Transfer (3D-VRT) Equation

NASA Astrophysics Data System (ADS)

Jin, Ya-Qiu; Liang, Zichang

2005-01-01

To solve 3D-VRT equation for the model of spatially inhomogeneous scatter media, the finite enclosure of the scatter media is geometrically divided, in both the vertical z and horizontal (x,y) directions, to form very thin multi-boxes. The zero-th order emission, first-order Mueller matrix of each thin box and an iterative approach of high-order radiative transfer are applied to deriving high-order scattering and emission of whole inhomogeneous scatter media. Numerical results of polarized brightness temperature at microwave frequency and under different radiometer's resolutions from inhomogeneous scatter model such as vegetation canopy and embedded alien target are simulated and discussed.

Design and Stress Analysis of Low-Noise Adjusted Bearing Contact Spiral Bevel Gears

NASA Technical Reports Server (NTRS)

Litvin, Faydor L.; Fuentes, Alfonso; Mullins, Baxter R.; Woods, Ron

2002-01-01

An integrated computerized approach for design and stress analysis of low-noise spiral bevel gear drives with adjusted bearing contact has been developed. The computation procedure is an iterative process, requiring four separate steps that provide: (a) a parabolic function of transmission errors that is able to reduce the effect of errors of alignment, and (b) reduction of the shift of bearing contact caused by misalignment. Application of finite element analysis permits the contact and bending stresses to be determined and investigate the formation of the bearing contact. The design of finite element models and boundary conditions is automated and does not require an intermediate CAD computer program. A commercially available finite element analysis computer program with contact capability was used to conduct the stress analysis. The theory developed is illustrated with numerical examples.

TAP 2: A finite element program for thermal analysis of convectively cooled structures

NASA Technical Reports Server (NTRS)

Thornton, E. A.

1980-01-01

A finite element computer program (TAP 2) for steady-state and transient thermal analyses of convectively cooled structures is presented. The program has a finite element library of six elements: two conduction/convection elements to model heat transfer in a solid, two convection elements to model heat transfer in a fluid, and two integrated conduction/convection elements to represent combined heat transfer in tubular and plate/fin fluid passages. Nonlinear thermal analysis due to temperature-dependent thermal parameters is performed using the Newton-Raphson iteration method. Transient analyses are performed using an implicit Crank-Nicolson time integration scheme with consistent or lumped capacitance matrices as an option. Program output includes nodal temperatures and element heat fluxes. Pressure drops in fluid passages may be computed as an option. User instructions and sample problems are presented in appendixes.

MHOST: An efficient finite element program for inelastic analysis of solids and structures

NASA Technical Reports Server (NTRS)

Nakazawa, S.

1988-01-01

An efficient finite element program for 3-D inelastic analysis of gas turbine hot section components was constructed and validated. A novel mixed iterative solution strategy is derived from the augmented Hu-Washizu variational principle in order to nodally interpolate coordinates, displacements, deformation, strains, stresses and material properties. A series of increasingly sophisticated material models incorporated in MHOST include elasticity, secant plasticity, infinitesimal and finite deformation plasticity, creep and unified viscoplastic constitutive model proposed by Walker. A library of high performance elements is built into this computer program utilizing the concepts of selective reduced integrations and independent strain interpolations. A family of efficient solution algorithms is implemented in MHOST for linear and nonlinear equation solution including the classical Newton-Raphson, modified, quasi and secant Newton methods with optional line search and the conjugate gradient method.

Hierarchy of Certain Types of DNA Splicing Systems

NASA Astrophysics Data System (ADS)

Yusof, Yuhani; Sarmin, Nor Haniza; Goode, T. Elizabeth; Mahmud, Mazri; Heng, Fong Wan

A Head splicing system (H-system)consists of a finite set of strings (words) written over a finite alphabet, along with a finite set of rules that acts on the strings by iterated cutting and pasting to create a splicing language. Any interpretation that is aligned with Tom Head's original idea is one in which the strings represent double-stranded deoxyribonucleic acid (dsDNA) and the rules represent the cutting and pasting action of restriction enzymes and ligase, respectively. A new way of writing the rule sets is adopted so as to make the biological interpretation transparent. This approach is used in a formal language- theoretic analysis of the hierarchy of certain classes of splicing systems, namely simple, semi-simple and semi-null splicing systems. The relations between such systems and their associated languages are given as theorems, corollaries and counterexamples.

Multi-grid finite element method used for enhancing the reconstruction accuracy in Cerenkov luminescence tomography

NASA Astrophysics Data System (ADS)

Guo, Hongbo; He, Xiaowei; Liu, Muhan; Zhang, Zeyu; Hu, Zhenhua; Tian, Jie

2017-03-01

Cerenkov luminescence tomography (CLT), as a promising optical molecular imaging modality, can be applied to cancer diagnostic and therapeutic. Most researches about CLT reconstruction are based on the finite element method (FEM) framework. However, the quality of FEM mesh grid is still a vital factor to restrict the accuracy of the CLT reconstruction result. In this paper, we proposed a multi-grid finite element method framework, which was able to improve the accuracy of reconstruction. Meanwhile, the multilevel scheme adaptive algebraic reconstruction technique (MLS-AART) based on a modified iterative algorithm was applied to improve the reconstruction accuracy. In numerical simulation experiments, the feasibility of our proposed method were evaluated. Results showed that the multi-grid strategy could obtain 3D spatial information of Cerenkov source more accurately compared with the traditional single-grid FEM.

Optimization design combined with coupled structural-electrostatic analysis for the electrostatically controlled deployable membrane reflector

NASA Astrophysics Data System (ADS)

Liu, Chao; Yang, Guigeng; Zhang, Yiqun

2015-01-01

The electrostatically controlled deployable membrane reflector (ECDMR) is a promising scheme to construct large size and high precision space deployable reflector antennas. This paper presents a novel design method for the large size and small F/D ECDMR considering the coupled structure-electrostatic problem. First, the fully coupled structural-electrostatic system is described by a three field formulation, in which the structure and passive electrical field is modeled by finite element method, and the deformation of the electrostatic domain is predicted by a finite element formulation of a fictitious elastic structure. A residual formulation of the structural-electrostatic field finite element model is established and solved by Newton-Raphson method. The coupled structural-electrostatic analysis procedure is summarized. Then, with the aid of this coupled analysis procedure, an integrated optimization method of membrane shape accuracy and stress uniformity is proposed, which is divided into inner and outer iterative loops. The initial state of relatively high shape accuracy and uniform stress distribution is achieved by applying the uniform prestress on the membrane design shape and optimizing the voltages, in which the optimal voltage is computed by a sensitivity analysis. The shape accuracy is further improved by the iterative prestress modification using the reposition balance method. Finally, the results of the uncoupled and coupled methods are compared and the proposed optimization method is applied to design an ECDMR. The results validate the effectiveness of this proposed methods.

Analysis of the ITER central solenoid insert (CSI) coil stability tests

NASA Astrophysics Data System (ADS)

Savoldi, L.; Bonifetto, R.; Breschi, M.; Isono, T.; Martovetsky, N.; Ozeki, H.; Zanino, R.

2017-07-01

At the end of the test campaign of the ITER Central Solenoid Insert (CSI) coil in 2015, after 16,000 electromagnetic (EM) cycles, some tests were devoted to the study of the conductor stability, through the measurement of the Minimum Quench Energy (MQE). The tests were performed by means of an inductive heater (IH), located in the high-field region of the CSI and wrapped around the conductor. The calorimetric calibration of the IH is presented here, aimed at assessing the energy deposited in the conductor for different values of the IH electrical operating conditions. The MQE of the conductor of the ITER CS module 3L can be estimated as ∼200 J ± 20%, deposited on the whole conductor on a length of ∼10 cm (the IH length) in ∼40 ms, at current and magnetic field conditions relevant for the ITER CS operation. The repartition of the energy deposited in the conductor under the IH is computed to be ∼10% in the cable and 90% in the jacket by means of a 3D Finite Elements EM model. It is shown how this repartition implies that the bundle (cable + helium) heat capacity is fully available for stability on the time scale of the tested disturbances. This repartition is used in input to the thermal-hydraulic analysis performed with the 4C code, to assess the capability of the model to accurately reproduce the stability threshold of the conductor. The MQE computed by the code for this disturbance is in good agreement with the measured value, with an underestimation within 15% of the experimental value.

The Research of Multiple Attenuation Based on Feedback Iteration and Independent Component Analysis

NASA Astrophysics Data System (ADS)

Xu, X.; Tong, S.; Wang, L.

2017-12-01

How to solve the problem of multiple suppression is a difficult problem in seismic data processing. The traditional technology for multiple attenuation is based on the principle of the minimum output energy of the seismic signal, this criterion is based on the second order statistics, and it can't achieve the multiple attenuation when the primaries and multiples are non-orthogonal. In order to solve the above problems, we combine the feedback iteration method based on the wave equation and the improved independent component analysis (ICA) based on high order statistics to suppress the multiple waves. We first use iterative feedback method to predict the free surface multiples of each order. Then, in order to predict multiples from real multiple in amplitude and phase, we design an expanded pseudo multi-channel matching filtering method to get a more accurate matching multiple result. Finally, we present the improved fast ICA algorithm which is based on the maximum non-Gauss criterion of output signal to the matching multiples and get better separation results of the primaries and the multiples. The advantage of our method is that we don't need any priori information to the prediction of the multiples, and can have a better separation result. The method has been applied to several synthetic data generated by finite-difference model technique and the Sigsbee2B model multiple data, the primaries and multiples are non-orthogonal in these models. The experiments show that after three to four iterations, we can get the perfect multiple results. Using our matching method and Fast ICA adaptive multiple subtraction, we can not only effectively preserve the effective wave energy in seismic records, but also can effectively suppress the free surface multiples, especially the multiples related to the middle and deep areas.

Sound transmission through a poroelastic layered panel

NASA Astrophysics Data System (ADS)

Nagler, Loris; Rong, Ping; Schanz, Martin; von Estorff, Otto

2014-04-01

Multi-layered panels are often used to improve the acoustics in cars, airplanes, rooms, etc. For such an application these panels include porous and/or fibrous layers. The proposed numerical method is an approach to simulate the acoustical behavior of such multi-layered panels. The model assumes plate-like structures and, hence, combines plate theories for the different layers. The poroelastic layer is modelled with a recently developed plate theory. This theory uses a series expansion in thickness direction with subsequent analytical integration in this direction to reduce the three dimensions to two. The same idea is used to model either air gaps or fibrous layers. The latter are modeled as equivalent fluid and can be handled like an air gap, i.e., a kind of `air plate' is used. The coupling of the layers is done by using the series expansion to express the continuity conditions on the surfaces of the plates. The final system is solved with finite elements, where domain decomposition techniques in combination with preconditioned iterative solvers are applied to solve the final system of equations. In a large frequency range, the comparison with measurements shows very good agreement. From the numerical solution process it can be concluded that different preconditioners for the different layers are necessary. A reuse of the Krylov subspace of the iterative solvers pays if several excitations have to be computed but not that much in the loop over the frequencies.

An Embedded Statistical Method for Coupling Molecular Dynamics and Finite Element Analyses

NASA Technical Reports Server (NTRS)

Saether, E.; Glaessgen, E.H.; Yamakov, V.

2008-01-01

The coupling of molecular dynamics (MD) simulations with finite element methods (FEM) yields computationally efficient models that link fundamental material processes at the atomistic level with continuum field responses at higher length scales. The theoretical challenge involves developing a seamless connection along an interface between two inherently different simulation frameworks. Various specialized methods have been developed to solve particular classes of problems. Many of these methods link the kinematics of individual MD atoms with FEM nodes at their common interface, necessarily requiring that the finite element mesh be refined to atomic resolution. Some of these coupling approaches also require simulations to be carried out at 0 K and restrict modeling to two-dimensional material domains due to difficulties in simulating full three-dimensional material processes. In the present work, a new approach to MD-FEM coupling is developed based on a restatement of the standard boundary value problem used to define a coupled domain. The method replaces a direct linkage of individual MD atoms and finite element (FE) nodes with a statistical averaging of atomistic displacements in local atomic volumes associated with each FE node in an interface region. The FEM and MD computational systems are effectively independent and communicate only through an iterative update of their boundary conditions. With the use of statistical averages of the atomistic quantities to couple the two computational schemes, the developed approach is referred to as an embedded statistical coupling method (ESCM). ESCM provides an enhanced coupling methodology that is inherently applicable to three-dimensional domains, avoids discretization of the continuum model to atomic scale resolution, and permits finite temperature states to be applied.

A New Concurrent Multiscale Methodology for Coupling Molecular Dynamics and Finite Element Analyses

NASA Technical Reports Server (NTRS)

Yamakov, Vesselin; Saether, Erik; Glaessgen, Edward H/.

2008-01-01

The coupling of molecular dynamics (MD) simulations with finite element methods (FEM) yields computationally efficient models that link fundamental material processes at the atomistic level with continuum field responses at higher length scales. The theoretical challenge involves developing a seamless connection along an interface between two inherently different simulation frameworks. Various specialized methods have been developed to solve particular classes of problems. Many of these methods link the kinematics of individual MD atoms with FEM nodes at their common interface, necessarily requiring that the finite element mesh be refined to atomic resolution. Some of these coupling approaches also require simulations to be carried out at 0 K and restrict modeling to two-dimensional material domains due to difficulties in simulating full three-dimensional material processes. In the present work, a new approach to MD-FEM coupling is developed based on a restatement of the standard boundary value problem used to define a coupled domain. The method replaces a direct linkage of individual MD atoms and finite element (FE) nodes with a statistical averaging of atomistic displacements in local atomic volumes associated with each FE node in an interface region. The FEM and MD computational systems are effectively independent and communicate only through an iterative update of their boundary conditions. With the use of statistical averages of the atomistic quantities to couple the two computational schemes, the developed approach is referred to as an embedded statistical coupling method (ESCM). ESCM provides an enhanced coupling methodology that is inherently applicable to three-dimensional domains, avoids discretization of the continuum model to atomic scale resolution, and permits finite temperature states to be applied.

Advanced Software for Analysis of High-Speed Rolling-Element Bearings

NASA Technical Reports Server (NTRS)

Poplawski, J. V.; Rumbarger, J. H.; Peters, S. M.; Galatis, H.; Flower, R.

2003-01-01

COBRA-AHS is a package of advanced software for analysis of rigid or flexible shaft systems supported by rolling-element bearings operating at high speeds under complex mechanical and thermal loads. These loads can include centrifugal and thermal loads generated by motions of bearing components. COBRA-AHS offers several improvements over prior commercial bearing-analysis programs: It includes innovative probabilistic fatigue-life-estimating software that provides for computation of three-dimensional stress fields and incorporates stress-based (in contradistinction to prior load-based) mathematical models of fatigue life. It interacts automatically with the ANSYS finite-element code to generate finite-element models for estimating distributions of temperature and temperature-induced changes in dimensions in iterative thermal/dimensional analyses: thus, for example, it can be used to predict changes in clearances and thermal lockup. COBRA-AHS provides an improved graphical user interface that facilitates the iterative cycle of analysis and design by providing analysis results quickly in graphical form, enabling the user to control interactive runs without leaving the program environment, and facilitating transfer of plots and printed results for inclusion in design reports. Additional features include roller-edge stress prediction and influence of shaft and housing distortion on bearing performance.

An Iterative Decambering Approach for Post-Stall Prediction of Wing Characteristics using known Section Data

NASA Technical Reports Server (NTRS)

Mukherjee, Rinku; Gopalarathnam, Ashok; Kim, Sung Wan

2003-01-01

An iterative decambering approach for the post stall prediction of wings using known section data as inputs is presented. The method can currently be used for incompressible .ow and can be extended to compressible subsonic .ow using Mach number correction schemes. A detailed discussion of past work on this topic is presented first. Next, an overview of the decambering approach is presented and is illustrated by applying the approach to the prediction of the two-dimensional C(sub l) and C(sub m) curves for an airfoil. The implementation of the approach for iterative decambering of wing sections is then discussed. A novel feature of the current e.ort is the use of a multidimensional Newton iteration for taking into consideration the coupling between the di.erent sections of the wing. The approach lends itself to implementation in a variety of finite-wing analysis methods such as lifting-line theory, discrete-vortex Weissinger's method, and vortex lattice codes. Results are presented for a rectangular wing for a from 0 to 25 deg. The results are compared for both increasing and decreasing directions of a, and they show that a hysteresis loop can be predicted for post-stall angles of attack.

Iterative Nonlinear Tikhonov Algorithm with Constraints for Electromagnetic Tomography

NASA Technical Reports Server (NTRS)

Xu, Feng; Deshpande, Manohar

2012-01-01

Low frequency electromagnetic tomography such as the capacitance tomography (ECT) has been proposed for monitoring and mass-gauging of gas-liquid two-phase system under microgravity condition in NASA's future long-term space missions. Due to the ill-posed inverse problem of ECT, images reconstructed using conventional linear algorithms often suffer from limitations such as low resolution and blurred edges. Hence, new efficient high resolution nonlinear imaging algorithms are needed for accurate two-phase imaging. The proposed Iterative Nonlinear Tikhonov Regularized Algorithm with Constraints (INTAC) is based on an efficient finite element method (FEM) forward model of quasi-static electromagnetic problem. It iteratively minimizes the discrepancy between FEM simulated and actual measured capacitances by adjusting the reconstructed image using the Tikhonov regularized method. More importantly, it enforces the known permittivity of two phases to the unknown pixels which exceed the reasonable range of permittivity in each iteration. This strategy does not only stabilize the converging process, but also produces sharper images. Simulations show that resolution improvement of over 2 times can be achieved by INTAC with respect to conventional approaches. Strategies to further improve spatial imaging resolution are suggested, as well as techniques to accelerate nonlinear forward model and thus increase the temporal resolution.

Finite-temperature time-dependent variation with multiple Davydov states

NASA Astrophysics Data System (ADS)

Wang, Lu; Fujihashi, Yuta; Chen, Lipeng; Zhao, Yang

2017-03-01

The Dirac-Frenkel time-dependent variational approach with Davydov Ansätze is a sophisticated, yet efficient technique to obtain an accurate solution to many-body Schrödinger equations for energy and charge transfer dynamics in molecular aggregates and light-harvesting complexes. We extend this variational approach to finite temperature dynamics of the spin-boson model by adopting a Monte Carlo importance sampling method. In order to demonstrate the applicability of this approach, we compare calculated real-time quantum dynamics of the spin-boson model with that from numerically exact iterative quasiadiabatic propagator path integral (QUAPI) technique. The comparison shows that our variational approach with the single Davydov Ansätze is in excellent agreement with the QUAPI method at high temperatures, while the two differ at low temperatures. Accuracy in dynamics calculations employing a multitude of Davydov trial states is found to improve substantially over the single Davydov Ansatz, especially at low temperatures. At a moderate computational cost, our variational approach with the multiple Davydov Ansatz is shown to provide accurate spin-boson dynamics over a wide range of temperatures and bath spectral densities.

Three-dimensional electrical impedance tomography: a topology optimization approach.

PubMed

Mello, Luís Augusto Motta; de Lima, Cícero Ribeiro; Amato, Marcelo Britto Passos; Lima, Raul Gonzalez; Silva, Emílio Carlos Nelli

2008-02-01

Electrical impedance tomography is a technique to estimate the impedance distribution within a domain, based on measurements on its boundary. In other words, given the mathematical model of the domain, its geometry and boundary conditions, a nonlinear inverse problem of estimating the electric impedance distribution can be solved. Several impedance estimation algorithms have been proposed to solve this problem. In this paper, we present a three-dimensional algorithm, based on the topology optimization method, as an alternative. A sequence of linear programming problems, allowing for constraints, is solved utilizing this method. In each iteration, the finite element method provides the electric potential field within the model of the domain. An electrode model is also proposed (thus, increasing the accuracy of the finite element results). The algorithm is tested using numerically simulated data and also experimental data, and absolute resistivity values are obtained. These results, corresponding to phantoms with two different conductive materials, exhibit relatively well-defined boundaries between them, and show that this is a practical and potentially useful technique to be applied to monitor lung aeration, including the possibility of imaging a pneumothorax.

The solution of linear systems of equations with a structural analysis code on the NAS CRAY-2

NASA Technical Reports Server (NTRS)

Poole, Eugene L.; Overman, Andrea L.

1988-01-01

Two methods for solving linear systems of equations on the NAS Cray-2 are described. One is a direct method; the other is an iterative method. Both methods exploit the architecture of the Cray-2, particularly the vectorization, and are aimed at structural analysis applications. To demonstrate and evaluate the methods, they were installed in a finite element structural analysis code denoted the Computational Structural Mechanics (CSM) Testbed. A description of the techniques used to integrate the two solvers into the Testbed is given. Storage schemes, memory requirements, operation counts, and reformatting procedures are discussed. Finally, results from the new methods are compared with results from the initial Testbed sparse Choleski equation solver for three structural analysis problems. The new direct solvers described achieve the highest computational rates of the methods compared. The new iterative methods are not able to achieve as high computation rates as the vectorized direct solvers but are best for well conditioned problems which require fewer iterations to converge to the solution.

Generalized conjugate-gradient methods for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1991-01-01

A generalized conjugate-gradient method is used to solve the two-dimensional, compressible Navier-Stokes equations of fluid flow. The equations are discretized with an implicit, upwind finite-volume formulation. Preconditioning techniques are incorporated into the new solver to accelerate convergence of the overall iterative method. The superiority of the new solver is demonstrated by comparisons with a conventional line Gauss-Siedel Relaxation solver. Computational test results for transonic flow (trailing edge flow in a transonic turbine cascade) and hypersonic flow (M = 6.0 shock-on-shock phenoena on a cylindrical leading edge) are presented. When applied to the transonic cascade case, the new solver is 4.4 times faster in terms of number of iterations and 3.1 times faster in terms of CPU time than the Relaxation solver. For the hypersonic shock case, the new solver is 3.0 times faster in terms of number of iterations and 2.2 times faster in terms of CPU time than the Relaxation solver.

Some error bounds for K-iterated Gaussian recursive filters

NASA Astrophysics Data System (ADS)

Cuomo, Salvatore; Galletti, Ardelio; Giunta, Giulio; Marcellino, Livia

2016-10-01

Recursive filters (RFs) have achieved a central role in several research fields over the last few years. For example, they are used in image processing, in data assimilation and in electrocardiogram denoising. More in particular, among RFs, the Gaussian RFs are an efficient computational tool for approximating Gaussian-based convolutions and are suitable for digital image processing and applications of the scale-space theory. As is a common knowledge, the Gaussian RFs, applied to signals with support in a finite domain, generate distortions and artifacts, mostly localized at the boundaries. Heuristic and theoretical improvements have been proposed in literature to deal with this issue (namely boundary conditions). They include the case in which a Gaussian RF is applied more than once, i.e. the so called K-iterated Gaussian RFs. In this paper, starting from a summary of the comprehensive mathematical background, we consider the case of the K-iterated first-order Gaussian RF and provide the study of its numerical stability and some component-wise theoretical error bounds.

Investigation of Conjugate Heat Transfer in Turbine Blades and Vanes

NASA Technical Reports Server (NTRS)

Kassab, A. J.; Kapat, J. S.

2001-01-01

We report on work carried out to develop a 3-D coupled Finite Volume/BEM-based temperature forward/flux back (TFFB) coupling algorithm to solve the conjugate heat transfer (CHT) which arises naturally in analysis of systems exposed to a convective environment. Here, heat conduction within a structure is coupled to heat transfer to the external fluid which is convecting heat into or out of the solid structure. There are two basic approaches to solving coupled fluid structural systems. The first is a direct coupling where the solution of the different fields is solved simultaneously in one large set of equations. The second approach is a loose coupling strategy where each set of field equations is solved to provide boundary conditions for the other. The equations are solved in turn until an iterated convergence criterion is met at the fluid-solid interface. The loose coupling strategy is particularly attractive when coupling auxiliary field equations to computational fluid dynamics codes. We adopt the latter method in which the BEM is used to solve heat conduction inside a structure which is exposed to a convective field which in turn is resolved by solving the NASA Glenn compressible Navier-Stokes finite volume code Glenn-HT. The BEM code features constant and bi-linear discontinuous elements and an ILU-preconditioned GMRES iterative solver for the resulting non-symmetric algebraic set arising in the conduction solution. Interface of flux and temperature is enforced at the solid/fluid interface, and a radial-basis function scheme is used to interpolated information between the CFD and BEM surface grids. Additionally, relaxation is implemented in passing the fluxes from the conduction solution to the fluid solution. Results from a simple test example are reported.

Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Inviscid Fluxes

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.

2010-01-01

Cell-centered and node-centered approaches have been compared for unstructured finite-volume discretization of inviscid fluxes. The grids range from regular grids to irregular grids, including mixed-element grids and grids with random perturbations of nodes. Accuracy, complexity, and convergence rates of defect-correction iterations are studied for eight nominally second-order accurate schemes: two node-centered schemes with weighted and unweighted least-squares (LSQ) methods for gradient reconstruction and six cell-centered schemes two node-averaging with and without clipping and four schemes that employ different stencils for LSQ gradient reconstruction. The cell-centered nearest-neighbor (CC-NN) scheme has the lowest complexity; a version of the scheme that involves smart augmentation of the LSQ stencil (CC-SA) has only marginal complexity increase. All other schemes have larger complexity; complexity of node-centered (NC) schemes are somewhat lower than complexity of cell-centered node-averaging (CC-NA) and full-augmentation (CC-FA) schemes. On highly anisotropic grids typical of those encountered in grid adaptation, discretization errors of five of the six cell-centered schemes converge with second order on all tested grids; the CC-NA scheme with clipping degrades solution accuracy to first order. The NC schemes converge with second order on regular and/or triangular grids and with first order on perturbed quadrilaterals and mixed-element grids. All schemes may produce large relative errors in gradient reconstruction on grids with perturbed nodes. Defect-correction iterations for schemes employing weighted least-square gradient reconstruction diverge on perturbed stretched grids. Overall, the CC-NN and CC-SA schemes offer the best options of the lowest complexity and secondorder discretization errors. On anisotropic grids over a curved body typical of turbulent flow simulations, the discretization errors converge with second order and are small for the CC-NN, CC-SA, and CC-FA schemes on all grids and for NC schemes on triangular grids; the discretization errors of the CC-NA scheme without clipping do not converge on irregular grids. Accurate gradient reconstruction can be achieved by introducing a local approximate mapping; without approximate mapping, only the NC scheme with weighted LSQ method provides accurate gradients. Defect correction iterations for the CC-NA scheme without clipping diverge; for the NC scheme with weighted LSQ method, the iterations either diverge or converge very slowly. The best option in curved geometries is the CC-SA scheme that offers low complexity, second-order discretization errors, and fast convergence.

A combined finite element-boundary element formulation for solution of axially symmetric bodies

NASA Technical Reports Server (NTRS)

Collins, Jeffrey D.; Volakis, John L.

1991-01-01

A new method is presented for the computation of electromagnetic scattering from axially symmetric bodies. To allow the simulation of inhomogeneous cross sections, the method combines the finite element and boundary element techniques. Interior to a fictitious surface enclosing the scattering body, the finite element method is used which results in a sparce submatrix, whereas along the enclosure the Stratton-Chu integral equation is enforced. By choosing the fictitious enclosure to be a right circular cylinder, most of the resulting boundary integrals are convolutional and may therefore be evaluated via the FFT with which the system is iteratively solved. In view of the sparce matrix associated with the interior fields, this reduces the storage requirement of the entire system to O(N) making the method attractive for large scale computations. The details of the corresponding formulation and its numerical implementation are described.

Three-dimensional forward modeling and inversion of marine CSEM data in anisotropic conductivity structures

NASA Astrophysics Data System (ADS)

Han, B.; Li, Y.

2016-12-01

We present a three-dimensional (3D) forward and inverse modeling code for marine controlled-source electromagnetic (CSEM) surveys in anisotropic media. The forward solution is based on a primary/secondary field approach, in which secondary fields are solved using a staggered finite-volume (FV) method and primary fields are solved for 1D isotropic background models analytically. It is shown that it is rather straightforward to extend the isotopic 3D FV algorithm to a triaxial anisotropic one, while additional coefficients are required to account for full tensor conductivity. To solve the linear system resulting from FV discretization of Maxwell' s equations, both iterative Krylov solvers (e.g. BiCGSTAB) and direct solvers (e.g. MUMPS) have been implemented, makes the code flexible for different computing platforms and different problems. For iterative soloutions, the linear system in terms of electromagnetic potentials (A-Phi) is used to precondition the original linear system, transforming the discretized Curl-Curl equations to discretized Laplace-like equations, thus much more favorable numerical properties can be obtained. Numerical experiments suggest that this A-Phi preconditioner can dramatically improve the convergence rate of an iterative solver and high accuracy can be achieved without divergence correction even for low frequencies. To efficiently calculate the sensitivities, i.e. the derivatives of CSEM data with respect to tensor conductivity, the adjoint method is employed. For inverse modeling, triaxial anisotropy is taken into account. Since the number of model parameters to be resolved of triaxial anisotropic medias is twice or thrice that of isotropic medias, the data-space version of the Gauss-Newton (GN) minimization method is preferred due to its lower computational cost compared with the traditional model-space GN method. We demonstrate the effectiveness of the code with synthetic examples.

Multigrid Methods for EHL Problems

NASA Technical Reports Server (NTRS)

Nurgat, Elyas; Berzins, Martin

1996-01-01

In many bearings and contacts, forces are transmitted through thin continuous fluid films which separate two contacting elements. Objects in contact are normally subjected to friction and wear which can be reduced effectively by using lubricants. If the lubricant film is sufficiently thin to prevent the opposing solids from coming into contact and carries the entire load, then we have hydrodynamic lubrication, where the lubricant film is determined by the motion and geometry of the solids. However, for loaded contacts of low geometrical conformity, such as gears, rolling contact bearings and cams, this is not the case due to high pressures and this is referred to as Elasto-Hydrodynamic Lubrication (EHL) In EHL, elastic deformation of the contacting elements and the increase in fluid viscosity with pressure are very significant and cannot be ignored. Since the deformation results in changing the geometry of the lubricating film, which in turn determines the pressure distribution, an EHL mathematical model must simultaneously satisfy the complex elasticity (integral) and the Reynolds lubrication (differential) equations. The nonlinear and coupled nature of the two equations makes numerical calculations computationally intensive. This is especially true for highly loaded problems found in practice. One novel feature of these problems is that the solution may exhibit sharp pressure spikes in the outlet region. To this date both finite element and finite difference methods have been used to solve EHL problems with perhaps greater emphasis on the use of the finite difference approach. In both cases, a major computational difficulty is ensuring convergence of the nonlinear equations solver to a steady state solution. Two successful methods for achieving this are direct iteration and multigrid methods. Direct iteration methods (e.g Gauss Seidel) have long been used in conjunction with finite difference discretizations on regular meshes. Perhaps one of the best examples of the application of such methods is the recent Effective Influence Method of Dowson and Wang. Multigrid methods have also been used with great success by Venner and Venner and Lubrecht with a good summary being given by Venner. As both these finite difference discretization based approaches appear to provide an efficient way of solving EHL problems, it is important to understand their relative merits. This paper is a first attempt at providing such an understanding in the context of EHL point contact problem, (contact of two spheres), in which the contact zone is a point and an ellipse or circle for unloaded and loaded dry contacts respectively. Since the film thickness and the contact width are generally small compared to the local radius of curvature of the two surfaces, the reduced geometry of the surfaces in the contact area can be accurately approximated to the contact between a paraboloid and a flat surface. The layout of the remainder of this paper is as follows. In section 2 we introduce the form of the equations to be solved. The Effective Influence Newton Method is described in Section 3 while Section 4 describes the Multigrid method to be used. Sections 5 and 6 describe the test problems to be used in the comparison between the two methods and compare the performance of the two methods. Section 7 concludes the paper with an argument of the two methods and suggests some future research directions.

Advances in contact algorithms and their application to tires

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Tanner, John A.

1988-01-01

Currently used techniques for tire contact analysis are reviewed. Discussion focuses on the different techniques used in modeling frictional forces and the treatment of contact conditions. A status report is presented on a new computational strategy for the modeling and analysis of tires, including the solution of the contact problem. The key elements of the proposed strategy are: (1) use of semianalytic mixed finite elements in which the shell variables are represented by Fourier series in the circumferential direction and piecewise polynomials in the meridional direction; (2) use of perturbed Lagrangian formulation for the determination of the contact area and pressure; and (3) application of multilevel iterative procedures and reduction techniques to generate the response of the tire. Numerical results are presented to demonstrate the effectiveness of a proposed procedure for generating the tire response associated with different Fourier harmonics.

Effects of ray profile modeling on resolution recovery in clinical CT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hofmann, Christian; Knaup, Michael; Kachelrieß, Marc, E-mail: marc.kachelriess@dkfz-heidelberg.de

2014-02-15

Purpose: Iterative image reconstruction gains more and more interest in clinical routine, as it promises to reduce image noise (and thereby patient dose), to reduce artifacts, or to improve spatial resolution. However, among vendors and researchers, there is no consensus of how to best achieve these goals. The authors are focusing on the aspect of geometric ray profile modeling, which is realized by some algorithms, while others model the ray as a straight line. The authors incorporate ray-modeling (RM) in nonregularized iterative reconstruction. That means, instead of using one simple single needle beam to represent the x-ray, the authors evaluatemore » the double integral of attenuation path length over the finite source distribution and the finite detector element size in the numerical forward projection. Our investigations aim at analyzing the resolution recovery (RR) effects of RM. Resolution recovery means that frequencies can be recovered beyond the resolution limit of the imaging system. In order to evaluate, whether clinical CT images can benefit from modeling the geometrical properties of each x-ray, the authors performed a 2D simulation study of a clinical CT fan-beam geometry that includes the precise modeling of these geometrical properties. Methods: All simulations and reconstructions are performed in native fan-beam geometry. A water phantom with resolution bar patterns and a Forbild thorax phantom with circular resolution patterns representing calcifications in the heart region are simulated. An FBP reconstruction with a Ram–Lak kernel is used as a reference reconstruction. The FBP is compared to iterative reconstruction techniques with and without RM: An ordered subsets convex (OSC) algorithm without any RM (OSC), an OSC where the forward projection is modeled concerning the finite focal spot and detector size (OSC-RM) and an OSC with RM and with a matched forward and backprojection pair (OSC-T-RM, T for transpose). In all cases, noise was matched to be able to focus on comparing spatial resolution. The authors use two different simulation settings. Both are based on the geometry of a typical clinical CT system (0.7 mm detector element size at isocenter, 1024 projections per rotation). Setting one has an exaggerated source width of 5.0 mm. Setting two has a realistically small source width of 0.5 mm. The authors also investigate the transition from setting one to two. To quantify image quality, the authors analyze line profiles through the resolution patterns to define a contrast factor (CF) for contrast-resolution plots, and the authors compare the normalized cross-correlation (NCC) with respect to the ground truth of the circular resolution patterns. To independently analyze whether RM is of advantage, the authors implemented several iterative reconstruction algorithms: The statistical iterative reconstruction algorithm OSC, the ordered subsets simultaneous algebraic reconstruction technique (OSSART) and another statistical iterative reconstruction algorithm, denoted with ordered subsets maximum likelihood (OSML) algorithm. All algorithms were implemented both without RM (denoted as OSC, OSSART, and OSML) and with RM (denoted as OSC-RM, OSSART-RM, and OSML-RM). Results: For the unrealistic case of a 5.0 mm focal spot the CF can be improved by a factor of two due to RM: the 4.2 LP/cm bar pattern, which is the first bar pattern that cannot be resolved without RM, can be easily resolved with RM. For the realistic case of a 0.5 mm focus, all results show approximately the same CF. The NCC shows no significant dependency on RM when the source width is smaller than 2.0 mm (as in clinical CT). From 2.0 mm to 5.0 mm focal spot size increasing improvements can be observed with RM. Conclusions: Geometric RM in iterative reconstruction helps improving spatial resolution, if the ray cross-section is significantly larger than the ray sampling distance. In clinical CT, however, the ray is not much thicker than the distance between neighboring ray centers, as the focal spot size is small and detector crosstalk is negligible, due to reflective coatings between detector elements. Therefore,RM appears not to be necessary in clinical CT to achieve resolution recovery.« less

Finite element probabilistic risk assessment of transmission line insulation flashovers caused by lightning strokes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bacvarov, D.C.

1981-01-01

A new method for probabilistic risk assessment of transmission line insulation flashovers caused by lightning strokes is presented. The utilized approach of applying the finite element method for probabilistic risk assessment is demonstrated to be very powerful. The reasons for this are two. First, the finite element method is inherently suitable for analysis of three dimensional spaces where the parameters, such as three variate probability densities of the lightning currents, are non-uniformly distributed. Second, the finite element method permits non-uniform discretization of the three dimensional probability spaces thus yielding high accuracy in critical regions, such as the area of themore » low probability events, while at the same time maintaining coarse discretization in the non-critical areas to keep the number of grid points and the size of the problem to a manageable low level. The finite element probabilistic risk assessment method presented here is based on a new multidimensional search algorithm. It utilizes an efficient iterative technique for finite element interpolation of the transmission line insulation flashover criteria computed with an electro-magnetic transients program. Compared to other available methods the new finite element probabilistic risk assessment method is significantly more accurate and approximately two orders of magnitude computationally more efficient. The method is especially suited for accurate assessment of rare, very low probability events.« less

Comparison of a 3-D GPU-Assisted Maxwell Code and Ray Tracing for Reflectometry on ITER

NASA Astrophysics Data System (ADS)

Gady, Sarah; Kubota, Shigeyuki; Johnson, Irena

2015-11-01

Electromagnetic wave propagation and scattering in magnetized plasmas are important diagnostics for high temperature plasmas. 1-D and 2-D full-wave codes are standard tools for measurements of the electron density profile and fluctuations; however, ray tracing results have shown that beam propagation in tokamak plasmas is inherently a 3-D problem. The GPU-Assisted Maxwell Code utilizes the FDTD (Finite-Difference Time-Domain) method for solving the Maxwell equations with the cold plasma approximation in a 3-D geometry. Parallel processing with GPGPU (General-Purpose computing on Graphics Processing Units) is used to accelerate the computation. Previously, we reported on initial comparisons of the code results to 1-D numerical and analytical solutions, where the size of the computational grid was limited by the on-board memory of the GPU. In the current study, this limitation is overcome by using domain decomposition and an additional GPU. As a practical application, this code is used to study the current design of the ITER Low Field Side Reflectometer (LSFR) for the Equatorial Port Plug 11 (EPP11). A detailed examination of Gaussian beam propagation in the ITER edge plasma will be presented, as well as comparisons with ray tracing. This work was made possible by funding from the Department of Energy for the Summer Undergraduate Laboratory Internship (SULI) program. This work is supported by the US DOE Contract No.DE-AC02-09CH11466 and DE-FG02-99-ER54527.

Multi-hybrid method for investigation of EM scattering from inhomogeneous object above a dielectric rough surface

NASA Astrophysics Data System (ADS)

Li, Jie; Guo, LiXin; He, Qiong; Wei, Bing

2012-10-01

An iterative strategy combining Kirchhoff approximation^(KA) with the hybrid finite element-boundary integral (FE-BI) method is presented in this paper to study the interactions between the inhomogeneous object and the underlying rough surface. KA is applied to study scattering from underlying rough surfaces, whereas FE-BI deals with scattering from the above target. Both two methods use updated excitation sources. Huygens equivalence principle and an iterative strategy are employed to consider the multi-scattering effects. This hybrid FE-BI-KA scheme is an improved and generalized version of previous hybrid Kirchhoff approximation-method of moments (KA-MoM). This newly presented hybrid method has the following advantages: (1) the feasibility of modeling multi-scale scattering problems (large scale underlying surface and small scale target); (2) low memory requirement as in hybrid KA-MoM; (3) the ability to deal with scattering from inhomogeneous (including coated or layered) scatterers above rough surfaces. The numerical results are given to evaluate the accuracy of the multi-hybrid technique; the computing time and memory requirements consumed in specific numerical simulation of FE-BI-KA are compared with those of MoM. The convergence performance is analyzed by studying the iteration number variation caused by related parameters. Then bistatic scattering from inhomogeneous object of different configurations above dielectric Gaussian rough surface is calculated and the influences of dielectric compositions and surface roughness on the scattering pattern are discussed.

Data Sciences Summer Institute Topology Optimization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Watts, Seth

DSSI_TOPOPT is a 2D topology optimization code that designs stiff structures made of a single linear elastic material and void space. The code generates a finite element mesh of a rectangular design domain on which the user specifies displacement and load boundary conditions. The code iteratively designs a structure that minimizes the compliance (maximizes the stiffness) of the structure under the given loading, subject to an upper bound on the amount of material used. Depending on user options, the code can evaluate the performance of a user-designed structure, or create a design from scratch. Output includes the finite element mesh,more » design, and visualizations of the design.« less

Progress on a Taylor weak statement finite element algorithm for high-speed aerodynamic flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Freels, J. D.

1989-01-01

A new finite element numerical Computational Fluid Dynamics (CFD) algorithm has matured to the point of efficiently solving two-dimensional high speed real-gas compressible flow problems in generalized coordinates on modern vector computer systems. The algorithm employs a Taylor Weak Statement classical Galerkin formulation, a variably implicit Newton iteration, and a tensor matrix product factorization of the linear algebra Jacobian under a generalized coordinate transformation. Allowing for a general two-dimensional conservation law system, the algorithm has been exercised on the Euler and laminar forms of the Navier-Stokes equations. Real-gas fluid properties are admitted, and numerical results verify solution accuracy, efficiency, and stability over a range of test problem parameters.

Equilibrium paths of an imperfect plate with respect to its aspect ratio

NASA Astrophysics Data System (ADS)

Psotny, Martin

2017-07-01

The stability analysis of a rectangular plate loaded in compression is presented, a specialized code based on FEM has been created. Special finite element with 48 degrees of freedom has been used for analysis. The nonlinear finite element method equations are derived from the variational principle of minimum of total potential energy. To trace the complete nonlinear equilibrium paths, the Newton-Raphson iteration algorithm is used, load versus displacement control was changed during the calculation process. The peculiarities of the effects of the initial imperfections on the load-deflection paths are investigated with respect to aspect ratio of the plate. Special attention is paid to the influence of imperfections on the post-critical buckling mode.

Finite-element solutions for geothermal systems

NASA Technical Reports Server (NTRS)

Chen, J. C.; Conel, J. E.

1977-01-01

Vector potential and scalar potential are used to formulate the governing equations for a single-component and single-phase geothermal system. By assuming an initial temperature field, the fluid velocity can be determined which, in turn, is used to calculate the convective heat transfer. The energy equation is then solved by considering convected heat as a distributed source. Using the resulting temperature to compute new source terms, the final results are obtained by iterations of the procedure. Finite-element methods are proposed for modeling of realistic geothermal systems; the advantages of such methods are discussed. The developed methodology is then applied to a sample problem. Favorable agreement is obtained by comparisons with a previous study.

MPSalsa Version 1.5: A Finite Element Computer Program for Reacting Flow Problems: Part 1 - Theoretical Development

DOE Office of Scientific and Technical Information (OSTI.GOV)

Devine, K.D.; Hennigan, G.L.; Hutchinson, S.A.

1999-01-01

The theoretical background for the finite element computer program, MPSalsa Version 1.5, is presented in detail. MPSalsa is designed to solve laminar or turbulent low Mach number, two- or three-dimensional incompressible and variable density reacting fluid flows on massively parallel computers, using a Petrov-Galerkin finite element formulation. The code has the capability to solve coupled fluid flow (with auxiliary turbulence equations), heat transport, multicomponent species transport, and finite-rate chemical reactions, and to solve coupled multiple Poisson or advection-diffusion-reaction equations. The program employs the CHEMKIN library to provide a rigorous treatment of multicomponent ideal gas kinetics and transport. Chemical reactions occurringmore » in the gas phase and on surfaces are treated by calls to CHEMKIN and SURFACE CHEMK3N, respectively. The code employs unstructured meshes, using the EXODUS II finite element database suite of programs for its input and output files. MPSalsa solves both transient and steady flows by using fully implicit time integration, an inexact Newton method and iterative solvers based on preconditioned Krylov methods as implemented in the Aztec. solver library.« less

A Matlab-based finite-difference solver for the Poisson problem with mixed Dirichlet-Neumann boundary conditions

NASA Astrophysics Data System (ADS)

Reimer, Ashton S.; Cheviakov, Alexei F.

2013-03-01

A Matlab-based finite-difference numerical solver for the Poisson equation for a rectangle and a disk in two dimensions, and a spherical domain in three dimensions, is presented. The solver is optimized for handling an arbitrary combination of Dirichlet and Neumann boundary conditions, and allows for full user control of mesh refinement. The solver routines utilize effective and parallelized sparse vector and matrix operations. Computations exhibit high speeds, numerical stability with respect to mesh size and mesh refinement, and acceptable error values even on desktop computers. Catalogue identifier: AENQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License v3.0 No. of lines in distributed program, including test data, etc.: 102793 No. of bytes in distributed program, including test data, etc.: 369378 Distribution format: tar.gz Programming language: Matlab 2010a. Computer: PC, Macintosh. Operating system: Windows, OSX, Linux. RAM: 8 GB (8, 589, 934, 592 bytes) Classification: 4.3. Nature of problem: To solve the Poisson problem in a standard domain with “patchy surface”-type (strongly heterogeneous) Neumann/Dirichlet boundary conditions. Solution method: Finite difference with mesh refinement. Restrictions: Spherical domain in 3D; rectangular domain or a disk in 2D. Unusual features: Choice between mldivide/iterative solver for the solution of large system of linear algebraic equations that arise. Full user control of Neumann/Dirichlet boundary conditions and mesh refinement. Running time: Depending on the number of points taken and the geometry of the domain, the routine may take from less than a second to several hours to execute.

Two-level Schwartz methods for nonconforming finite elements and discontinuous coefficients

NASA Technical Reports Server (NTRS)

Sarkis, Marcus

1993-01-01

Two-level domain decomposition methods are developed for a simple nonconforming approximation of second order elliptic problems. A bound is established for the condition number of these iterative methods, which grows only logarithmically with the number of degrees of freedom in each subregion. This bound holds for two and three dimensions and is independent of jumps in the value of the coefficients.

Theoretical performance of foil journal bearings

NASA Technical Reports Server (NTRS)

Carpino, M.; Peng, J.-P.

1991-01-01

A modified forward iteration approach for the coupled solution of foil bearings is presented. The method is used to predict the steady state theoretical performance of a journal type gas bearing constructed from an inextensible shell supported by an elastic foundation. Bending effects are treated as negligible. Finite element methods are used to predict both the foil deflections and the pressure distribution in the gas film.

Domain Derivatives in Dielectric Rough Surface Scattering

DTIC Science & Technology

2015-01-01

and require the gradient of the objective function in the unknown model parameter vector at each stage of iteration. For large N, finite...differencing becomes numerically intensive, and an efficient alternative is domain differentiation in which the full gradient is obtained by solving a single...derivative calculation of the gradient for a locally perturbed dielectric interface. The method is non-variational, and algebraic in nature in that it

A modified Dodge algorithm for the parabolized Navier-Stokes equation and compressible duct flows

NASA Technical Reports Server (NTRS)

Cooke, C. H.

1981-01-01

A revised version of Dodge's split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition. Qualitive agreement with analytical predictions and experimental results was obtained for some flows with well-known solutions.

Performance analysis of successive over relaxation method for solving glioma growth model

NASA Astrophysics Data System (ADS)

Hussain, Abida; Faye, Ibrahima; Muthuvalu, Mohana Sundaram

2016-11-01

Brain tumor is one of the prevalent cancers in the world that lead to death. In light of the present information of the properties of gliomas, mathematical models have been developed by scientists to quantify the proliferation and invasion dynamics of glioma. In this study, one-dimensional glioma growth model is considered, and finite difference method is used to discretize the problem. Then, two stationary methods, namely Gauss-Seidel (GS) and Successive Over Relaxation (SOR) are used to solve the governing algebraic system. The performance of the methods are evaluated in terms of number of iteration and computational time. On the basis of performance analysis, SOR method is shown to be more superior compared to GS method.

Fast Bound Methods for Large Scale Simulation with Application for Engineering Optimization

NASA Technical Reports Server (NTRS)

Patera, Anthony T.; Peraire, Jaime; Zang, Thomas A. (Technical Monitor)

2002-01-01

In this work, we have focused on fast bound methods for large scale simulation with application for engineering optimization. The emphasis is on the development of techniques that provide both very fast turnaround and a certificate of Fidelity; these attributes ensure that the results are indeed relevant to - and trustworthy within - the engineering context. The bound methodology which underlies this work has many different instantiations: finite element approximation; iterative solution techniques; and reduced-basis (parameter) approximation. In this grant we have, in fact, treated all three, but most of our effort has been concentrated on the first and third. We describe these below briefly - but with a pointer to an Appendix which describes, in some detail, the current "state of the art."

The numerical calculation of laminar boundary-layer separation

NASA Technical Reports Server (NTRS)

Klineberg, J. M.; Steger, J. L.

1974-01-01

Iterative finite-difference techniques are developed for integrating the boundary-layer equations, without approximation, through a region of reversed flow. The numerical procedures are used to calculate incompressible laminar separated flows and to investigate the conditions for regular behavior at the point of separation. Regular flows are shown to be characterized by an integrable saddle-type singularity that makes it difficult to obtain numerical solutions which pass continuously into the separated region. The singularity is removed and continuous solutions ensured by specifying the wall shear distribution and computing the pressure gradient as part of the solution. Calculated results are presented for several separated flows and the accuracy of the method is verified. A computer program listing and complete solution case are included.

ECP Milestone Report WBS 2.3.4.13 ECP/VTK-m FY18Q1 [MS-18/01-03] Multiblock / Gradients / Release STDA05-5.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moreland, Kenneth D.; Pugmire, David; Geveci, Berk

The FY18Q1 milestone of the ECP/VTK-m project includes the implementation of a multiblock data set, the completion of a gradients filtering operation, and the release of version 1.1 of the VTK-m software. With the completion of this milestone, the new multiblock data set allows us to iteratively schedule algorithms on composite data structures such as assemblies or hierarchies like AMR. The new gradient algorithms approximate derivatives of fields in 3D structures with finite differences. Finally, the release of VTK-m version 1.1 tags a stable release of the software that can more easily be incorporated into external projects.

Genetic Algorithm Design of a 3D Printed Heat Sink

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Tong; Ozpineci, Burak; Ayers, Curtis William

2016-01-01

In this paper, a genetic algorithm- (GA-) based approach is discussed for designing heat sinks based on total heat generation and dissipation for a pre-specified size andshape. This approach combines random iteration processesand genetic algorithms with finite element analysis (FEA) to design the optimized heat sink. With an approach that prefers survival of the fittest , a more powerful heat sink can bedesigned which can cool power electronics more efficiently. Some of the resulting designs can only be 3D printed due totheir complexity. In addition to describing the methodology, this paper also includes comparisons of different cases to evaluate themore » performance of the newly designed heat sinkcompared to commercially available heat sinks.« less

Application of multigrid methods to the solution of liquid crystal equations on a SIMD computer

NASA Technical Reports Server (NTRS)

Farrell, Paul A.; Ruttan, Arden; Zeller, Reinhardt R.

1993-01-01

We will describe a finite difference code for computing the equilibrium configurations of the order-parameter tensor field for nematic liquid crystals in rectangular regions by minimization of the Landau-de Gennes Free Energy functional. The implementation of the free energy functional described here includes magnetic fields, quadratic gradient terms, and scalar bulk terms through the fourth order. Boundary conditions include the effects of strong surface anchoring. The target architectures for our implementation are SIMD machines, with interconnection networks which can be configured as 2 or 3 dimensional grids, such as the Wavetracer DTC. We also discuss the relative efficiency of a number of iterative methods for the solution of the linear systems arising from this discretization on such architectures.

CALCULATION OF GAMMA SPECTRA IN A PLASTIC SCINTILLATOR FOR ENERGY CALIBRATIONAND DOSE COMPUTATION.

PubMed

Kim, Chankyu; Yoo, Hyunjun; Kim, Yewon; Moon, Myungkook; Kim, Jong Yul; Kang, Dong Uk; Lee, Daehee; Kim, Myung Soo; Cho, Minsik; Lee, Eunjoong; Cho, Gyuseong

2016-09-01

Plastic scintillation detectors have practical advantages in the field of dosimetry. Energy calibration of measured gamma spectra is important for dose computation, but it is not simple in the plastic scintillators because of their different characteristics and a finite resolution. In this study, the gamma spectra in a polystyrene scintillator were calculated for the energy calibration and dose computation. Based on the relationship between the energy resolution and estimated energy broadening effect in the calculated spectra, the gamma spectra were simply calculated without many iterations. The calculated spectra were in agreement with the calculation by an existing method and measurements. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Scattering and emission from inhomogeneous vegetation canopy and alien target beneath by using three-dimensional vector radiative transfer (3D-VRT) equation

NASA Astrophysics Data System (ADS)

Jin, Ya-Qiu; Liang, Zichang

2005-05-01

To solve the 3D-VRT equation for the model of spatially inhomogeneous scatter media, the finite enclosure of the scatter media is geometrically divided, in both vertical z and transversal (x,y) directions, to form very thin multi-boxes. The zeroth order emission, first-order Mueller matrix of each thin box and an iterative approach of high-order radiative transfer are applied to derive high-order scattering and emission of whole inhomogeneous scatter media. Numerical results of polarized brightness temperature at microwave frequency and under different radiometer resolutions from inhomogeneous scatter model such as vegetation canopy and alien target beneath canopy are simulated and discussed.

On some Aitken-like acceleration of the Schwarz method

NASA Astrophysics Data System (ADS)

Garbey, M.; Tromeur-Dervout, D.

2002-12-01

In this paper we present a family of domain decomposition based on Aitken-like acceleration of the Schwarz method seen as an iterative procedure with a linear rate of convergence. We first present the so-called Aitken-Schwarz procedure for linear differential operators. The solver can be a direct solver when applied to the Helmholtz problem with five-point finite difference scheme on regular grids. We then introduce the Steffensen-Schwarz variant which is an iterative domain decomposition solver that can be applied to linear and nonlinear problems. We show that these solvers have reasonable numerical efficiency compared to classical fast solvers for the Poisson problem or multigrids for more general linear and nonlinear elliptic problems. However, the salient feature of our method is that our algorithm has high tolerance to slow network in the context of distributed parallel computing and is attractive, generally speaking, to use with computer architecture for which performance is limited by the memory bandwidth rather than the flop performance of the CPU. This is nowadays the case for most parallel. computer using the RISC processor architecture. We will illustrate this highly desirable property of our algorithm with large-scale computing experiments.

Accelerating 4D flow MRI by exploiting vector field divergence regularization.

PubMed

Santelli, Claudio; Loecher, Michael; Busch, Julia; Wieben, Oliver; Schaeffter, Tobias; Kozerke, Sebastian

2016-01-01

To improve velocity vector field reconstruction from undersampled four-dimensional (4D) flow MRI by penalizing divergence of the measured flow field. Iterative image reconstruction in which magnitude and phase are regularized separately in alternating iterations was implemented. The approach allows incorporating prior knowledge of the flow field being imaged. In the present work, velocity data were regularized to reduce divergence, using either divergence-free wavelets (DFW) or a finite difference (FD) method using the ℓ1-norm of divergence and curl. The reconstruction methods were tested on a numerical phantom and in vivo data. Results of the DFW and FD approaches were compared with data obtained with standard compressed sensing (CS) reconstruction. Relative to standard CS, directional errors of vector fields and divergence were reduced by 55-60% and 38-48% for three- and six-fold undersampled data with the DFW and FD methods. Velocity vector displays of the numerical phantom and in vivo data were found to be improved upon DFW or FD reconstruction. Regularization of vector field divergence in image reconstruction from undersampled 4D flow data is a valuable approach to improve reconstruction accuracy of velocity vector fields. © 2014 Wiley Periodicals, Inc.

Iterative image reconstruction in elastic inhomogenous media with application to transcranial photoacoustic tomography

NASA Astrophysics Data System (ADS)

Poudel, Joemini; Matthews, Thomas P.; Mitsuhashi, Kenji; Garcia-Uribe, Alejandro; Wang, Lihong V.; Anastasio, Mark A.

2017-03-01

Photoacoustic computed tomography (PACT) is an emerging computed imaging modality that exploits optical contrast and ultrasonic detection principles to form images of the photoacoustically induced initial pressure distribution within tissue. The PACT reconstruction problem corresponds to a time-domain inverse source problem, where the initial pressure distribution is recovered from the measurements recorded on an aperture outside the support of the source. A major challenge in transcranial PACT brain imaging is to compensate for aberrations in the measured data due to the propagation of the photoacoustic wavefields through the skull. To properly account for these effects, a wave equation-based inversion method should be employed that can model the heterogeneous elastic properties of the medium. In this study, an iterative image reconstruction method for 3D transcranial PACT is developed based on the elastic wave equation. To accomplish this, a forward model based on a finite-difference time-domain discretization of the elastic wave equation is established. Subsequently, gradient-based methods are employed for computing penalized least squares estimates of the initial source distribution that produced the measured photoacoustic data. The developed reconstruction algorithm is validated and investigated through computer-simulation studies.

Numerical simulation of double‐diffusive finger convection

USGS Publications Warehouse

Hughes, Joseph D.; Sanford, Ward E.; Vacher, H. Leonard

2005-01-01

A hybrid finite element, integrated finite difference numerical model is developed for the simulation of double‐diffusive and multicomponent flow in two and three dimensions. The model is based on a multidimensional, density‐dependent, saturated‐unsaturated transport model (SUTRA), which uses one governing equation for fluid flow and another for solute transport. The solute‐transport equation is applied sequentially to each simulated species. Density coupling of the flow and solute‐transport equations is accounted for and handled using a sequential implicit Picard iterative scheme. High‐resolution data from a double‐diffusive Hele‐Shaw experiment, initially in a density‐stable configuration, is used to verify the numerical model. The temporal and spatial evolution of simulated double‐diffusive convection is in good agreement with experimental results. Numerical results are very sensitive to discretization and correspond closest to experimental results when element sizes adequately define the spatial resolution of observed fingering. Numerical results also indicate that differences in the molecular diffusivity of sodium chloride and the dye used to visualize experimental sodium chloride concentrations are significant and cause inaccurate mapping of sodium chloride concentrations by the dye, especially at late times. As a result of reduced diffusion, simulated dye fingers are better defined than simulated sodium chloride fingers and exhibit more vertical mass transfer.

Development and evaluation of a local grid refinement method for block-centered finite-difference groundwater models using shared nodes

USGS Publications Warehouse

Mehl, S.; Hill, M.C.

2002-01-01

A new method of local grid refinement for two-dimensional block-centered finite-difference meshes is presented in the context of steady-state groundwater-flow modeling. The method uses an iteration-based feedback with shared nodes to couple two separate grids. The new method is evaluated by comparison with results using a uniform fine mesh, a variably spaced mesh, and a traditional method of local grid refinement without a feedback. Results indicate: (1) The new method exhibits quadratic convergence for homogeneous systems and convergence equivalent to uniform-grid refinement for heterogeneous systems. (2) Coupling the coarse grid with the refined grid in a numerically rigorous way allowed for improvement in the coarse-grid results. (3) For heterogeneous systems, commonly used linear interpolation of heads from the large model onto the boundary of the refined model produced heads that are inconsistent with the physics of the flow field. (4) The traditional method works well in situations where the better resolution of the locally refined grid has little influence on the overall flow-system dynamics, but if this is not true, lack of a feedback mechanism produced errors in head up to 3.6% and errors in cell-to-cell flows up to 25%. ?? 2002 Elsevier Science Ltd. All rights reserved.

Implementing a finite-state off-normal and fault response system for disruption avoidance in tokamaks

NASA Astrophysics Data System (ADS)

Eidietis, N. W.; Choi, W.; Hahn, S. H.; Humphreys, D. A.; Sammuli, B. S.; Walker, M. L.

2018-05-01

A finite-state off-normal and fault response (ONFR) system is presented that provides the supervisory logic for comprehensive disruption avoidance and machine protection in tokamaks. Robust event handling is critical for ITER and future large tokamaks, where plasma parameters will necessarily approach stability limits and many systems will operate near their engineering limits. Events can be classified as off-normal plasmas events, e.g. neoclassical tearing modes or vertical displacements events, or faults, e.g. coil power supply failures. The ONFR system presented provides four critical features of a robust event handling system: sequential responses to cascading events, event recovery, simultaneous handling of multiple events and actuator prioritization. The finite-state logic is implemented in Matlab®/Stateflow® to allow rapid development and testing in an easily understood graphical format before automated export to the real-time plasma control system code. Experimental demonstrations of the ONFR algorithm on the DIII-D and KSTAR tokamaks are presented. In the most complex demonstration, the ONFR algorithm asynchronously applies ‘catch and subdue’ electron cyclotron current drive (ECCD) injection scheme to suppress a virulent 2/1 neoclassical tearing mode, subsequently shuts down ECCD for machine protection when the plasma becomes over-dense, and enables rotating 3D field entrainment of the ensuing locked mode to allow a safe rampdown, all in the same discharge without user intervention. When multiple ONFR states are active simultaneously and requesting the same actuator (e.g. neutral beam injection or gyrotrons), actuator prioritization is accomplished by sorting the pre-assigned priority values of each active ONFR state and giving complete control of the actuator to the state with highest priority. This early experience makes evident that additional research is required to develop an improved actuator sharing protocol, as well as a methodology to minimize the number and topological complexity of states as the finite-state ONFR system is scaled to a large, highly constrained device like ITER.

Implementing a finite-state off-normal and fault response system for disruption avoidance in tokamaks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eidietis, N. W.; Choi, W.; Hahn, S. H.

A finite-state off-normal and fault response (ONFR) system is presented that provides the supervisory logic for comprehensive disruption avoidance and machine protection in tokamaks. Robust event handling is critical for ITER and future large tokamaks, where plasma parameters will necessarily approach stability limits and many systems will operate near their engineering limits. Events can be classified as off-normal plasmas events, e.g. neoclassical tearing modes or vertical displacements events, or faults, e.g. coil power supply failures. The ONFR system presented provides four critical features of a robust event handling system: sequential responses to cascading events, event recovery, simultaneous handling of multiplemore » events and actuator prioritization. The finite-state logic is implemented in Matlab*/Stateflow* to allow rapid development and testing in an easily understood graphical format before automated export to the real-time plasma control system code. Experimental demonstrations of the ONFR algorithm on the DIII-D and KSTAR tokamaks are presented. In the most complex demonstration, the ONFR algorithm asynchronously applies “catch and subdue” electron cyclotron current drive (ECCD) injection scheme to suppress a virulent 2/1 neoclassical tearing mode, subsequently shuts down ECCD for machine protection when the plasma becomes over-dense, and enables rotating 3D field entrainment of the ensuing locked mode to allow a safe rampdown, all in the same discharge without user intervention. When multiple ONFR states are active simultaneously and requesting the same actuator (e.g. neutral beam injection or gyrotrons), actuator prioritization is accomplished by sorting the pre-assigned priority values of each active ONFR state and giving complete control of the actuator to the state with highest priority. This early experience makes evident that additional research is required to develop an improved actuator sharing protocol, as well as a methodology to minimize the number and topological complexity of states as the finite-state ONFR system is scaled to a large, highly constrained device like ITER.« less

Implementing a finite-state off-normal and fault response system for disruption avoidance in tokamaks

DOE PAGES

Eidietis, N. W.; Choi, W.; Hahn, S. H.; ...

2018-03-29

A finite-state off-normal and fault response (ONFR) system is presented that provides the supervisory logic for comprehensive disruption avoidance and machine protection in tokamaks. Robust event handling is critical for ITER and future large tokamaks, where plasma parameters will necessarily approach stability limits and many systems will operate near their engineering limits. Events can be classified as off-normal plasmas events, e.g. neoclassical tearing modes or vertical displacements events, or faults, e.g. coil power supply failures. The ONFR system presented provides four critical features of a robust event handling system: sequential responses to cascading events, event recovery, simultaneous handling of multiplemore » events and actuator prioritization. The finite-state logic is implemented in Matlab*/Stateflow* to allow rapid development and testing in an easily understood graphical format before automated export to the real-time plasma control system code. Experimental demonstrations of the ONFR algorithm on the DIII-D and KSTAR tokamaks are presented. In the most complex demonstration, the ONFR algorithm asynchronously applies “catch and subdue” electron cyclotron current drive (ECCD) injection scheme to suppress a virulent 2/1 neoclassical tearing mode, subsequently shuts down ECCD for machine protection when the plasma becomes over-dense, and enables rotating 3D field entrainment of the ensuing locked mode to allow a safe rampdown, all in the same discharge without user intervention. When multiple ONFR states are active simultaneously and requesting the same actuator (e.g. neutral beam injection or gyrotrons), actuator prioritization is accomplished by sorting the pre-assigned priority values of each active ONFR state and giving complete control of the actuator to the state with highest priority. This early experience makes evident that additional research is required to develop an improved actuator sharing protocol, as well as a methodology to minimize the number and topological complexity of states as the finite-state ONFR system is scaled to a large, highly constrained device like ITER.« less

Fast time- and frequency-domain finite-element methods for electromagnetic analysis

NASA Astrophysics Data System (ADS)

Lee, Woochan

Fast electromagnetic analysis in time and frequency domain is of critical importance to the design of integrated circuits (IC) and other advanced engineering products and systems. Many IC structures constitute a very large scale problem in modeling and simulation, the size of which also continuously grows with the advancement of the processing technology. This results in numerical problems beyond the reach of existing most powerful computational resources. Different from many other engineering problems, the structure of most ICs is special in the sense that its geometry is of Manhattan type and its dielectrics are layered. Hence, it is important to develop structure-aware algorithms that take advantage of the structure specialties to speed up the computation. In addition, among existing time-domain methods, explicit methods can avoid solving a matrix equation. However, their time step is traditionally restricted by the space step for ensuring the stability of a time-domain simulation. Therefore, making explicit time-domain methods unconditionally stable is important to accelerate the computation. In addition to time-domain methods, frequency-domain methods have suffered from an indefinite system that makes an iterative solution difficult to converge fast. The first contribution of this work is a fast time-domain finite-element algorithm for the analysis and design of very large-scale on-chip circuits. The structure specialty of on-chip circuits such as Manhattan geometry and layered permittivity is preserved in the proposed algorithm. As a result, the large-scale matrix solution encountered in the 3-D circuit analysis is turned into a simple scaling of the solution of a small 1-D matrix, which can be obtained in linear (optimal) complexity with negligible cost. Furthermore, the time step size is not sacrificed, and the total number of time steps to be simulated is also significantly reduced, thus achieving a total cost reduction in CPU time. The second contribution is a new method for making an explicit time-domain finite-element method (TDFEM) unconditionally stable for general electromagnetic analysis. In this method, for a given time step, we find the unstable modes that are the root cause of instability, and deduct them directly from the system matrix resulting from a TDFEM based analysis. As a result, an explicit TDFEM simulation is made stable for an arbitrarily large time step irrespective of the space step. The third contribution is a new method for full-wave applications from low to very high frequencies in a TDFEM based on matrix exponential. In this method, we directly deduct the eigenmodes having large eigenvalues from the system matrix, thus achieving a significantly increased time step in the matrix exponential based TDFEM. The fourth contribution is a new method for transforming the indefinite system matrix of a frequency-domain FEM to a symmetric positive definite one. We deduct non-positive definite component directly from the system matrix resulting from a frequency-domain FEM-based analysis. The resulting new representation of the finite-element operator ensures an iterative solution to converge in a small number of iterations. We then add back the non-positive definite component to synthesize the original solution with negligible cost.

3-D minimum-structure inversion of magnetotelluric data using the finite-element method and tetrahedral grids

NASA Astrophysics Data System (ADS)

Jahandari, H.; Farquharson, C. G.

2017-11-01

Unstructured grids enable representing arbitrary structures more accurately and with fewer cells compared to regular structured grids. These grids also allow more efficient refinements compared to rectilinear meshes. In this study, tetrahedral grids are used for the inversion of magnetotelluric (MT) data, which allows for the direct inclusion of topography in the model, for constraining an inversion using a wireframe-based geological model and for local refinement at the observation stations. A minimum-structure method with an iterative model-space Gauss-Newton algorithm for optimization is used. An iterative solver is employed for solving the normal system of equations at each Gauss-Newton step and the sensitivity matrix-vector products that are required by this solver are calculated using pseudo-forward problems. This method alleviates the need to explicitly form the Hessian or Jacobian matrices which significantly reduces the required computation memory. Forward problems are formulated using an edge-based finite-element approach and a sparse direct solver is used for the solutions. This solver allows saving and re-using the factorization of matrices for similar pseudo-forward problems within a Gauss-Newton iteration which greatly minimizes the computation time. Two examples are presented to show the capability of the algorithm: the first example uses a benchmark model while the second example represents a realistic geological setting with topography and a sulphide deposit. The data that are inverted are the full-tensor impedance and the magnetic transfer function vector. The inversions sufficiently recovered the models and reproduced the data, which shows the effectiveness of unstructured grids for complex and realistic MT inversion scenarios. The first example is also used to demonstrate the computational efficiency of the presented model-space method by comparison with its data-space counterpart.

3D unstructured-mesh radiation transport codes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Morel, J.

1997-12-31

Three unstructured-mesh radiation transport codes are currently being developed at Los Alamos National Laboratory. The first code is ATTILA, which uses an unstructured tetrahedral mesh in conjunction with standard Sn (discrete-ordinates) angular discretization, standard multigroup energy discretization, and linear-discontinuous spatial differencing. ATTILA solves the standard first-order form of the transport equation using source iteration in conjunction with diffusion-synthetic acceleration of the within-group source iterations. DANTE is designed to run primarily on workstations. The second code is DANTE, which uses a hybrid finite-element mesh consisting of arbitrary combinations of hexahedra, wedges, pyramids, and tetrahedra. DANTE solves several second-order self-adjoint forms of the transport equation including the even-parity equation, the odd-parity equation, and a new equation called the self-adjoint angular flux equation. DANTE also offers three angular discretization options:more » $$S{_}n$$ (discrete-ordinates), $$P{_}n$$ (spherical harmonics), and $$SP{_}n$$ (simplified spherical harmonics). DANTE is designed to run primarily on massively parallel message-passing machines, such as the ASCI-Blue machines at LANL and LLNL. The third code is PERICLES, which uses the same hybrid finite-element mesh as DANTE, but solves the standard first-order form of the transport equation rather than a second-order self-adjoint form. DANTE uses a standard $$S{_}n$$ discretization in angle in conjunction with trilinear-discontinuous spatial differencing, and diffusion-synthetic acceleration of the within-group source iterations. PERICLES was initially designed to run on workstations, but a version for massively parallel message-passing machines will be built. The three codes will be described in detail and computational results will be presented.« less

Probabilistic Structures Analysis Methods (PSAM) for select space propulsion system components

NASA Technical Reports Server (NTRS)

1991-01-01

The basic formulation for probabilistic finite element analysis is described and demonstrated on a few sample problems. This formulation is based on iterative perturbation that uses the factorized stiffness on the unperturbed system as the iteration preconditioner for obtaining the solution to the perturbed problem. This approach eliminates the need to compute, store and manipulate explicit partial derivatives of the element matrices and force vector, which not only reduces memory usage considerably, but also greatly simplifies the coding and validation tasks. All aspects for the proposed formulation were combined in a demonstration problem using a simplified model of a curved turbine blade discretized with 48 shell elements, and having random pressure and temperature fields with partial correlation, random uniform thickness, and random stiffness at the root.

Modelling the physics in iterative reconstruction for transmission computed tomography

PubMed Central

Nuyts, Johan; De Man, Bruno; Fessler, Jeffrey A.; Zbijewski, Wojciech; Beekman, Freek J.

2013-01-01

There is an increasing interest in iterative reconstruction (IR) as a key tool to improve quality and increase applicability of X-ray CT imaging. IR has the ability to significantly reduce patient dose, it provides the flexibility to reconstruct images from arbitrary X-ray system geometries and it allows to include detailed models of photon transport and detection physics, to accurately correct for a wide variety of image degrading effects. This paper reviews discretisation issues and modelling of finite spatial resolution, Compton scatter in the scanned object, data noise and the energy spectrum. Widespread implementation of IR with highly accurate model-based correction, however, still requires significant effort. In addition, new hardware will provide new opportunities and challenges to improve CT with new modelling. PMID:23739261

Tension Cutoff and Parameter Identification for the Viscoplastic Cap Model.

DTIC Science & Technology

1983-04-01

computer program "VPDRVR" which employs a Crank-Nicolson time integration scheme and a Newton-Raphson iterative solution procedure. Numerical studies were...parameters was illustrated for triaxial stress and uniaxial strain loading for a well- studied sand material (McCormick Ranch Sand). Lastly, a finite element...viscoplastic tension-cutoff cri- terion and to establish parameter identification techniques with experimental data. Herein lies the impetus of this study

Probabilistic homogenization of random composite with ellipsoidal particle reinforcement by the iterative stochastic finite element method

NASA Astrophysics Data System (ADS)

Sokołowski, Damian; Kamiński, Marcin

2018-01-01

This study proposes a framework for determination of basic probabilistic characteristics of the orthotropic homogenized elastic properties of the periodic composite reinforced with ellipsoidal particles and a high stiffness contrast between the reinforcement and the matrix. Homogenization problem, solved by the Iterative Stochastic Finite Element Method (ISFEM) is implemented according to the stochastic perturbation, Monte Carlo simulation and semi-analytical techniques with the use of cubic Representative Volume Element (RVE) of this composite containing single particle. The given input Gaussian random variable is Young modulus of the matrix, while 3D homogenization scheme is based on numerical determination of the strain energy of the RVE under uniform unit stretches carried out in the FEM system ABAQUS. The entire series of several deterministic solutions with varying Young modulus of the matrix serves for the Weighted Least Squares Method (WLSM) recovery of polynomial response functions finally used in stochastic Taylor expansions inherent for the ISFEM. A numerical example consists of the High Density Polyurethane (HDPU) reinforced with the Carbon Black particle. It is numerically investigated (1) if the resulting homogenized characteristics are also Gaussian and (2) how the uncertainty in matrix Young modulus affects the effective stiffness tensor components and their PDF (Probability Density Function).

Investigation of a Parabolic Iterative Solver for Three-dimensional Configurations

NASA Technical Reports Server (NTRS)

Nark, Douglas M.; Watson, Willie R.; Mani, Ramani

2007-01-01

A parabolic iterative solution procedure is investigated that seeks to extend the parabolic approximation used within the internal propagation module of the duct noise propagation and radiation code CDUCT-LaRC. The governing convected Helmholtz equation is split into a set of coupled equations governing propagation in the positive and negative directions. The proposed method utilizes an iterative procedure to solve the coupled equations in an attempt to account for possible reflections from internal bifurcations, impedance discontinuities, and duct terminations. A geometry consistent with the NASA Langley Curved Duct Test Rig is considered and the effects of acoustic treatment and non-anechoic termination are included. Two numerical implementations are studied and preliminary results indicate that improved accuracy in predicted amplitude and phase can be obtained for modes at a cut-off ratio of 1.7. Further predictions for modes at a cut-off ratio of 1.1 show improvement in predicted phase at the expense of increased amplitude error. Possible methods of improvement are suggested based on analytic and numerical analysis. It is hoped that coupling the parabolic iterative approach with less efficient, high fidelity finite element approaches will ultimately provide the capability to perform efficient, higher fidelity acoustic calculations within complex 3-D geometries for impedance eduction and noise propagation and radiation predictions.

Multi-scale transport in the DIII-D ITER baseline scenario with direct electron heating and projection to ITER

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grierson, B. A.; Staebler, G. M.; Solomon, W. M.

Multi-scale fluctuations measured by turbulence diagnostics spanning long and short wavelength spatial scales impact energy confinement and the scale-lengths of plasma kinetic profiles in the DIII-D ITER baseline scenario with direct electron heating. Contrasting discharge phases with ECH + neutral beam injection (NBI) and NBI only at similar rotation reveal higher energy confinement and lower fluctuations when only NBI heating is used. Modeling of the core transport with TGYRO using the TGLF turbulent transport model and NEO neoclassical transport reproduces the experimental profile changes upon application of direct electron heating and indicates that multi-scale transport mechanisms are responsible for changesmore » in the temperature and density profiles. Intermediate and high-k fluctuations appear responsible for the enhanced electron thermal flux, and intermediate-k electron modes produce an inward particle pinch that increases the inverse density scale length. Projection to ITER is performed with TGLF and indicates a density profile that has a finite scale length due to intermediate-k electron modes at low collisionality and increases the fusion gain. Finally, for a range of E×B shear, the dominant mechanism that increases fusion performance is suppression of outward low-k particle flux and increased density peaking.« less

Multi-scale transport in the DIII-D ITER baseline scenario with direct electron heating and projection to ITER

DOE PAGES

Grierson, B. A.; Staebler, G. M.; Solomon, W. M.; ...

2018-02-01

Multi-scale fluctuations measured by turbulence diagnostics spanning long and short wavelength spatial scales impact energy confinement and the scale-lengths of plasma kinetic profiles in the DIII-D ITER baseline scenario with direct electron heating. Contrasting discharge phases with ECH + neutral beam injection (NBI) and NBI only at similar rotation reveal higher energy confinement and lower fluctuations when only NBI heating is used. Modeling of the core transport with TGYRO using the TGLF turbulent transport model and NEO neoclassical transport reproduces the experimental profile changes upon application of direct electron heating and indicates that multi-scale transport mechanisms are responsible for changesmore » in the temperature and density profiles. Intermediate and high-k fluctuations appear responsible for the enhanced electron thermal flux, and intermediate-k electron modes produce an inward particle pinch that increases the inverse density scale length. Projection to ITER is performed with TGLF and indicates a density profile that has a finite scale length due to intermediate-k electron modes at low collisionality and increases the fusion gain. Finally, for a range of E×B shear, the dominant mechanism that increases fusion performance is suppression of outward low-k particle flux and increased density peaking.« less

Multi-scale transport in the DIII-D ITER baseline scenario with direct electron heating and projection to ITER

NASA Astrophysics Data System (ADS)

Grierson, B. A.; Staebler, G. M.; Solomon, W. M.; McKee, G. R.; Holland, C.; Austin, M.; Marinoni, A.; Schmitz, L.; Pinsker, R. I.; DIII-D Team

2018-02-01

Multi-scale fluctuations measured by turbulence diagnostics spanning long and short wavelength spatial scales impact energy confinement and the scale-lengths of plasma kinetic profiles in the DIII-D ITER baseline scenario with direct electron heating. Contrasting discharge phases with ECH + neutral beam injection (NBI) and NBI only at similar rotation reveal higher energy confinement and lower fluctuations when only NBI heating is used. Modeling of the core transport with TGYRO using the TGLF turbulent transport model and NEO neoclassical transport reproduces the experimental profile changes upon application of direct electron heating and indicates that multi-scale transport mechanisms are responsible for changes in the temperature and density profiles. Intermediate and high-k fluctuations appear responsible for the enhanced electron thermal flux, and intermediate-k electron modes produce an inward particle pinch that increases the inverse density scale length. Projection to ITER is performed with TGLF and indicates a density profile that has a finite scale length due to intermediate-k electron modes at low collisionality and increases the fusion gain. For a range of E × B shear, the dominant mechanism that increases fusion performance is suppression of outward low-k particle flux and increased density peaking.

A pseudo energy-invariant method for relativistic wave equations with Riesz space-fractional derivatives

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.; Hendy, A. S.; De Staelen, R. H.

2018-03-01

In this work, we investigate a general nonlinear wave equation with Riesz space-fractional derivatives that generalizes various classical hyperbolic models, including the sine-Gordon and the Klein-Gordon equations from relativistic quantum mechanics. A finite-difference discretization of the model is provided using fractional centered differences. The method is a technique that is capable of preserving an energy-like quantity at each iteration. Some computational comparisons against solutions available in the literature are performed in order to assess the capability of the method to preserve the invariant. Our experiments confirm that the technique yields good approximations to the solutions considered. As an application of our scheme, we provide simulations that confirm, for the first time in the literature, the presence of the phenomenon of nonlinear supratransmission in Riesz space-fractional Klein-Gordon equations driven by a harmonic perturbation at the boundary.

Fourth-order partial differential equation noise removal on welding images

DOE Office of Scientific and Technical Information (OSTI.GOV)

Halim, Suhaila Abd; Ibrahim, Arsmah; Sulong, Tuan Nurul Norazura Tuan

2015-10-22

Partial differential equation (PDE) has become one of the important topics in mathematics and is widely used in various fields. It can be used for image denoising in the image analysis field. In this paper, a fourth-order PDE is discussed and implemented as a denoising method on digital images. The fourth-order PDE is solved computationally using finite difference approach and then implemented on a set of digital radiographic images with welding defects. The performance of the discretized model is evaluated using Peak Signal to Noise Ratio (PSNR). Simulation is carried out on the discretized model on different level of Gaussianmore » noise in order to get the maximum PSNR value. The convergence criteria chosen to determine the number of iterations required is measured based on the highest PSNR value. Results obtained show that the fourth-order PDE model produced promising results as an image denoising tool compared with median filter.« less

On conjugate gradient type methods and polynomial preconditioners for a class of complex non-Hermitian matrices

NASA Technical Reports Server (NTRS)

Freund, Roland

1988-01-01

Conjugate gradient type methods are considered for the solution of large linear systems Ax = b with complex coefficient matrices of the type A = T + i(sigma)I where T is Hermitian and sigma, a real scalar. Three different conjugate gradient type approaches with iterates defined by a minimal residual property, a Galerkin type condition, and an Euclidian error minimization, respectively, are investigated. In particular, numerically stable implementations based on the ideas behind Paige and Saunder's SYMMLQ and MINRES for real symmetric matrices are proposed. Error bounds for all three methods are derived. It is shown how the special shift structure of A can be preserved by using polynomial preconditioning. Results on the optimal choice of the polynomial preconditioner are given. Also, some numerical experiments for matrices arising from finite difference approximations to the complex Helmholtz equation are reported.

Solution of the 2-D steady-state radiative transfer equation in participating media with specular reflections using SUPG and DG finite elements

NASA Astrophysics Data System (ADS)

Le Hardy, D.; Favennec, Y.; Rousseau, B.

2016-08-01

The 2D radiative transfer equation coupled with specular reflection boundary conditions is solved using finite element schemes. Both Discontinuous Galerkin and Streamline-Upwind Petrov-Galerkin variational formulations are fully developed. These two schemes are validated step-by-step for all involved operators (transport, scattering, reflection) using analytical formulations. Numerical comparisons of the two schemes, in terms of convergence rate, reveal that the quadratic SUPG scheme proves efficient for solving such problems. This comparison constitutes the main issue of the paper. Moreover, the solution process is accelerated using block SOR-type iterative methods, for which the determination of the optimal parameter is found in a very cheap way.

Finite-Strain Fractional-Order Viscoelastic (FOV) Material Models and Numerical Methods for Solving Them

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Diethelm, Kai; Gray, Hugh R. (Technical Monitor)

2002-01-01

Fraction-order viscoelastic (FOV) material models have been proposed and studied in 1D since the 1930's, and were extended into three dimensions in the 1970's under the assumption of infinitesimal straining. It was not until 1997 that Drozdov introduced the first finite-strain FOV constitutive equations. In our presentation, we shall continue in this tradition by extending the standard, FOV, fluid and solid, material models introduced in 1971 by Caputo and Mainardi into 3D constitutive formula applicable for finite-strain analyses. To achieve this, we generalize both the convected and co-rotational derivatives of tensor fields to fractional order. This is accomplished by defining them first as body tensor fields and then mapping them into space as objective Cartesian tensor fields. Constitutive equations are constructed using both variants for fractional rate, and their responses are contrasted in simple shear. After five years of research and development, we now possess a basic suite of numerical tools necessary to study finite-strain FOV constitutive equations and their iterative refinement into a mature collection of material models. Numerical methods still need to be developed for efficiently solving fraction al-order integrals, derivatives, and differential equations in a finite element setting where such constitutive formulae would need to be solved at each Gauss point in each element of a finite model, which can number into the millions in today's analysis.

A stable partitioned FSI algorithm for incompressible flow and deforming beams

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, L., E-mail: lil19@rpi.edu; Henshaw, W.D., E-mail: henshw@rpi.edu; Banks, J.W., E-mail: banksj3@rpi.edu

2016-05-01

An added-mass partitioned (AMP) algorithm is described for solving fluid–structure interaction (FSI) problems coupling incompressible flows with thin elastic structures undergoing finite deformations. The new AMP scheme is fully second-order accurate and stable, without sub-time-step iterations, even for very light structures when added-mass effects are strong. The fluid, governed by the incompressible Navier–Stokes equations, is solved in velocity-pressure form using a fractional-step method; large deformations are treated with a mixed Eulerian-Lagrangian approach on deforming composite grids. The motion of the thin structure is governed by a generalized Euler–Bernoulli beam model, and these equations are solved in a Lagrangian frame usingmore » two approaches, one based on finite differences and the other on finite elements. The key AMP interface condition is a generalized Robin (mixed) condition on the fluid pressure. This condition, which is derived at a continuous level, has no adjustable parameters and is applied at the discrete level to couple the partitioned domain solvers. Special treatment of the AMP condition is required to couple the finite-element beam solver with the finite-difference-based fluid solver, and two coupling approaches are described. A normal-mode stability analysis is performed for a linearized model problem involving a beam separating two fluid domains, and it is shown that the AMP scheme is stable independent of the ratio of the mass of the fluid to that of the structure. A traditional partitioned (TP) scheme using a Dirichlet–Neumann coupling for the same model problem is shown to be unconditionally unstable if the added mass of the fluid is too large. A series of benchmark problems of increasing complexity are considered to illustrate the behavior of the AMP algorithm, and to compare the behavior with that of the TP scheme. The results of all these benchmark problems verify the stability and accuracy of the AMP scheme. Results for one benchmark problem modeling blood flow in a deforming artery are also compared with corresponding results available in the literature.« less

Iterated Stretching of Viscoelastic Jets

NASA Technical Reports Server (NTRS)

Chang, Hsueh-Chia; Demekhin, Evgeny A.; Kalaidin, Evgeny

1999-01-01

We examine, with asymptotic analysis and numerical simulation, the iterated stretching dynamics of FENE and Oldroyd-B jets of initial radius r(sub 0), shear viscosity nu, Weissenberg number We, retardation number S, and capillary number Ca. The usual Rayleigh instability stretches the local uniaxial extensional flow region near a minimum in jet radius into a primary filament of radius [Ca(1 - S)/ We](sup 1/2)r(sub 0) between two beads. The strain-rate within the filament remains constant while its radius (elastic stress) decreases (increases) exponentially in time with a long elastic relaxation time 3We(r(sup 2, sub 0)/nu). Instabilities convected from the bead relieve the tension at the necks during this slow elastic drainage and trigger a filament recoil. Secondary filaments then form at the necks from the resulting stretching. This iterated stretching is predicted to occur successively to generate high-generation filaments of radius r(sub n), (r(sub n)/r(sub 0)) = square root of 2[r(sub n-1)/r(sub 0)](sup 3/2) until finite-extensibility effects set in.

Real-time MRI-guided hyperthermia treatment using a fast adaptive algorithm

NASA Astrophysics Data System (ADS)

Stakhursky, Vadim L.; Arabe, Omar; Cheng, Kung-Shan; MacFall, James; Maccarini, Paolo; Craciunescu, Oana; Dewhirst, Mark; Stauffer, Paul; Das, Shiva K.

2009-04-01

Magnetic resonance (MR) imaging is promising for monitoring and guiding hyperthermia treatments. The goal of this work is to investigate the stability of an algorithm for online MR thermal image guided steering and focusing of heat into the target volume. The control platform comprised a four-antenna mini-annular phased array (MAPA) applicator operating at 140 MHz (used for extremity sarcoma heating) and a GE Signa Excite 1.5 T MR system, both of which were driven by a control workstation. MR proton resonance frequency shift images acquired during heating were used to iteratively update a model of the heated object, starting with an initial finite element computed model estimate. At each iterative step, the current model was used to compute a focusing vector, which was then used to drive the next iteration, until convergence. Perturbation of the driving vector was used to prevent the process from stalling away from the desired focus. Experimental validation of the performance of the automatic treatment platform was conducted with two cylindrical phantom studies, one homogeneous and one muscle equivalent with tumor tissue (conductivity 50% higher) inserted, with initial focal spots being intentionally rotated 90° and 50° away from the desired focus, mimicking initial setup errors in applicator rotation. The integrated MR-HT treatment platform steered the focus of heating into the desired target volume in two quite different phantom tissue loads which model expected patient treatment configurations. For the homogeneous phantom test where the target was intentionally offset by 90° rotation of the applicator, convergence to the proper phase focus in the target occurred after 16 iterations of the algorithm. For the more realistic test with a muscle equivalent phantom with tumor inserted with 50° applicator displacement, only two iterations were necessary to steer the focus into the tumor target. Convergence improved the heating efficacy (the ratio of integral temperature in the tumor to integral temperature in normal tissue) by up to six-fold, compared to the first iteration. The integrated MR-HT treatment algorithm successfully steered the focus of heating into the desired target volume for both the simple homogeneous and the more challenging muscle equivalent phantom with tumor insert models of human extremity sarcomas after 16 and 2 iterations, correspondingly. The adaptive method for MR thermal image guided focal steering shows promise when tested in phantom experiments on a four-antenna phased array applicator.

Effect of Geometrical Imperfection on Buckling Failure of ITER VVPSS Tank

NASA Astrophysics Data System (ADS)

Jha, Saroj Kumar; Gupta, Girish Kumar; Pandey, Manish Kumar; Bhattacharya, Avik; Jogi, Gaurav; Bhardwaj, Anil Kumar

2017-04-01

The ‘Vacuum Vessel Pressure Suppression System’ (VVPSS) is part of ITER machine, which is designed to protect the ITER Vacuum Vessel and its connected systems, from an over-pressure situation. It is comprised of a partially evacuated tank of stainless steel approximately 46 m long and 6 m in diameter and thickness 30 mm. It is to hold approximately 675 tonnes of water at room temperature to condense the steam resulting from the adverse water leakage into the Vacuum Vessel chamber. For any vacuum vessel, geometrical imperfection has significant effect on buckling failure and structural integrity. Major geometrical imperfection in VVPSS tank depends on form tolerances. To study the effect of geometrical imperfection on buckling failure of VVPSS tank, finite element analysis (FEA) has been performed in line with ASME section VIII division 2 part 5 [1], ‘design by analysis method’. Linear buckling analysis has been performed to get the buckled shape and displacement. Geometrical imperfection due to form tolerance is incorporated in FEA model of VVPSS tank by scaling the resulted buckled shape by a factor ‘60’. This buckled shape model is used as input geometry for plastic collapse and buckling failure assessment. Plastic collapse and buckling failure of VVPSS tank has been assessed by using the elastic-plastic analysis method. This analysis has been performed for different values of form tolerance. The results of analysis show that displacement and load proportionality factor (LPF) vary inversely with form tolerance. For higher values of form tolerance LPF reduces significantly with high values of displacement.

Seismic tomography of the southern California crust based on spectral-element and adjoint methods

NASA Astrophysics Data System (ADS)

Tape, Carl; Liu, Qinya; Maggi, Alessia; Tromp, Jeroen

2010-01-01

We iteratively improve a 3-D tomographic model of the southern California crust using numerical simulations of seismic wave propagation based on a spectral-element method (SEM) in combination with an adjoint method. The initial 3-D model is provided by the Southern California Earthquake Center. The data set comprises three-component seismic waveforms (i.e. both body and surface waves), filtered over the period range 2-30 s, from 143 local earthquakes recorded by a network of 203 stations. Time windows for measurements are automatically selected by the FLEXWIN algorithm. The misfit function in the tomographic inversion is based on frequency-dependent multitaper traveltime differences. The gradient of the misfit function and related finite-frequency sensitivity kernels for each earthquake are computed using an adjoint technique. The kernels are combined using a source subspace projection method to compute a model update at each iteration of a gradient-based minimization algorithm. The inversion involved 16 iterations, which required 6800 wavefield simulations. The new crustal model, m16, is described in terms of independent shear (VS) and bulk-sound (VB) wave speed variations. It exhibits strong heterogeneity, including local changes of +/-30 per cent with respect to the initial 3-D model. The model reveals several features that relate to geological observations, such as sedimentary basins, exhumed batholiths, and contrasting lithologies across faults. The quality of the new model is validated by quantifying waveform misfits of full-length seismograms from 91 earthquakes that were not used in the tomographic inversion. The new model provides more accurate synthetic seismograms that will benefit seismic hazard assessment.

Adjoint Tomography of the Southern California Crust (Invited) (Invited)

NASA Astrophysics Data System (ADS)

Tape, C.; Liu, Q.; Maggi, A.; Tromp, J.

2009-12-01

We iteratively improve a three-dimensional tomographic model of the southern California crust using numerical simulations of seismic wave propagation based on a spectral-element method (SEM) in combination with an adjoint method. The initial 3D model is provided by the Southern California Earthquake Center. The dataset comprises three-component seismic waveforms (i.e. both body and surface waves), filtered over the period range 2-30 s, from 143 local earthquakes recorded by a network of 203 stations. Time windows for measurements are automatically selected by the FLEXWIN algorithm. The misfit function in the tomographic inversion is based on frequency-dependent multitaper traveltime differences. The gradient of the misfit function and related finite-frequency sensitivity kernels for each earthquake are computed using an adjoint technique. The kernels are combined using a source subspace projection method to compute a model update at each iteration of a gradient-based minimization algorithm. The inversion involved 16 iterations, which required 6800 wavefield simulations and a total of 0.8 million CPU hours. The new crustal model, m16, is described in terms of independent shear (Vs) and bulk-sound (Vb) wavespeed variations. It exhibits strong heterogeneity, including local changes of ±30% with respect to the initial 3D model. The model reveals several features that relate to geologic observations, such as sedimentary basins, exhumed batholiths, and contrasting lithologies across faults. The quality of the new model is validated by quantifying waveform misfits of full-length seismograms from 91 earthquakes that were not used in the tomographic inversion. The new model provides more accurate synthetic seismograms that will benefit seismic hazard assessment.

Iterative updating of model error for Bayesian inversion

NASA Astrophysics Data System (ADS)

Calvetti, Daniela; Dunlop, Matthew; Somersalo, Erkki; Stuart, Andrew

2018-02-01

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when optimization algorithms are used to find a single estimate, or to speed up Markov chain Monte Carlo (MCMC) calculations in the Bayesian framework. The use of an approximate model introduces a discrepancy, or modeling error, that may have a detrimental effect on the solution of the ill-posed inverse problem, or it may severely distort the estimate of the posterior distribution. In the Bayesian paradigm, the modeling error can be considered as a random variable, and by using an estimate of the probability distribution of the unknown, one may estimate the probability distribution of the modeling error and incorporate it into the inversion. We introduce an algorithm which iterates this idea to update the distribution of the model error, leading to a sequence of posterior distributions that are demonstrated empirically to capture the underlying truth with increasing accuracy. Since the algorithm is not based on rejections, it requires only limited full model evaluations. We show analytically that, in the linear Gaussian case, the algorithm converges geometrically fast with respect to the number of iterations when the data is finite dimensional. For more general models, we introduce particle approximations of the iteratively generated sequence of distributions; we also prove that each element of the sequence converges in the large particle limit under a simplifying assumption. We show numerically that, as in the linear case, rapid convergence occurs with respect to the number of iterations. Additionally, we show through computed examples that point estimates obtained from this iterative algorithm are superior to those obtained by neglecting the model error.

Conservative and bounded volume-of-fluid advection on unstructured grids

NASA Astrophysics Data System (ADS)

Ivey, Christopher B.; Moin, Parviz

2017-12-01

This paper presents a novel Eulerian-Lagrangian piecewise-linear interface calculation (PLIC) volume-of-fluid (VOF) advection method, which is three-dimensional, unsplit, and discretely conservative and bounded. The approach is developed with reference to a collocated node-based finite-volume two-phase flow solver that utilizes the median-dual mesh constructed from non-convex polyhedra. The proposed advection algorithm satisfies conservation and boundedness of the liquid volume fraction irrespective of the underlying flux polyhedron geometry, which differs from contemporary unsplit VOF schemes that prescribe topologically complicated flux polyhedron geometries in efforts to satisfy conservation. Instead of prescribing complicated flux-polyhedron geometries, which are prone to topological failures, our VOF advection scheme, the non-intersecting flux polyhedron advection (NIFPA) method, builds the flux polyhedron iteratively such that its intersection with neighboring flux polyhedra, and any other unavailable volume, is empty and its total volume matches the calculated flux volume. During each iteration, a candidate nominal flux polyhedron is extruded using an iteration dependent scalar. The candidate is subsequently intersected with the volume guaranteed available to it at the time of the flux calculation to generate the candidate flux polyhedron. The difference in the volume of the candidate flux polyhedron and the actual flux volume is used to calculate extrusion during the next iteration. The choice in nominal flux polyhedron impacts the cost and accuracy of the scheme; however, it does not impact the methods underlying conservation and boundedness. As such, various robust nominal flux polyhedron are proposed and tested using canonical periodic kinematic test cases: Zalesak's disk and two- and three-dimensional deformation. The tests are conducted on the median duals of a quadrilateral and triangular primal mesh, in two-dimensions, and on the median duals of a hexahedral, wedge and tetrahedral primal mesh, in three-dimensions. Comparisons are made with the adaptation of a conventional unsplit VOF advection scheme to our collocated node-based flow solver. Depending on the choice in the nominal flux polyhedron, the NIFPA scheme presented accuracies ranging from zeroth to second order and calculation times that differed by orders of magnitude. For the nominal flux polyhedra which demonstrate second-order accuracy on all tests and meshes, the NIFPA method's cost was comparable to the traditional topologically complex second-order accurate VOF advection scheme.

A modified Dodge algorithm for the parabolized Navier-Stokes equations and compressible duct flows

NASA Technical Reports Server (NTRS)

Cooke, C. H.; Dwoyer, D. M.

1983-01-01

A revised version of Dodge's split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition. Qualitative agreement with analytical predictions and experimental results was obtained for some flows with well-known solutions. Previously announced in STAR as N82-16363

Effect of partial heating at mid of vertical plate adjacent to porous medium

NASA Astrophysics Data System (ADS)

Mulla, Mohammed Fahimuddin; Pallan, Khalid. M.; Al-Rashed, A. A. A. A.

2018-05-01

Heat and mass transfer in porous medium due to heating of vertical plate at mid-section is analyzed for various physical parameters. The heat and mass transfer in porous medium is modeled with the help of momentum, energy and concentration equations in terms of non-dimensional partial differential equations. The partial differential equations are converted into simpler form of algebraic equations with the help of finite element method. A computer code is developed to assemble the matrix form of algebraic equations into global matrices and then to solve them in an iterative manner to obtain the temperature, concentration and streamline distribution inside the porous medium. It is found that the heat transfer behavior of porous medium heated at middle section is considerably different from other cases.

Numerical simulation of an electrothermal deicer pad. M.S. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Marano, J. J.

1983-01-01

A numerical simulation is developed to investigate the removal of ice from composite aircraft blades by means of electrothermal deicing. The model considers one dimensional, unsteady state heat transfer in the composite blade-ice body. The heat conduction equations are approximated by using the Crank-Nicolson finite difference scheme, and the phase change in the ice layer is handled using the Enthalpy method. To solve the system of equations which result, Gauss-Seidel iteration is used. The simulation computes the temperature profile in the composite blade-ice body, as well as the movement of the ice-water interface, as a function of time. This information can be used to evaluate deicer performance. The simulation can also be used to solve a variety of other heat conduction problems involving composite bodies.

An Improved Treatment of External Boundary for Three-Dimensional Flow Computations

NASA Technical Reports Server (NTRS)

Tsynkov, Semyon V.; Vatsa, Veer N.

1997-01-01

We present an innovative numerical approach for setting highly accurate nonlocal boundary conditions at the external computational boundaries when calculating three-dimensional compressible viscous flows over finite bodies. The approach is based on application of the difference potentials method by V. S. Ryaben'kii and extends our previous technique developed for the two-dimensional case. The new boundary conditions methodology has been successfully combined with the NASA-developed code TLNS3D and used for the analysis of wing-shaped configurations in subsonic and transonic flow regimes. As demonstrated by the computational experiments, the improved external boundary conditions allow one to greatly reduce the size of the computational domain while still maintaining high accuracy of the numerical solution. Moreover, they may provide for a noticeable speedup of convergence of the multigrid iterations.

Genetic algorithms and MCML program for recovery of optical properties of homogeneous turbid media

PubMed Central

Morales Cruzado, Beatriz; y Montiel, Sergio Vázquez; Atencio, José Alberto Delgado

2013-01-01

In this paper, we present and validate a new method for optical properties recovery of turbid media with slab geometry. This method is an iterative method that compares diffuse reflectance and transmittance, measured using integrating spheres, with those obtained using the known algorithm MCML. The search procedure is based in the evolution of a population due to selection of the best individual, i.e., using a genetic algorithm. This new method includes several corrections such as non-linear effects in integrating spheres measurements and loss of light due to the finite size of the sample. As a potential application and proof-of-principle experiment of this new method, we use this new algorithm in the recovery of optical properties of blood samples at different degrees of coagulation. PMID:23504404

Solution of the Fokker-Planck equation with mixing of angular harmonics by beam-beam charge exchange

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mikkelsen, D.R.

1989-09-01

A method for solving the linear Fokker-Planck equation with anisotropic beam-beam charge exchange loss is presented. The 2-D equation is transformed to a system of coupled 1-D equations which are solved iteratively as independent equations. Although isotropic approximations to the beam-beam losses lead to inaccurate fast ion distributions, typically only a few angular harmonics are needed to include accurately the effect of the beam-beam charge exchange loss on the usual integrals of the fast ion distribution. Consequently, the algorithm converges very rapidly and is much more efficient than a 2-D finite difference method. A convenient recursion formula for the couplingmore » coefficients is given and generalization of the method is discussed. 13 refs., 2 figs.« less

Exact exchange-correlation potentials of singlet two-electron systems

NASA Astrophysics Data System (ADS)

Ryabinkin, Ilya G.; Ospadov, Egor; Staroverov, Viktor N.

2017-10-01

We suggest a non-iterative analytic method for constructing the exchange-correlation potential, v XC ( r ) , of any singlet ground-state two-electron system. The method is based on a convenient formula for v XC ( r ) in terms of quantities determined only by the system's electronic wave function, exact or approximate, and is essentially different from the Kohn-Sham inversion technique. When applied to Gaussian-basis-set wave functions, the method yields finite-basis-set approximations to the corresponding basis-set-limit v XC ( r ) , whereas the Kohn-Sham inversion produces physically inappropriate (oscillatory and divergent) potentials. The effectiveness of the procedure is demonstrated by computing accurate exchange-correlation potentials of several two-electron systems (helium isoelectronic series, H2, H3 + ) using common ab initio methods and Gaussian basis sets.

One-Dimensional Ablation with Pyrolysis Gas Flow Using a Full Newton's Method and Finite Control Volume Procedure

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Blackwell, Ben F.; Edwards, Jack R.

2007-01-01

The development and verification of a one-dimensional material thermal response code with ablation is presented. The implicit time integrator, control volume finite element spatial discretization, and Newton's method for nonlinear iteration on the entire system of residual equations have been implemented and verified for the thermochemical ablation of internally decomposing materials. This study is a continuation of the work presented in "One-Dimensional Ablation with Pyrolysis Gas Flow Using a Full Newton's Method and Finite Control Volume Procedure" (AIAA-2006-2910), which described the derivation, implementation, and verification of the constant density solid energy equation terms and boundary conditions. The present study extends the model to decomposing materials including decomposition kinetics, pyrolysis gas flow through the porous char layer, and a mixture (solid and gas) energy equation. Verification results are presented for the thermochemical ablation of a carbon-phenolic ablator which involves the solution of the entire system of governing equations.

Towards mechanism-based simulation of impact damage using exascale computing

NASA Astrophysics Data System (ADS)

Shterenlikht, Anton; Margetts, Lee; McDonald, Samuel; Bourne, Neil K.

2017-01-01

Over the past 60 years, the finite element method has been very successful in modelling deformation in engineering structures. However the method requires the definition of constitutive models that represent the response of the material to applied loads. There are two issues. Firstly, the models are often difficult to define. Secondly, there is often no physical connection between the models and the mechanisms that accommodate deformation. In this paper, we present a potentially disruptive two-level strategy which couples the finite element method at the macroscale with cellular automata at the mesoscale. The cellular automata are used to simulate mechanisms, such as crack propagation. The stress-strain relationship emerges as a continuum mechanics scale interpretation of changes at the micro- and meso-scales. Iterative two-way updating between the cellular automata and finite elements drives the simulation forward as the material undergoes progressive damage at high strain rates. The strategy is particularly attractive on large-scale computing platforms as both methods scale well on tens of thousands of CPUs.

A high order accurate finite element algorithm for high Reynolds number flow prediction

NASA Technical Reports Server (NTRS)

Baker, A. J.

1978-01-01

A Galerkin-weighted residuals formulation is employed to establish an implicit finite element solution algorithm for generally nonlinear initial-boundary value problems. Solution accuracy, and convergence rate with discretization refinement, are quantized in several error norms, by a systematic study of numerical solutions to several nonlinear parabolic and a hyperbolic partial differential equation characteristic of the equations governing fluid flows. Solutions are generated using selective linear, quadratic and cubic basis functions. Richardson extrapolation is employed to generate a higher-order accurate solution to facilitate isolation of truncation error in all norms. Extension of the mathematical theory underlying accuracy and convergence concepts for linear elliptic equations is predicted for equations characteristic of laminar and turbulent fluid flows at nonmodest Reynolds number. The nondiagonal initial-value matrix structure introduced by the finite element theory is determined intrinsic to improved solution accuracy and convergence. A factored Jacobian iteration algorithm is derived and evaluated to yield a consequential reduction in both computer storage and execution CPU requirements while retaining solution accuracy.

A locally conservative stabilized continuous Galerkin finite element method for two-phase flow in poroelastic subsurfaces

NASA Astrophysics Data System (ADS)

Deng, Q.; Ginting, V.; McCaskill, B.; Torsu, P.

2017-10-01

We study the application of a stabilized continuous Galerkin finite element method (CGFEM) in the simulation of multiphase flow in poroelastic subsurfaces. The system involves a nonlinear coupling between the fluid pressure, subsurface's deformation, and the fluid phase saturation, and as such, we represent this coupling through an iterative procedure. Spatial discretization of the poroelastic system employs the standard linear finite element in combination with a numerical diffusion term to maintain stability of the algebraic system. Furthermore, direct calculation of the normal velocities from pressure and deformation does not entail a locally conservative field. To alleviate this drawback, we propose an element based post-processing technique through which local conservation can be established. The performance of the method is validated through several examples illustrating the convergence of the method, the effectivity of the stabilization term, and the ability to achieve locally conservative normal velocities. Finally, the efficacy of the method is demonstrated through simulations of realistic multiphase flow in poroelastic subsurfaces.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wannamaker, Philip E.

We have developed an algorithm for the inversion of magnetotelluric (MT) data to a 3D earth resistivity model based upon the finite element method. Hexahedral edge finite elements are implemented to accommodate discontinuities in the electric field across resistivity boundaries, and to accurately simulate topographic variations. All matrices are reduced and solved using direct solution modules which avoids ill-conditioning endemic to iterative solvers such as conjugate gradients, principally PARDISO for the finite element system and PLASMA for the parameter step estimate. Large model parameterizations can be handled by transforming the Gauss-Newton estimator to data-space form. Accuracy of the forward problemmore » and jacobians has been checked by comparison to integral equations results and by limiting asymptotes. Inverse accuracy and performance has been verified against the public Dublin Secret Test Model 2 and the well-known Mount St Helens 3D MT data set. This algorithm we believe is the most capable yet for forming 3D images of earth resistivity structure and their implications for geothermal fluids and pathways.« less

An analytical/numerical correlation study of the multiple concentric cylinder model for the thermoplastic response of metal matrix composites

NASA Technical Reports Server (NTRS)

Pindera, Marek-Jerzy; Salzar, Robert S.; Williams, Todd O.

1993-01-01

The utility of a recently developed analytical micromechanics model for the response of metal matrix composites under thermal loading is illustrated by comparison with the results generated using the finite-element approach. The model is based on the concentric cylinder assemblage consisting of an arbitrary number of elastic or elastoplastic sublayers with isotropic or orthotropic, temperature-dependent properties. The elastoplastic boundary-value problem of an arbitrarily layered concentric cylinder is solved using the local/global stiffness matrix formulation (originally developed for elastic layered media) and Mendelson's iterative technique of successive elastic solutions. These features of the model facilitate efficient investigation of the effects of various microstructural details, such as functionally graded architectures of interfacial layers, on the evolution of residual stresses during cool down. The available closed-form expressions for the field variables can readily be incorporated into an optimization algorithm in order to efficiently identify optimal configurations of graded interfaces for given applications. Comparison of residual stress distributions after cool down generated using finite-element analysis and the present micromechanics model for four composite systems with substantially different temperature-dependent elastic, plastic, and thermal properties illustrates the efficacy of the developed analytical scheme.

Asymptotic theory of two-dimensional trailing-edge flows

NASA Technical Reports Server (NTRS)

Melnik, R. E.; Chow, R.

1975-01-01

Problems of laminar and turbulent viscous interaction near trailing edges of streamlined bodies are considered. Asymptotic expansions of the Navier-Stokes equations in the limit of large Reynolds numbers are used to describe the local solution near the trailing edge of cusped or nearly cusped airfoils at small angles of attack in compressible flow. A complicated inverse iterative procedure, involving finite-difference solutions of the triple-deck equations coupled with asymptotic solutions of the boundary values, is used to accurately solve the viscous interaction problem. Results are given for the correction to the boundary-layer solution for drag of a finite flat plate at zero angle of attack and for the viscous correction to the lift of an airfoil at incidence. A rational asymptotic theory is developed for treating turbulent interactions near trailing edges and is shown to lead to a multilayer structure of turbulent boundary layers. The flow over most of the boundary layer is described by a Lighthill model of inviscid rotational flow. The main features of the model are discussed and a sample solution for the skin friction is obtained and compared with the data of Schubauer and Klebanoff for a turbulent flow in a moderately large adverse pressure gradient.

A Simple Algebraic Grid Adaptation Scheme with Applications to Two- and Three-dimensional Flow Problems

NASA Technical Reports Server (NTRS)

Hsu, Andrew T.; Lytle, John K.

1989-01-01

An algebraic adaptive grid scheme based on the concept of arc equidistribution is presented. The scheme locally adjusts the grid density based on gradients of selected flow variables from either finite difference or finite volume calculations. A user-prescribed grid stretching can be specified such that control of the grid spacing can be maintained in areas of known flowfield behavior. For example, the grid can be clustered near a wall for boundary layer resolution and made coarse near the outer boundary of an external flow. A grid smoothing technique is incorporated into the adaptive grid routine, which is found to be more robust and efficient than the weight function filtering technique employed by other researchers. Since the present algebraic scheme requires no iteration or solution of differential equations, the computer time needed for grid adaptation is trivial, making the scheme useful for three-dimensional flow problems. Applications to two- and three-dimensional flow problems show that a considerable improvement in flowfield resolution can be achieved by using the proposed adaptive grid scheme. Although the scheme was developed with steady flow in mind, it is a good candidate for unsteady flow computations because of its efficiency.

A Rigorous Solution for Finite-State Inflow throughout the Flowfield

NASA Astrophysics Data System (ADS)

Fei, Zhongyang

In this research, the Hseih/Duffy model is extended to all three velocity components of inflow across the rotor disk in a mathematically rigorous way so that it can be used to calculate the inflow below the rotor disk plane. This establishes a complete dynamic inflow model for the entire flow field with finite state method. The derivation is for the case of general skewed angle. The cost of the new method is that one needs to compute the co-states of the inflow equations in the upper hemisphere along with the normal states. Numerical comparisons with exact solutions for the z-component of flow in axial and skewed angle flow demonstrate excellent correlation with closed-form solutions. The simulations also illustrate that the model is valid at both the frequency domain and the time domain. Meanwhile, in order to accelerate the convergence, an optimization of even terms is used to minimize the error in the axial component of the induced velocity in the on and on/off disk region. A novel method for calculating associate Legendre function of the second kind is also developed to solve the problem of divergence of Q¯mn (ieta) for large eta with the iterative method. An application of the new model is also conducted to compute inflow in the wake of a rotor with a finite number of blades. The velocities are plotted at different distances from the rotor disk and are compared with the Glauert prediction for axial flow and wake swirl. In the finite-state model, the angular momentum does not jump instantaneously across the disk, but it does transition rapidly across the disk to correct Glauert value.

On Dynamics of Spinning Structures

NASA Technical Reports Server (NTRS)

Gupta, K. K.; Ibrahim, A.

2012-01-01

This paper provides details of developments pertaining to vibration analysis of gyroscopic systems, that involves a finite element structural discretization followed by the solution of the resulting matrix eigenvalue problem by a progressive, accelerated simultaneous iteration technique. Thus Coriolis, centrifugal and geometrical stiffness matrices are derived for shell and line elements, followed by the eigensolution details as well as solution of representative problems that demonstrates the efficacy of the currently developed numerical procedures and tools.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cao, Yong; Chu, Yuchuan; He, Xiaoming

This paper proposes a domain decomposition method for the coupled stationary Navier-Stokes and Darcy equations with the Beavers-Joseph-Saffman interface condition in order to improve the efficiency of the finite element method. The physical interface conditions are directly utilized to construct the boundary conditions on the interface and then decouple the Navier-Stokes and Darcy equations. Newton iteration will be used to deal with the nonlinear systems. Numerical results are presented to illustrate the features of the proposed method.

A new approach to blind deconvolution of astronomical images

NASA Astrophysics Data System (ADS)

Vorontsov, S. V.; Jefferies, S. M.

2017-05-01

We readdress the strategy of finding approximate regularized solutions to the blind deconvolution problem, when both the object and the point-spread function (PSF) have finite support. Our approach consists in addressing fixed points of an iteration in which both the object x and the PSF y are approximated in an alternating manner, discarding the previous approximation for x when updating x (similarly for y), and considering the resultant fixed points as candidates for a sensible solution. Alternating approximations are performed by truncated iterative least-squares descents. The number of descents in the object- and in the PSF-space play a role of two regularization parameters. Selection of appropriate fixed points (which may not be unique) is performed by relaxing the regularization gradually, using the previous fixed point as an initial guess for finding the next one, which brings an approximation of better spatial resolution. We report the results of artificial experiments with noise-free data, targeted at examining the potential capability of the technique to deconvolve images of high complexity. We also show the results obtained with two sets of satellite images acquired using ground-based telescopes with and without adaptive optics compensation. The new approach brings much better results when compared with an alternating minimization technique based on positivity-constrained conjugate gradients, where the iterations stagnate when addressing data of high complexity. In the alternating-approximation step, we examine the performance of three different non-blind iterative deconvolution algorithms. The best results are provided by the non-negativity-constrained successive over-relaxation technique (+SOR) supplemented with an adaptive scheduling of the relaxation parameter. Results of comparable quality are obtained with steepest descents modified by imposing the non-negativity constraint, at the expense of higher numerical costs. The Richardson-Lucy (or expectation-maximization) algorithm fails to locate stable fixed points in our experiments, due apparently to inappropriate regularization properties.

Extending substructure based iterative solvers to multiple load and repeated analyses

NASA Technical Reports Server (NTRS)

Farhat, Charbel

1993-01-01

Direct solvers currently dominate commercial finite element structural software, but do not scale well in the fine granularity regime targeted by emerging parallel processors. Substructure based iterative solvers--often called also domain decomposition algorithms--lend themselves better to parallel processing, but must overcome several obstacles before earning their place in general purpose structural analysis programs. One such obstacle is the solution of systems with many or repeated right hand sides. Such systems arise, for example, in multiple load static analyses and in implicit linear dynamics computations. Direct solvers are well-suited for these problems because after the system matrix has been factored, the multiple or repeated solutions can be obtained through relatively inexpensive forward and backward substitutions. On the other hand, iterative solvers in general are ill-suited for these problems because they often must restart from scratch for every different right hand side. In this paper, we present a methodology for extending the range of applications of domain decomposition methods to problems with multiple or repeated right hand sides. Basically, we formulate the overall problem as a series of minimization problems over K-orthogonal and supplementary subspaces, and tailor the preconditioned conjugate gradient algorithm to solve them efficiently. The resulting solution method is scalable, whereas direct factorization schemes and forward and backward substitution algorithms are not. We illustrate the proposed methodology with the solution of static and dynamic structural problems, and highlight its potential to outperform forward and backward substitutions on parallel computers. As an example, we show that for a linear structural dynamics problem with 11640 degrees of freedom, every time-step beyond time-step 15 is solved in a single iteration and consumes 1.0 second on a 32 processor iPSC-860 system; for the same problem and the same parallel processor, a pair of forward/backward substitutions at each step consumes 15.0 seconds.

FINIFLUX: An implicit finite element model for quantification of groundwater fluxes and hyporheic exchange in streams and rivers using radon

NASA Astrophysics Data System (ADS)

Frei, S.; Gilfedder, B. S.

2015-08-01

A quantitative understanding of groundwater-surface water interactions is vital for sustainable management of water quantity and quality. The noble gas radon-222 (Rn) is becoming increasingly used as a sensitive tracer to quantify groundwater discharge to wetlands, lakes, and rivers: a development driven by technical and methodological advances in Rn measurement. However, quantitative interpretation of these data is not trivial, and the methods used to date are based on the simplest solutions to the mass balance equation (e.g., first-order finite difference and inversion). Here we present a new implicit numerical model (FINIFLUX) based on finite elements for quantifying groundwater discharge to streams and rivers using Rn surveys at the reach scale (1-50 km). The model is coupled to a state-of-the-art parameter optimization code Parallel-PEST to iteratively solve the mass balance equation for groundwater discharge and hyporheic exchange. The major benefit of this model is that it is programed to be very simple to use, reduces nonuniqueness, and provides numerically stable estimates of groundwater fluxes and hyporheic residence times from field data. FINIFLUX was tested against an analytical solution and then implemented on two German rivers of differing magnitude, the Salzach (˜112 m3 s-1) and the Rote Main (˜4 m3 s-1). We show that using previous inversion techniques numerical instability can lead to physically impossible negative values, whereas the new model provides stable positive values for all scenarios. We hope that by making FINIFLUX freely available to the community that Rn might find wider application in quantifying groundwater discharge to streams and rivers and thus assist in a combined management of surface and groundwater systems.

Vector form Intrinsic Finite Element Method for the Two-Dimensional Analysis of Marine Risers with Large Deformations

NASA Astrophysics Data System (ADS)

Li, Xiaomin; Guo, Xueli; Guo, Haiyan

2018-06-01

Robust numerical models that describe the complex behaviors of risers are needed because these constitute dynamically sensitive systems. This paper presents a simple and efficient algorithm for the nonlinear static and dynamic analyses of marine risers. The proposed approach uses the vector form intrinsic finite element (VFIFE) method, which is based on vector mechanics theory and numerical calculation. In this method, the risers are described by a set of particles directly governed by Newton's second law and are connected by weightless elements that can only resist internal forces. The method does not require the integration of the stiffness matrix, nor does it need iterations to solve the governing equations. Due to these advantages, the method can easily increase or decrease the element and change the boundary conditions, thus representing an innovative concept of solving nonlinear behaviors, such as large deformation and large displacement. To prove the feasibility of the VFIFE method in the analysis of the risers, rigid and flexible risers belonging to two different categories of marine risers, which usually have differences in modeling and solving methods, are employed in the present study. In the analysis, the plane beam element is adopted in the simulation of interaction forces between the particles and the axial force, shear force, and bending moment are also considered. The results are compared with the conventional finite element method (FEM) and those reported in the related literature. The findings revealed that both the rigid and flexible risers could be modeled in a similar unified analysis model and that the VFIFE method is feasible for solving problems related to the complex behaviors of marine risers.

Influence of Reinforcement Anisotropy on the Stress Distribution in Tension and Shear of a Fusion Magnet Insulation System

NASA Astrophysics Data System (ADS)

Humer, K.; Raff, S.; Prokopec, R.; Weber, H. W.

2008-03-01

A glass fiber reinforced plastic laminate, which consists of half-overlapped wrapped Kapton/R-glass-fiber reinforcing tapes vacuum-pressure impregnated in a cyanate ester/epoxy blend, is proposed as the insulation system for the ITER Toroidal Field coils. In order to assess its mechanical performance under the actual operating conditions, cryogenic (77 K) tensile and interlaminar shear tests were done after irradiation to the ITER design fluence of 1×1022 m-2 (E>0.1 MeV). The data were then used for a Finite Element Method (FEM) stress analysis. We find that the mechanical strength and the fracture behavior as well as the stress distribution and the failure criteria are strongly influenced by the winding direction and the wrapping technique of the reinforcing tapes.

Application of Conjugate Gradient methods to tidal simulation

USGS Publications Warehouse

Barragy, E.; Carey, G.F.; Walters, R.A.

1993-01-01

A harmonic decomposition technique is applied to the shallow water equations to yield a complex, nonsymmetric, nonlinear, Helmholtz type problem for the sea surface and an accompanying complex, nonlinear diagonal problem for the velocities. The equation for the sea surface is linearized using successive approximation and then discretized with linear, triangular finite elements. The study focuses on applying iterative methods to solve the resulting complex linear systems. The comparative evaluation includes both standard iterative methods for the real subsystems and complex versions of the well known Bi-Conjugate Gradient and Bi-Conjugate Gradient Squared methods. Several Incomplete LU type preconditioners are discussed, and the effects of node ordering, rejection strategy, domain geometry and Coriolis parameter (affecting asymmetry) are investigated. Implementation details for the complex case are discussed. Performance studies are presented and comparisons made with a frontal solver. ?? 1993.

A method for the dynamic and thermal stress analysis of space shuttle surface insulation

NASA Technical Reports Server (NTRS)

Ojalvo, I. U.; Levy, A.; Austin, F.

1975-01-01

The thermal protection system of the space shuttle consists of thousands of separate insulation tiles bonded to the orbiter's surface through a soft strain-isolation layer. The individual tiles are relatively thick and possess nonuniform properties. Therefore, each is idealized by finite-element assemblages containing up to 2500 degrees of freedom. Since the tiles affixed to a given structural panel will, in general, interact with one another, application of the standard direct-stiffness method would require equation systems involving excessive numbers of unknowns. This paper presents a method which overcomes this problem through an efficient iterative procedure which requires treatment of only a single tile at any given time. Results of associated static, dynamic, and thermal stress analyses and sufficient conditions for convergence of the iterative solution method are given.

Inverse source problems in elastodynamics

NASA Astrophysics Data System (ADS)

Bao, Gang; Hu, Guanghui; Kian, Yavar; Yin, Tao

2018-04-01

We are concerned with time-dependent inverse source problems in elastodynamics. The source term is supposed to be the product of a spatial function and a temporal function with compact support. We present frequency-domain and time-domain approaches to show uniqueness in determining the spatial function from wave fields on a large sphere over a finite time interval. The stability estimate of the temporal function from the data of one receiver and the uniqueness result using partial boundary data are proved. Our arguments rely heavily on the use of the Fourier transform, which motivates inversion schemes that can be easily implemented. A Landweber iterative algorithm for recovering the spatial function and a non-iterative inversion scheme based on the uniqueness proof for recovering the temporal function are proposed. Numerical examples are demonstrated in both two and three dimensions.

A constrained modulus reconstruction technique for breast cancer assessment.

PubMed

Samani, A; Bishop, J; Plewes, D B

2001-09-01

A reconstruction technique for breast tissue elasticity modulus is described. This technique assumes that the geometry of normal and suspicious tissues is available from a contrast-enhanced magnetic resonance image. Furthermore, it is assumed that the modulus is constant throughout each tissue volume. The technique, which uses quasi-static strain data, is iterative where each iteration involves modulus updating followed by stress calculation. Breast mechanical stimulation is assumed to be done by two compressional rigid plates. As a result, stress is calculated using the finite element method based on the well-controlled boundary conditions of the compression plates. Using the calculated stress and the measured strain, modulus updating is done element-by-element based on Hooke's law. Breast tissue modulus reconstruction using simulated data and phantom modulus reconstruction using experimental data indicate that the technique is robust.

A finite element based method for solution of optimal control problems

NASA Technical Reports Server (NTRS)

Bless, Robert R.; Hodges, Dewey H.; Calise, Anthony J.

1989-01-01

A temporal finite element based on a mixed form of the Hamiltonian weak principle is presented for optimal control problems. The mixed form of this principle contains both states and costates as primary variables that are expanded in terms of elemental values and simple shape functions. Unlike other variational approaches to optimal control problems, however, time derivatives of the states and costates do not appear in the governing variational equation. Instead, the only quantities whose time derivatives appear therein are virtual states and virtual costates. Also noteworthy among characteristics of the finite element formulation is the fact that in the algebraic equations which contain costates, they appear linearly. Thus, the remaining equations can be solved iteratively without initial guesses for the costates; this reduces the size of the problem by about a factor of two. Numerical results are presented herein for an elementary trajectory optimization problem which show very good agreement with the exact solution along with excellent computational efficiency and self-starting capability. The goal is to evaluate the feasibility of this approach for real-time guidance applications. To this end, a simplified two-stage, four-state model for an advanced launch vehicle application is presented which is suitable for finite element solution.

Iterative and variational homogenization methods for filled elastomers

NASA Astrophysics Data System (ADS)

Goudarzi, Taha

Elastomeric composites have increasingly proved invaluable in commercial technological applications due to their unique mechanical properties, especially their ability to undergo large reversible deformation in response to a variety of stimuli (e.g., mechanical forces, electric and magnetic fields, changes in temperature). Modern advances in organic materials science have revealed that elastomeric composites hold also tremendous potential to enable new high-end technologies, especially as the next generation of sensors and actuators featured by their low cost together with their biocompatibility, and processability into arbitrary shapes. This potential calls for an in-depth investigation of the macroscopic mechanical/physical behavior of elastomeric composites directly in terms of their microscopic behavior with the objective of creating the knowledge base needed to guide their bottom-up design. The purpose of this thesis is to generate a mathematical framework to describe, explain, and predict the macroscopic nonlinear elastic behavior of filled elastomers, arguably the most prominent class of elastomeric composites, directly in terms of the behavior of their constituents --- i.e., the elastomeric matrix and the filler particles --- and their microstructure --- i.e., the content, size, shape, and spatial distribution of the filler particles. This will be accomplished via a combination of novel iterative and variational homogenization techniques capable of accounting for interphasial phenomena and finite deformations. Exact and approximate analytical solutions for the fundamental nonlinear elastic response of dilute suspensions of rigid spherical particles (either firmly bonded or bonded through finite size interphases) in Gaussian rubber are first generated. These results are in turn utilized to construct approximate solutions for the nonlinear elastic response of non-Gaussian elastomers filled with a random distribution of rigid particles (again, either firmly bonded or bonded through finite size interphases) at finite concentrations. Three-dimensional finite element simulations are also carried out to gain further insight into the proposed theoretical solutions. Inter alia, we make use of these solutions to examine the effects of particle concentration, mono- and poly-dispersity of the filler particle size, and the presence of finite size interphases on the macroscopic response of filled elastomers. The solutions are found able to explain and describe experimental results that to date have been understood only in part. More generally, the solutions provide a robust tool to efficiently guide the design of filled elastomers with desired macroscopic properties. The homogenization techniques developed in this work are not limited to nonlinear elasticity, but can be readily utilized to study multi-functional properties as well. For demonstration purposes, we work out a novel exact solution for the macroscopic dielectric response of filled elastomers with interphasial space charges.

The finite element model for the propagation of light in scattering media: a direct method for domains with nonscattering regions.

PubMed

Arridge, S R; Dehghani, H; Schweiger, M; Okada, E

2000-01-01

We present a method for handling nonscattering regions within diffusing domains. The method develops from an iterative radiosity-diffusion approach using Green's functions that was computationally slow. Here we present an improved implementation using a finite element method (FEM) that is direct. The fundamental idea is to introduce extra equations into the standard diffusion FEM to represent nondiffusive light propagation across a nonscattering region. By appropriate mesh node ordering the computational time is not much greater than for diffusion alone. We compare results from this method with those from a discrete ordinate transport code, and with Monte Carlo calculations. The agreement is very good, and, in addition, our scheme allows us to easily model time-dependent and frequency domain problems.

High-order solution methods for grey discrete ordinates thermal radiative transfer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maginot, Peter G., E-mail: maginot1@llnl.gov; Ragusa, Jean C., E-mail: jean.ragusa@tamu.edu; Morel, Jim E., E-mail: morel@tamu.edu

This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

High-order solution methods for grey discrete ordinates thermal radiative transfer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

This paper presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

High-order solution methods for grey discrete ordinates thermal radiative transfer

DOE PAGES

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

2016-09-29

This paper presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

Finite element implementation of state variable-based viscoplasticity models

NASA Technical Reports Server (NTRS)

Iskovitz, I.; Chang, T. Y. P.; Saleeb, A. F.

1991-01-01

The implementation of state variable-based viscoplasticity models is made in a general purpose finite element code for structural applications of metals deformed at elevated temperatures. Two constitutive models, Walker's and Robinson's models, are studied in conjunction with two implicit integration methods: the trapezoidal rule with Newton-Raphson iterations and an asymptotic integration algorithm. A comparison is made between the two integration methods, and the latter method appears to be computationally more appealing in terms of numerical accuracy and CPU time. However, in order to make the asymptotic algorithm robust, it is necessary to include a self adaptive scheme with subincremental step control and error checking of the Jacobian matrix at the integration points. Three examples are given to illustrate the numerical aspects of the integration methods tested.

A multilevel finite element method for Fredholm integral eigenvalue problems

NASA Astrophysics Data System (ADS)

Xie, Hehu; Zhou, Tao

2015-12-01

In this work, we proposed a multigrid finite element (MFE) method for solving the Fredholm integral eigenvalue problems. The main motivation for such studies is to compute the Karhunen-Loève expansions of random fields, which play an important role in the applications of uncertainty quantification. In our MFE framework, solving the eigenvalue problem is converted to doing a series of integral iterations and eigenvalue solving in the coarsest mesh. Then, any existing efficient integration scheme can be used for the associated integration process. The error estimates are provided, and the computational complexity is analyzed. It is noticed that the total computational work of our method is comparable with a single integration step in the finest mesh. Several numerical experiments are presented to validate the efficiency of the proposed numerical method.

Accuracy and convergence of coupled finite-volume/Monte Carlo codes for plasma edge simulations of nuclear fusion reactors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghoos, K., E-mail: kristel.ghoos@kuleuven.be; Dekeyser, W.; Samaey, G.

2016-10-01

The plasma and neutral transport in the plasma edge of a nuclear fusion reactor is usually simulated using coupled finite volume (FV)/Monte Carlo (MC) codes. However, under conditions of future reactors like ITER and DEMO, convergence issues become apparent. This paper examines the convergence behaviour and the numerical error contributions with a simplified FV/MC model for three coupling techniques: Correlated Sampling, Random Noise and Robbins Monro. Also, practical procedures to estimate the errors in complex codes are proposed. Moreover, first results with more complex models show that an order of magnitude speedup can be achieved without any loss in accuracymore » by making use of averaging in the Random Noise coupling technique.« less

A hybrid finite-difference and analytic element groundwater model

USGS Publications Warehouse

Haitjema, Henk M.; Feinstein, Daniel T.; Hunt, Randall J.; Gusyev, Maksym

2010-01-01

Regional finite-difference models tend to have large cell sizes, often on the order of 1–2 km on a side. Although the regional flow patterns in deeper formations may be adequately represented by such a model, the intricate surface water and groundwater interactions in the shallower layers are not. Several stream reaches and nearby wells may occur in a single cell, precluding any meaningful modeling of the surface water and groundwater interactions between the individual features. We propose to replace the upper MODFLOW layer or layers, in which the surface water and groundwater interactions occur, by an analytic element model (GFLOW) that does not employ a model grid; instead, it represents wells and surface waters directly by the use of point-sinks and line-sinks. For many practical cases it suffices to provide GFLOW with the vertical leakage rates calculated in the original coarse MODFLOW model in order to obtain a good representation of surface water and groundwater interactions. However, when the combined transmissivities in the deeper (MODFLOW) layers dominate, the accuracy of the GFLOW solution diminishes. For those cases, an iterative coupling procedure, whereby the leakages between the GFLOW and MODFLOW model are updated, appreciably improves the overall solution, albeit at considerable computational cost. The coupled GFLOW–MODFLOW model is applicable to relatively large areas, in many cases to the entire model domain, thus forming an attractive alternative to local grid refinement or inset models.

Higher-order ice-sheet modelling accelerated by multigrid on graphics cards

NASA Astrophysics Data System (ADS)

Brædstrup, Christian; Egholm, David

2013-04-01

Higher-order ice flow modelling is a very computer intensive process owing primarily to the nonlinear influence of the horizontal stress coupling. When applied for simulating long-term glacial landscape evolution, the ice-sheet models must consider very long time series, while both high temporal and spatial resolution is needed to resolve small effects. The use of higher-order and full stokes models have therefore seen very limited usage in this field. However, recent advances in graphics card (GPU) technology for high performance computing have proven extremely efficient in accelerating many large-scale scientific computations. The general purpose GPU (GPGPU) technology is cheap, has a low power consumption and fits into a normal desktop computer. It could therefore provide a powerful tool for many glaciologists working on ice flow models. Our current research focuses on utilising the GPU as a tool in ice-sheet and glacier modelling. To this extent we have implemented the Integrated Second-Order Shallow Ice Approximation (iSOSIA) equations on the device using the finite difference method. To accelerate the computations, the GPU solver uses a non-linear Red-Black Gauss-Seidel iterator coupled with a Full Approximation Scheme (FAS) multigrid setup to further aid convergence. The GPU finite difference implementation provides the inherent parallelization that scales from hundreds to several thousands of cores on newer cards. We demonstrate the efficiency of the GPU multigrid solver using benchmark experiments.

A Fortran 77 computer code for damped least-squares inversion of Slingram electromagnetic anomalies over thin tabular conductors

NASA Astrophysics Data System (ADS)

Dondurur, Derman; Sarı, Coşkun

2004-07-01

A FORTRAN 77 computer code is presented that permits the inversion of Slingram electromagnetic anomalies to an optimal conductor model. Damped least-squares inversion algorithm is used to estimate the anomalous body parameters, e.g. depth, dip and surface projection point of the target. Iteration progress is controlled by maximum relative error value and iteration continued until a tolerance value was satisfied, while the modification of Marquardt's parameter is controlled by sum of the squared errors value. In order to form the Jacobian matrix, the partial derivatives of theoretical anomaly expression with respect to the parameters being optimised are calculated by numerical differentiation by using first-order forward finite differences. A theoretical and two field anomalies are inserted to test the accuracy and applicability of the present inversion program. Inversion of the field data indicated that depth and the surface projection point parameters of the conductor are estimated correctly, however, considerable discrepancies appeared on the estimated dip angles. It is therefore concluded that the most important factor resulting in the misfit between observed and calculated data is due to the fact that the theory used for computing Slingram anomalies is valid for only thin conductors and this assumption might have caused incorrect dip estimates in the case of wide conductors.

A quantum algorithm for obtaining the lowest eigenstate of a Hamiltonian assisted with an ancillary qubit system

NASA Astrophysics Data System (ADS)

Bang, Jeongho; Lee, Seung-Woo; Lee, Chang-Woo; Jeong, Hyunseok

2015-01-01

We propose a quantum algorithm to obtain the lowest eigenstate of any Hamiltonian simulated by a quantum computer. The proposed algorithm begins with an arbitrary initial state of the simulated system. A finite series of transforms is iteratively applied to the initial state assisted with an ancillary qubit. The fraction of the lowest eigenstate in the initial state is then amplified up to 1. We prove that our algorithm can faithfully work for any arbitrary Hamiltonian in the theoretical analysis. Numerical analyses are also carried out. We firstly provide a numerical proof-of-principle demonstration with a simple Hamiltonian in order to compare our scheme with the so-called "Demon-like algorithmic cooling (DLAC)", recently proposed in Xu (Nat Photonics 8:113, 2014). The result shows a good agreement with our theoretical analysis, exhibiting the comparable behavior to the best `cooling' with the DLAC method. We then consider a random Hamiltonian model for further analysis of our algorithm. By numerical simulations, we show that the total number of iterations is proportional to , where is the difference between the two lowest eigenvalues and is an error defined as the probability that the finally obtained system state is in an unexpected (i.e., not the lowest) eigenstate.

LOFA analysis in helium and Pb-Li circuits of LLCB TBM by FE simulation

NASA Astrophysics Data System (ADS)

Chaudhuri, Paritosh; Ranjithkumar, S.; Sharma, Deepak; Danani, Chandan

2017-04-01

One of the main ITER objectives is to demonstrate the feasibility of the breeding blanket concepts that would lead to tritium self-sufficiency and the extraction of a high-grade heat for electricity production. India has developed the LLCB TBM to be tested in ITER for the validation of design concepts for tritium breeding blankets relevant DEMO and future power reactor. LLCB concept has the unique features of combination of both solid (lithium titanate as packed pebble bed) and liquid breeders (molten lead lithium). India specific IN-RAFMS is the structural material for TBM. The First Wall is actively cooled by high-pressure helium (He) gas [1]. It is important to validate the design of TBM to withstand various loads acting on it including accident analysis like LOCA, LOFA etc. Detailed thermal-hydraulic simulation studies including LOFA in helium and Pb-Li circuits of LLCB TBM have been performed using Finite Element using ANSYS. These analyses will provide important information about the temperature distribution in different materials used in TBM during steady state and transient condition. Thermal-hydraulic safety requirement has also been envisaged for the initiation the FPPS (Fusion Power Shutdown System) during LOFA. All these analysis will be presented in detail in this paper.

Efficient Coupling of Fluid-Plasma and Monte-Carlo-Neutrals Models for Edge Plasma Transport

NASA Astrophysics Data System (ADS)

Dimits, A. M.; Cohen, B. I.; Friedman, A.; Joseph, I.; Lodestro, L. L.; Rensink, M. E.; Rognlien, T. D.; Sjogreen, B.; Stotler, D. P.; Umansky, M. V.

2017-10-01

UEDGE has been valuable for modeling transport in the tokamak edge and scrape-off layer due in part to its efficient fully implicit solution of coupled fluid neutrals and plasma models. We are developing an implicit coupling of the kinetic Monte-Carlo (MC) code DEGAS-2, as the neutrals model component, to the UEDGE plasma component, based on an extension of the Jacobian-free Newton-Krylov (JFNK) method to MC residuals. The coupling components build on the methods and coding already present in UEDGE. For the linear Krylov iterations, a procedure has been developed to ``extract'' a good preconditioner from that of UEDGE. This preconditioner may also be used to greatly accelerate the convergence rate of a relaxed fixed-point iteration, which may provide a useful ``intermediate'' algorithm. The JFNK method also requires calculation of Jacobian-vector products, for which any finite-difference procedure is inaccurate when a MC component is present. A semi-analytical procedure that retains the standard MC accuracy and fully kinetic neutrals physics is therefore being developed. Prepared for US DOE by LLNL under Contract DE-AC52-07NA27344 and LDRD project 15-ERD-059, by PPPL under Contract DE-AC02-09CH11466, and supported in part by the U.S. DOE, OFES.

A gauged finite-element potential formulation for accurate inductive and galvanic modelling of 3-D electromagnetic problems

NASA Astrophysics Data System (ADS)

Ansari, S. M.; Farquharson, C. G.; MacLachlan, S. P.

2017-07-01

In this paper, a new finite-element solution to the potential formulation of the geophysical electromagnetic (EM) problem that explicitly implements the Coulomb gauge, and that accurately computes the potentials and hence inductive and galvanic components, is proposed. The modelling scheme is based on using unstructured tetrahedral meshes for domain subdivision, which enables both realistic Earth models of complex geometries to be considered and efficient spatially variable refinement of the mesh to be done. For the finite-element discretization edge and nodal elements are used for approximating the vector and scalar potentials respectively. The issue of non-unique, incorrect potentials from the numerical solution of the usual incomplete-gauged potential system is demonstrated for a benchmark model from the literature that uses an electric-type EM source, through investigating the interface continuity conditions for both the normal and tangential components of the potential vectors, and by showing inconsistent results obtained from iterative and direct linear equation solvers. By explicitly introducing the Coulomb gauge condition as an extra equation, and by augmenting the Helmholtz equation with the gradient of a Lagrange multiplier, an explicitly gauged system for the potential formulation is formed. The solution to the discretized form of this system is validated for the above-mentioned example and for another classic example that uses a magnetic EM source. In order to stabilize the iterative solution of the gauged system, a block diagonal pre-conditioning scheme that is based upon the Schur complement of the potential system is used. For all examples, both the iterative and direct solvers produce the same responses for the potentials, demonstrating the uniqueness of the numerical solution for the potentials and fixing the problems with the interface conditions between cells observed for the incomplete-gauged system. These solutions of the gauged system also produce the physically anticipated behaviours for the inductive and galvanic components of the electric field. For a realistic geophysical scenario, the gauged scheme is also used to synthesize the magnetic field response of a model of the Ovoid ore deposit at Voisey's Bay, Labrador, Canada. The results are in good agreement with the helicopter-borne EM data from the real survey, and the inductive and galvanic parts of the current density show expected behaviours.

An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kühnlein, Christian, E-mail: christian.kuehnlein@ecmwf.int; Smolarkiewicz, Piotr K., E-mail: piotr.smolarkiewicz@ecmwf.int

An advancement of the unstructured-mesh finite-volume MPDATA (Multidimensional Positive Definite Advection Transport Algorithm) is presented that formulates the error-compensative pseudo-velocity of the scheme to rely only on face-normal advective fluxes to the dual cells, in contrast to the full vector employed in previous implementations. This is essentially achieved by expressing the temporal truncation error underlying the pseudo-velocity in a form consistent with the flux-divergence of the governing conservation law. The development is especially important for integrating fluid dynamics equations on non-rectilinear meshes whenever face-normal advective mass fluxes are employed for transport compatible with mass continuity—the latter being essential for flux-formmore » schemes. In particular, the proposed formulation enables large-time-step semi-implicit finite-volume integration of the compressible Euler equations using MPDATA on arbitrary hybrid computational meshes. Furthermore, it facilitates multiple error-compensative iterations of the finite-volume MPDATA and improved overall accuracy. The advancement combines straightforwardly with earlier developments, such as the nonoscillatory option, the infinite-gauge variant, and moving curvilinear meshes. A comprehensive description of the scheme is provided for a hybrid horizontally-unstructured vertically-structured computational mesh for efficient global atmospheric flow modelling. The proposed finite-volume MPDATA is verified using selected 3D global atmospheric benchmark simulations, representative of hydrostatic and non-hydrostatic flow regimes. Besides the added capabilities, the scheme retains fully the efficacy of established finite-volume MPDATA formulations.« less

Iterative reconstruction methods in atmospheric tomography: FEWHA, Kaczmarz and Gradient-based algorithm

NASA Astrophysics Data System (ADS)

Ramlau, R.; Saxenhuber, D.; Yudytskiy, M.

2014-07-01

The problem of atmospheric tomography arises in ground-based telescope imaging with adaptive optics (AO), where one aims to compensate in real-time for the rapidly changing optical distortions in the atmosphere. Many of these systems depend on a sufficient reconstruction of the turbulence profiles in order to obtain a good correction. Due to steadily growing telescope sizes, there is a strong increase in the computational load for atmospheric reconstruction with current methods, first and foremost the MVM. In this paper we present and compare three novel iterative reconstruction methods. The first iterative approach is the Finite Element- Wavelet Hybrid Algorithm (FEWHA), which combines wavelet-based techniques and conjugate gradient schemes to efficiently and accurately tackle the problem of atmospheric reconstruction. The method is extremely fast, highly flexible and yields superior quality. Another novel iterative reconstruction algorithm is the three step approach which decouples the problem in the reconstruction of the incoming wavefronts, the reconstruction of the turbulent layers (atmospheric tomography) and the computation of the best mirror correction (fitting step). For the atmospheric tomography problem within the three step approach, the Kaczmarz algorithm and the Gradient-based method have been developed. We present a detailed comparison of our reconstructors both in terms of quality and speed performance in the context of a Multi-Object Adaptive Optics (MOAO) system for the E-ELT setting on OCTOPUS, the ESO end-to-end simulation tool.

Numerical Analysis and Improved Algorithms for Lyapunov-Exponent Calculation of Discrete-Time Chaotic Systems

NASA Astrophysics Data System (ADS)

He, Jianbin; Yu, Simin; Cai, Jianping

2016-12-01

Lyapunov exponent is an important index for describing chaotic systems behavior, and the largest Lyapunov exponent can be used to determine whether a system is chaotic or not. For discrete-time dynamical systems, the Lyapunov exponents are calculated by an eigenvalue method. In theory, according to eigenvalue method, the more accurate calculations of Lyapunov exponent can be obtained with the increment of iterations, and the limits also exist. However, due to the finite precision of computer and other reasons, the results will be numeric overflow, unrecognized, or inaccurate, which can be stated as follows: (1) The iterations cannot be too large, otherwise, the simulation result will appear as an error message of NaN or Inf; (2) If the error message of NaN or Inf does not appear, then with the increment of iterations, all Lyapunov exponents will get close to the largest Lyapunov exponent, which leads to inaccurate calculation results; (3) From the viewpoint of numerical calculation, obviously, if the iterations are too small, then the results are also inaccurate. Based on the analysis of Lyapunov-exponent calculation in discrete-time systems, this paper investigates two improved algorithms via QR orthogonal decomposition and SVD orthogonal decomposition approaches so as to solve the above-mentioned problems. Finally, some examples are given to illustrate the feasibility and effectiveness of the improved algorithms.

Methodology for Sensitivity Analysis, Approximate Analysis, and Design Optimization in CFD for Multidisciplinary Applications

NASA Technical Reports Server (NTRS)

Taylor, Arthur C., III; Hou, Gene W.

1996-01-01

An incremental iterative formulation together with the well-known spatially split approximate-factorization algorithm, is presented for solving the large, sparse systems of linear equations that are associated with aerodynamic sensitivity analysis. This formulation is also known as the 'delta' or 'correction' form. For the smaller two dimensional problems, a direct method can be applied to solve these linear equations in either the standard or the incremental form, in which case the two are equivalent. However, iterative methods are needed for larger two-dimensional and three dimensional applications because direct methods require more computer memory than is currently available. Iterative methods for solving these equations in the standard form are generally unsatisfactory due to an ill-conditioned coefficient matrix; this problem is overcome when these equations are cast in the incremental form. The methodology is successfully implemented and tested using an upwind cell-centered finite-volume formulation applied in two dimensions to the thin-layer Navier-Stokes equations for external flow over an airfoil. In three dimensions this methodology is demonstrated with a marching-solution algorithm for the Euler equations to calculate supersonic flow over the High-Speed Civil Transport configuration (HSCT 24E). The sensitivity derivatives obtained with the incremental iterative method from a marching Euler code are used in a design-improvement study of the HSCT configuration that involves thickness. camber, and planform design variables.

A Representation for Fermionic Correlation Functions

NASA Astrophysics Data System (ADS)

Feldman, Joel; Knörrer, Horst; Trubowitz, Eugene

Let dμS(a) be a Gaussian measure on the finitely generated Grassmann algebra A. Given an even W(a)∈A, we construct an operator R on A such that for all f(a)∈A. This representation of the Schwinger functional iteratively builds up Feynman graphs by successively appending lines farther and farther from f. It allows the Pauli exclusion principle to be implemented quantitatively by a simple application of Gram's inequality.

CUDA GPU based full-Stokes finite difference modelling of glaciers

NASA Astrophysics Data System (ADS)

Brædstrup, C. F.; Egholm, D. L.

2012-04-01

Many have stressed the limitations of using the shallow shelf and shallow ice approximations when modelling ice streams or surging glaciers. Using a full-stokes approach requires either large amounts of computer power or time and is therefore seldom an option for most glaciologists. Recent advances in graphics card (GPU) technology for high performance computing have proven extremely efficient in accelerating many large scale scientific computations. The general purpose GPU (GPGPU) technology is cheap, has a low power consumption and fits into a normal desktop computer. It could therefore provide a powerful tool for many glaciologists. Our full-stokes ice sheet model implements a Red-Black Gauss-Seidel iterative linear solver to solve the full stokes equations. This technique has proven very effective when applied to the stokes equation in geodynamics problems, and should therefore also preform well in glaciological flow probems. The Gauss-Seidel iterator is known to be robust but several other linear solvers have a much faster convergence. To aid convergence, the solver uses a multigrid approach where values are interpolated and extrapolated between different grid resolutions to minimize the short wavelength errors efficiently. This reduces the iteration count by several orders of magnitude. The run-time is further reduced by using the GPGPU technology where each card has up to 448 cores. Researchers utilizing the GPGPU technique in other areas have reported between 2 - 11 times speedup compared to multicore CPU implementations on similar problems. The goal of these initial investigations into the possible usage of GPGPU technology in glacial modelling is to apply the enhanced resolution of a full-stokes solver to ice streams and surging glaciers. This is a area of growing interest because ice streams are the main drainage conjugates for large ice sheets. It is therefore crucial to understand this streaming behavior and it's impact up-ice.

Ames Optimized TCA Configuration

NASA Technical Reports Server (NTRS)

Cliff, Susan E.; Reuther, James J.; Hicks, Raymond M.

1999-01-01

Configuration design at Ames was carried out with the SYN87-SB (single block) Euler code using a 193 x 49 x 65 C-H grid. The Euler solver is coupled to the constrained (NPSOL) and the unconstrained (QNMDIF) optimization packages. Since the single block grid is able to model only wing-body configurations, the nacelle/diverter effects were included in the optimization process by SYN87's option to superimpose the nacelle/diverter interference pressures on the wing. These interference pressures were calculated using the AIRPLANE code. AIRPLANE is an Euler solver that uses a unstructured tetrahedral mesh and is capable of computations about arbitrary complete configurations. In addition, the buoyancy effects of the nacelle/diverters were also included in the design process by imposing the pressure field obtained during the design process onto the triangulated surfaces of the nacelle/diverter mesh generated by AIRPLANE. The interference pressures and nacelle buoyancy effects are added to the final forces after each flow field calculation. Full details of the (recently enhanced) ghost nacelle capability are given in a related talk. The pseudo nacelle corrections were greatly improved during this design cycle. During the Ref H and Cycle 1 design activities, the nacelles were only translated and pitched. In the cycle 2 design effort the nacelles can translate vertically, and pitch to accommodate the changes in the lower surface geometry. The diverter heights (between their leading and trailing edges) were modified during design as the shape of the lower wing changed, with the drag of the diverter changing accordingly. Both adjoint and finite difference gradients were used during optimization. The adjoint-based gradients were found to give good direction in the design space for configurations near the starting point, but as the design approached a minimum, the finite difference gradients were found to be more accurate. Use of finite difference gradients was limited by the CPU time limit available on the Cray machines. A typical optimization run using finite difference gradients can use only 30 to 40 design variables and one optimization iteration within the 8 hour queue limit for the chosen grid size and convergence level. The efficiency afforded by the adjoint method allowed for 50-120 design variables and 5-10 optimization iterations in the 8 hour queue. Geometric perturbations to the wing and fuselage were made using the Hicks/Henne (HH) shape functions. The HH functions were distributed uniformly along the chords of the wing defining sections and lofted linearly. During single-surface design, constraints on thickness and volume at selected wing stations were imposed. Both fuselage camber and cross-sectional area distributions were permitted to change during design. The major disadvantage to the use of these functions is the inherent surface waviness produced by repeated use of such functions. Many smoothing operations were required following optimization runs to produce a configuration with reasonable smoothness. Wagner functions were also used on the wing sections but were never used on the fuselage. The Wagner functions are a family of increasingly oscillatory functions that have also been used extensively in airfoil design. The leading and trailing edge regions of the wing were designed by use of polynomial and monomial functions respectively. Twist was attempted but was abandoned because of little performance improvement available from changing the baseline twist.

Stability of finite difference numerical simulations of acoustic logging-while-drilling with different perfectly matched layer schemes

NASA Astrophysics Data System (ADS)

Wang, Hua; Tao, Guo; Shang, Xue-Feng; Fang, Xin-Ding; Burns, Daniel R.

2013-12-01

In acoustic logging-while-drilling (ALWD) finite difference in time domain (FDTD) simulations, large drill collar occupies, most of the fluid-filled borehole and divides the borehole fluid into two thin fluid columns (radius ˜27 mm). Fine grids and large computational models are required to model the thin fluid region between the tool and the formation. As a result, small time step and more iterations are needed, which increases the cumulative numerical error. Furthermore, due to high impedance contrast between the drill collar and fluid in the borehole (the difference is >30 times), the stability and efficiency of the perfectly matched layer (PML) scheme is critical to simulate complicated wave modes accurately. In this paper, we compared four different PML implementations in a staggered grid finite difference in time domain (FDTD) in the ALWD simulation, including field-splitting PML (SPML), multiaxial PML(MPML), non-splitting PML (NPML), and complex frequency-shifted PML (CFS-PML). The comparison indicated that NPML and CFS-PML can absorb the guided wave reflection from the computational boundaries more efficiently than SPML and M-PML. For large simulation time, SPML, M-PML, and NPML are numerically unstable. However, the stability of M-PML can be improved further to some extent. Based on the analysis, we proposed that the CFS-PML method is used in FDTD to eliminate the numerical instability and to improve the efficiency of absorption in the PML layers for LWD modeling. The optimal values of CFS-PML parameters in the LWD simulation were investigated based on thousands of 3D simulations. For typical LWD cases, the best maximum value of the quadratic damping profile was obtained using one d 0. The optimal parameter space for the maximum value of the linear frequency-shifted factor ( α 0) and the scaling factor ( β 0) depended on the thickness of the PML layer. For typical formations, if the PML thickness is 10 grid points, the global error can be reduced to <1% using the optimal PML parameters, and the error will decrease as the PML thickness increases.

PAFAC- PLASTIC AND FAILURE ANALYSIS OF COMPOSITES

NASA Technical Reports Server (NTRS)

Bigelow, C. A.

1994-01-01

The increasing number of applications of fiber-reinforced composites in industry demands a detailed understanding of their material properties and behavior. A three-dimensional finite-element computer program called PAFAC (Plastic and Failure Analysis of Composites) has been developed for the elastic-plastic analysis of fiber-reinforced composite materials and structures. The evaluation of stresses and deformations at edges, cut-outs, and joints is essential in understanding the strength and failure for metal-matrix composites since the onset of plastic yielding starts very early in the loading process as compared to the composite's ultimate strength. Such comprehensive analysis can only be achieved by a finite-element program like PAFAC. PAFAC is particularly suited for the analysis of laminated metal-matrix composites. It can model the elastic-plastic behavior of the matrix phase while the fibers remain elastic. Since the PAFAC program uses a three-dimensional element, the program can also model the individual layers of the laminate to account for thickness effects. In PAFAC, the composite is modeled as a continuum reinforced by cylindrical fibers of vanishingly small diameter which occupy a finite volume fraction of the composite. In this way, the essential axial constraint of the phases is retained. Furthermore, the local stress and strain fields are uniform. The PAFAC finite-element solution is obtained using the displacement method. Solution of the nonlinear equilibrium equations is obtained with a Newton-Raphson iteration technique. The elastic-plastic behavior of composites consisting of aligned, continuous elastic filaments and an elastic-plastic matrix is described in terms of the constituent properties, their volume fractions, and mutual constraints between phases indicated by the geometry of the microstructure. The program uses an iterative procedure to determine the overall response of the laminate, then from the overall response determines the stress state in each phase of the composite material. Failure of the fibers or matrix within an element can also be modeled by PAFAC. PAFAC is written in FORTRAN IV for batch execution and has been implemented on a CDC CYBER 170 series computer with a segmented memory requirement of approximately 66K (octal) of 60 bit words. PAFAC was developed in 1982.

Associative memory in an analog iterated-map neural network

NASA Astrophysics Data System (ADS)

Marcus, C. M.; Waugh, F. R.; Westervelt, R. M.

1990-03-01

The behavior of an analog neural network with parallel dynamics is studied analytically and numerically for two associative-memory learning algorithms, the Hebb rule and the pseudoinverse rule. Phase diagrams in the parameter space of analog gain β and storage ratio α are presented. For both learning rules, the networks have large ``recall'' phases in which retrieval states exist and convergence to a fixed point is guaranteed by a global stability criterion. We also demonstrate numerically that using a reduced analog gain increases the probability of recall starting from a random initial state. This phenomenon is comparable to thermal annealing used to escape local minima but has the advantage of being deterministic, and therefore easily implemented in electronic hardware. Similarities and differences between analog neural networks and networks with two-state neurons at finite temperature are also discussed.

Recent applications of the transonic wing analysis computer code, TWING

NASA Technical Reports Server (NTRS)

Subramanian, N. R.; Holst, T. L.; Thomas, S. D.

1982-01-01

An evaluation of the transonic-wing-analysis computer code TWING is given. TWING utilizes a fully implicit approximate factorization iteration scheme to solve the full potential equation in conservative form. A numerical elliptic-solver grid-generation scheme is used to generate the required finite-difference mesh. Several wing configurations were analyzed, and the limits of applicability of this code was evaluated. Comparisons of computed results were made with available experimental data. Results indicate that the code is robust, accurate (when significant viscous effects are not present), and efficient. TWING generally produces solutions an order of magnitude faster than other conservative full potential codes using successive-line overrelaxation. The present method is applicable to a wide range of isolated wing configurations including high-aspect-ratio transport wings and low-aspect-ratio, high-sweep, fighter configurations.

Pull-in instability of paddle-type and double-sided NEMS sensors under the accelerating force

NASA Astrophysics Data System (ADS)

Keivani, M.; Khorsandi, J.; Mokhtari, J.; Kanani, A.; Abadian, N.; Abadyan, M.

2016-02-01

Paddle-type and double-sided nanostructures are potential for use as accelerometers in flying vehicles and aerospace applications. Herein the pull-in instability of the cantilever paddle-type and double-sided sensors in the Casimir regime are investigated under the acceleration. The D'Alembert principle is employed to transform the accelerating system into an equivalent static system by incorporating the accelerating force. Based on the couple stress theory (CST), the size-dependent constitutive equations of the sensors are derived. The governing nonlinear equations are solved by two approaches, i.e. modified variational iteration method and finite difference method. The influences of the Casimir force, geometrical parameters, acceleration and the size phenomenon on the instability performance have been demonstrated. The obtained results are beneficial to design and fabricate paddle-type and double-sided accelerometers.

Full two-dimensional transient solutions of electrothermal aircraft blade deicing

NASA Technical Reports Server (NTRS)

Masiulaniec, K. C.; Keith, T. G., Jr.; Dewitt, K. J.; Leffel, K. L.

1985-01-01

Two finite difference methods are presented for the analysis of transient, two-dimensional responses of an electrothermal de-icer pad of an aircraft wing or blade with attached variable ice layer thickness. Both models employ a Crank-Nicholson iterative scheme, and use an enthalpy formulation to handle the phase change in the ice layer. The first technique makes use of a 'staircase' approach, fitting the irregular ice boundary with square computational cells. The second technique uses a body fitted coordinate transform, and maps the exact shape of the irregular boundary into a rectangular body, with uniformally square computational cells. The numerical solution takes place in the transformed plane. Initial results accounting for variable ice layer thickness are presented. Details of planned de-icing tests at NASA-Lewis, which will provide empirical verification for the above two methods, are also presented.

Eigenmode computation of cavities with perturbed geometry using matrix perturbation methods applied on generalized eigenvalue problems

NASA Astrophysics Data System (ADS)

Gorgizadeh, Shahnam; Flisgen, Thomas; van Rienen, Ursula

2018-07-01

Generalized eigenvalue problems are standard problems in computational sciences. They may arise in electromagnetic fields from the discretization of the Helmholtz equation by for example the finite element method (FEM). Geometrical perturbations of the structure under concern lead to a new generalized eigenvalue problems with different system matrices. Geometrical perturbations may arise by manufacturing tolerances, harsh operating conditions or during shape optimization. Directly solving the eigenvalue problem for each perturbation is computationally costly. The perturbed eigenpairs can be approximated using eigenpair derivatives. Two common approaches for the calculation of eigenpair derivatives, namely modal superposition method and direct algebraic methods, are discussed in this paper. Based on the direct algebraic methods an iterative algorithm is developed for efficiently calculating the eigenvalues and eigenvectors of the perturbed geometry from the eigenvalues and eigenvectors of the unperturbed geometry.

MODFLOW-LGR-Modifications to the streamflow-routing package (SFR2) to route streamflow through locally refined grids

USGS Publications Warehouse

Mehl, Steffen W.; Hill, Mary C.

2011-01-01

This report documents modifications to the Streamflow-Routing Package (SFR2) to route streamflow through grids constructed using the multiple-refined-areas capability of shared node Local Grid Refinement (LGR) of MODFLOW-2005. MODFLOW-2005 is the U.S. Geological Survey modular, three-dimensional, finite-difference groundwater-flow model. LGR provides the capability to simulate groundwater flow by using one or more block-shaped, higher resolution local grids (child model) within a coarser grid (parent model). LGR accomplishes this by iteratively coupling separate MODFLOW-2005 models such that heads and fluxes are balanced across the shared interfacing boundaries. Compatibility with SFR2 allows for streamflow routing across grids. LGR can be used in two- and three-dimensional, steady-state and transient simulations and for simulations of confined and unconfined groundwater systems.

Methodology for sensitivity analysis, approximate analysis, and design optimization in CFD for multidisciplinary applications

NASA Technical Reports Server (NTRS)

Taylor, Arthur C., III; Hou, Gene W.

1994-01-01

The straightforward automatic-differentiation and the hand-differentiated incremental iterative methods are interwoven to produce a hybrid scheme that captures some of the strengths of each strategy. With this compromise, discrete aerodynamic sensitivity derivatives are calculated with the efficient incremental iterative solution algorithm of the original flow code. Moreover, the principal advantage of automatic differentiation is retained (i.e., all complicated source code for the derivative calculations is constructed quickly with accuracy). The basic equations for second-order sensitivity derivatives are presented; four methods are compared. Each scheme requires that large systems are solved first for the first-order derivatives and, in all but one method, for the first-order adjoint variables. Of these latter three schemes, two require no solutions of large systems thereafter. For the other two for which additional systems are solved, the equations and solution procedures are analogous to those for the first order derivatives. From a practical viewpoint, implementation of the second-order methods is feasible only with software tools such as automatic differentiation, because of the extreme complexity and large number of terms. First- and second-order sensitivities are calculated accurately for two airfoil problems, including a turbulent flow example; both geometric-shape and flow-condition design variables are considered. Several methods are tested; results are compared on the basis of accuracy, computational time, and computer memory. For first-order derivatives, the hybrid incremental iterative scheme obtained with automatic differentiation is competitive with the best hand-differentiated method; for six independent variables, it is at least two to four times faster than central finite differences and requires only 60 percent more memory than the original code; the performance is expected to improve further in the future.

MODFLOW–LGR—Documentation of ghost node local grid refinement (LGR2) for multiple areas and the boundary flow and head (BFH2) package

USGS Publications Warehouse

Mehl, Steffen W.; Hill, Mary C.

2013-01-01

This report documents the addition of ghost node Local Grid Refinement (LGR2) to MODFLOW-2005, the U.S. Geological Survey modular, transient, three-dimensional, finite-difference groundwater flow model. LGR2 provides the capability to simulate groundwater flow using multiple block-shaped higher-resolution local grids (a child model) within a coarser-grid parent model. LGR2 accomplishes this by iteratively coupling separate MODFLOW-2005 models such that heads and fluxes are balanced across the grid-refinement interface boundary. LGR2 can be used in two-and three-dimensional, steady-state and transient simulations and for simulations of confined and unconfined groundwater systems. Traditional one-way coupled telescopic mesh refinement methods can have large, often undetected, inconsistencies in heads and fluxes across the interface between two model grids. The iteratively coupled ghost-node method of LGR2 provides a more rigorous coupling in which the solution accuracy is controlled by convergence criteria defined by the user. In realistic problems, this can result in substantially more accurate solutions and require an increase in computer processing time. The rigorous coupling enables sensitivity analysis, parameter estimation, and uncertainty analysis that reflects conditions in both model grids. This report describes the method used by LGR2, evaluates accuracy and performance for two-and three-dimensional test cases, provides input instructions, and lists selected input and output files for an example problem. It also presents the Boundary Flow and Head (BFH2) Package, which allows the child and parent models to be simulated independently using the boundary conditions obtained through the iterative process of LGR2.

MODFLOW-2005, the U.S. Geological Survey modular ground-water model - documentation of shared node local grid refinement (LGR) and the boundary flow and head (BFH) package

USGS Publications Warehouse

Mehl, Steffen W.; Hill, Mary C.

2006-01-01

This report documents the addition of shared node Local Grid Refinement (LGR) to MODFLOW-2005, the U.S. Geological Survey modular, transient, three-dimensional, finite-difference ground-water flow model. LGR provides the capability to simulate ground-water flow using one block-shaped higher-resolution local grid (a child model) within a coarser-grid parent model. LGR accomplishes this by iteratively coupling two separate MODFLOW-2005 models such that heads and fluxes are balanced across the shared interfacing boundary. LGR can be used in two-and three-dimensional, steady-state and transient simulations and for simulations of confined and unconfined ground-water systems. Traditional one-way coupled telescopic mesh refinement (TMR) methods can have large, often undetected, inconsistencies in heads and fluxes across the interface between two model grids. The iteratively coupled shared-node method of LGR provides a more rigorous coupling in which the solution accuracy is controlled by convergence criteria defined by the user. In realistic problems, this can result in substantially more accurate solutions and require an increase in computer processing time. The rigorous coupling enables sensitivity analysis, parameter estimation, and uncertainty analysis that reflects conditions in both model grids. This report describes the method used by LGR, evaluates LGR accuracy and performance for two- and three-dimensional test cases, provides input instructions, and lists selected input and output files for an example problem. It also presents the Boundary Flow and Head (BFH) Package, which allows the child and parent models to be simulated independently using the boundary conditions obtained through the iterative process of LGR.

TRUST84. Sat-Unsat Flow in Deformable Media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Narasimhan, T.N.

1984-11-01

TRUST84 solves for transient and steady-state flow in variably saturated deformable media in one, two, or three dimensions. It can handle porous media, fractured media, or fractured-porous media. Boundary conditions may be an arbitrary function of time. Sources or sinks may be a function of time or of potential. The theoretical model considers a general three-dimensional field of flow in conjunction with a one-dimensional vertical deformation field. The governing equation expresses the conservation of fluid mass in an elemental volume that has a constant volume of solids. Deformation of the porous medium may be nonelastic. Permeability and the compressibility coefficientsmore » may be nonlinearly related to effective stress. Relationships between permeability and saturation with pore water pressure in the unsaturated zone may be characterized by hysteresis. The relation between pore pressure change and effective stress change may be a function of saturation. The basic calculational model of the conductive heat transfer code TRUMP is applied in TRUST84 to the flow of fluids in porous media. The model combines an integrated finite difference algorithm for numerically solving the governing equation with a mixed explicit-implicit iterative scheme in which the explicit changes in potential are first computed for all elements in the system, after which implicit corrections are made only for those elements for which the stable time-step is less than the time-step being used. Time-step sizes are automatically controlled to optimize the number of iterations, to control maximum change to potential during a time-step, and to obtain desired output information. Time derivatives, estimated on the basis of system behavior during the two previous time-steps, are used to start the iteration process and to evaluate nonlinear coefficients. Both heterogeneity and anisotropy can be handled.« less

Least-squares reverse time migration in elastic media

NASA Astrophysics Data System (ADS)

Ren, Zhiming; Liu, Yang; Sen, Mrinal K.

2017-02-01

Elastic reverse time migration (RTM) can yield accurate subsurface information (e.g. PP and PS reflectivity) by imaging the multicomponent seismic data. However, the existing RTM methods are still insufficient to provide satisfactory results because of the finite recording aperture, limited bandwidth and imperfect illumination. Besides, the P- and S-wave separation and the polarity reversal correction are indispensable in conventional elastic RTM. Here, we propose an iterative elastic least-squares RTM (LSRTM) method, in which the imaging accuracy is improved gradually with iteration. We first use the Born approximation to formulate the elastic de-migration operator, and employ the Lagrange multiplier method to derive the adjoint equations and gradients with respect to reflectivity. Then, an efficient inversion workflow (only four forward computations needed in each iteration) is introduced to update the reflectivity. Synthetic and field data examples reveal that the proposed LSRTM method can obtain higher-quality images than the conventional elastic RTM. We also analyse the influence of model parametrizations and misfit functions in elastic LSRTM. We observe that Lamé parameters, velocity and impedance parametrizations have similar and plausible migration results when the structures of different models are correlated. For an uncorrelated subsurface model, velocity and impedance parametrizations produce fewer artefacts caused by parameter crosstalk than the Lamé coefficient parametrization. Correlation- and convolution-type misfit functions are effective when amplitude errors are involved and the source wavelet is unknown, respectively. Finally, we discuss the dependence of elastic LSRTM on migration velocities and its antinoise ability. Imaging results determine that the new elastic LSRTM method performs well as long as the low-frequency components of migration velocities are correct. The quality of images of elastic LSRTM degrades with increasing noise.

Methodology for sensitivity analysis, approximate analysis, and design optimization in CFD for multidisciplinary applications

NASA Technical Reports Server (NTRS)

Taylor, Arthur C., III; Hou, Gene W.

1993-01-01

In this study involving advanced fluid flow codes, an incremental iterative formulation (also known as the delta or correction form) together with the well-known spatially-split approximate factorization algorithm, is presented for solving the very large sparse systems of linear equations which are associated with aerodynamic sensitivity analysis. For smaller 2D problems, a direct method can be applied to solve these linear equations in either the standard or the incremental form, in which case the two are equivalent. Iterative methods are needed for larger 2D and future 3D applications, however, because direct methods require much more computer memory than is currently available. Iterative methods for solving these equations in the standard form are generally unsatisfactory due to an ill-conditioning of the coefficient matrix; this problem can be overcome when these equations are cast in the incremental form. These and other benefits are discussed. The methodology is successfully implemented and tested in 2D using an upwind, cell-centered, finite volume formulation applied to the thin-layer Navier-Stokes equations. Results are presented for two sample airfoil problems: (1) subsonic low Reynolds number laminar flow; and (2) transonic high Reynolds number turbulent flow.

Scalable domain decomposition solvers for stochastic PDEs in high performance computing

DOE PAGES

Desai, Ajit; Khalil, Mohammad; Pettit, Chris; ...

2017-09-21

Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolutionmore » in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.« less

Error Field Assessment from Driven Mode Rotation: Results from Extrap-T2R Reversed-Field-Pinch and Perspectives for ITER

NASA Astrophysics Data System (ADS)

Volpe, F. A.; Frassinetti, L.; Brunsell, P. R.; Drake, J. R.; Olofsson, K. E. J.

2012-10-01

A new ITER-relevant non-disruptive error field (EF) assessment technique not restricted to low density and thus low beta was demonstrated at the Extrap-T2R reversed field pinch. Resistive Wall Modes (RWMs) were generated and their rotation sustained by rotating magnetic perturbations. In particular, stable modes of toroidal mode number n=8 and 10 and unstable modes of n=1 were used in this experiment. Due to finite EFs, and in spite of the applied perturbations rotating uniformly and having constant amplitude, the RWMs were observed to rotate non-uniformly and be modulated in amplitude (in the case of unstable modes, the observed oscillation was superimposed to the mode growth). This behavior was used to infer the amplitude and toroidal phase of n=1, 8 and 10 EFs. The method was first tested against known, deliberately applied EFs, and then against actual intrinsic EFs. Applying equal and opposite corrections resulted in longer discharges and more uniform mode rotation, indicating good EF compensation. The results agree with a simple theoretical model. Extensions to tearing modes, to the non-uniform plasma response to rotating perturbations, and to tokamaks, including ITER, will be discussed.

Scalable domain decomposition solvers for stochastic PDEs in high performance computing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Desai, Ajit; Khalil, Mohammad; Pettit, Chris

Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolutionmore » in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.« less

A new method for computation of eigenvector derivatives with distinct and repeated eigenvalues in structural dynamic analysis

NASA Astrophysics Data System (ADS)

Li, Zhengguang; Lai, Siu-Kai; Wu, Baisheng

2018-07-01

Determining eigenvector derivatives is a challenging task due to the singularity of the coefficient matrices of the governing equations, especially for those structural dynamic systems with repeated eigenvalues. An effective strategy is proposed to construct a non-singular coefficient matrix, which can be directly used to obtain the eigenvector derivatives with distinct and repeated eigenvalues. This approach also has an advantage that only requires eigenvalues and eigenvectors of interest, without solving the particular solutions of eigenvector derivatives. The Symmetric Quasi-Minimal Residual (SQMR) method is then adopted to solve the governing equations, only the existing factored (shifted) stiffness matrix from an iterative eigensolution such as the subspace iteration method or the Lanczos algorithm is utilized. The present method can deal with both cases of simple and repeated eigenvalues in a unified manner. Three numerical examples are given to illustrate the accuracy and validity of the proposed algorithm. Highly accurate approximations to the eigenvector derivatives are obtained within a few iteration steps, making a significant reduction of the computational effort. This method can be incorporated into a coupled eigensolver/derivative software module. In particular, it is applicable for finite element models with large sparse matrices.

Modelling of minority ion cyclotron current drive during the activated phase of ITER

NASA Astrophysics Data System (ADS)

Laxåback, M.; Hellsten, T.

2005-12-01

Neoclassical tearing modes, triggered by the long-period sawteeth expected in tokamaks with large non-thermal α-particle populations, may impose a severe β limit on experiments with large fusion yields and on reactors. Sawtooth destabilization by localized current drive could relax the β limit and improve plasma performance. 3He minority ion cyclotron current drive around the sawtooth inversion radius has been planned for ITER. Several ion species, including beam injected D ions and fusion born α particles, are however also resonant in the plasma and may represent a parasitic absorption of RF power. Modelling of minority ion cyclotron current drive in an ITER-FEAT-like plasma is presented, including the effects of ion trapping, finite ion drift orbit widths, wave-induced radial transport and the coupled evolution of wave fields and resonant ion distributions. The parasitic absorption of RF power by the other resonant species is concluded to be relatively small, but the 3He minority current drive is nevertheless negligible due to the strong collisionality of the 3He ions and the drag current by toroidally counter-rotating background ions and co-rotating electrons. H minority current drive is found to be a significantly more effective alternative.

Reliability issues for a bolometer detector for ITER at high operating temperatures.

PubMed

Meister, H; Kannamüller, M; Koll, J; Pathak, A; Penzel, F; Trautmann, T; Detemple, P; Schmitt, S; Langer, H

2012-10-01

The first detector prototypes for the ITER bolometer diagnostic featuring a 12.5 μm thick Pt-absorber have been realized and characterized in laboratory tests. The results show linear dependencies of the calibration parameters and are in line with measurements of prototypes with thinner absorbers. However, thermal cycling tests up to 450 °C of the prototypes with thick absorbers demonstrated that their reliability at these elevated operating temperatures is not yet sufficient. Profilometer measurements showed a deflection of the membrane hinting to stresses due to the deposition processes of the absorber. Finite element analysis (FEA) managed to reproduce the deflection and identified the highest stresses in the membrane in the region around the corners of the absorber. FEA was further used to identify changes in the geometry of the absorber with a positive impact on the intrinsic stresses of the membrane. However, further improvements are still necessary.

An iterative hyperelastic parameters reconstruction for breast cancer assessment

NASA Astrophysics Data System (ADS)

Mehrabian, Hatef; Samani, Abbas

2008-03-01

In breast elastography, breast tissues usually undergo large compressions resulting in significant geometric and structural changes, and consequently nonlinear mechanical behavior. In this study, an elastography technique is presented where parameters characterizing tissue nonlinear behavior is reconstructed. Such parameters can be used for tumor tissue classification. To model the nonlinear behavior, tissues are treated as hyperelastic materials. The proposed technique uses a constrained iterative inversion method to reconstruct the tissue hyperelastic parameters. The reconstruction technique uses a nonlinear finite element (FE) model for solving the forward problem. In this research, we applied Yeoh and Polynomial models to model the tissue hyperelasticity. To mimic the breast geometry, we used a computational phantom, which comprises of a hemisphere connected to a cylinder. This phantom consists of two types of soft tissue to mimic adipose and fibroglandular tissues and a tumor. Simulation results show the feasibility of the proposed method in reconstructing the hyperelastic parameters of the tumor tissue.

A new anisotropic mesh adaptation method based upon hierarchical a posteriori error estimates

NASA Astrophysics Data System (ADS)

Huang, Weizhang; Kamenski, Lennard; Lang, Jens

2010-03-01

A new anisotropic mesh adaptation strategy for finite element solution of elliptic differential equations is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in some metric space, with the metric tensor being computed based on hierarchical a posteriori error estimates. A global hierarchical error estimate is employed in this study to obtain reliable directional information of the solution. Instead of solving the global error problem exactly, which is costly in general, we solve it iteratively using the symmetric Gauß-Seidel method. Numerical results show that a few GS iterations are sufficient for obtaining a reasonably good approximation to the error for use in anisotropic mesh adaptation. The new method is compared with several strategies using local error estimators or recovered Hessians. Numerical results are presented for a selection of test examples and a mathematical model for heat conduction in a thermal battery with large orthotropic jumps in the material coefficients.

Conceptual design and structural analysis for an 8.4-m telescope

NASA Astrophysics Data System (ADS)

Mendoza, Manuel; Farah, Alejandro; Ruiz Schneider, Elfego

2004-09-01

This paper describes the conceptual design of the optics support structures of a telescope with a primary mirror of 8.4 m, the same size as a Large Binocular Telescope (LBT) primary mirror. The design goal is to achieve a structure for supporting the primary and secondary mirrors and keeping them joined as rigid as possible. With this purpose an optimization with several models was done. This iterative design process includes: specifications development, concepts generation and evaluation. Process included Finite Element Analysis (FEA) as well as other analytical calculations. Quality Function Deployment (QFD) matrix was used to obtain telescope tube and spider specifications. Eight spiders and eleven tubes geometric concepts were proposed. They were compared in decision matrixes using performance indicators and parameters. Tubes and spiders went under an iterative optimization process. The best tubes and spiders concepts were assembled together. All assemblies were compared and ranked according to their performance.

On a multigrid method for the coupled Stokes and porous media flow problem

NASA Astrophysics Data System (ADS)

Luo, P.; Rodrigo, C.; Gaspar, F. J.; Oosterlee, C. W.

2017-07-01

The multigrid solution of coupled porous media and Stokes flow problems is considered. The Darcy equation as the saturated porous medium model is coupled to the Stokes equations by means of appropriate interface conditions. We focus on an efficient multigrid solution technique for the coupled problem, which is discretized by finite volumes on staggered grids, giving rise to a saddle point linear system. Special treatment is required regarding the discretization at the interface. An Uzawa smoother is employed in multigrid, which is a decoupled procedure based on symmetric Gauss-Seidel smoothing for velocity components and a simple Richardson iteration for the pressure field. Since a relaxation parameter is part of a Richardson iteration, Local Fourier Analysis (LFA) is applied to determine the optimal parameters. Highly satisfactory multigrid convergence is reported, and, moreover, the algorithm performs well for small values of the hydraulic conductivity and fluid viscosity, that are relevant for applications.

Fourier-Accelerated Nodal Solvers (FANS) for homogenization problems

NASA Astrophysics Data System (ADS)

Leuschner, Matthias; Fritzen, Felix

2017-11-01

Fourier-based homogenization schemes are useful to analyze heterogeneous microstructures represented by 2D or 3D image data. These iterative schemes involve discrete periodic convolutions with global ansatz functions (mostly fundamental solutions). The convolutions are efficiently computed using the fast Fourier transform. FANS operates on nodal variables on regular grids and converges to finite element solutions. Compared to established Fourier-based methods, the number of convolutions is reduced by FANS. Additionally, fast iterations are possible by assembling the stiffness matrix. Due to the related memory requirement, the method is best suited for medium-sized problems. A comparative study involving established Fourier-based homogenization schemes is conducted for a thermal benchmark problem with a closed-form solution. Detailed technical and algorithmic descriptions are given for all methods considered in the comparison. Furthermore, many numerical examples focusing on convergence properties for both thermal and mechanical problems, including also plasticity, are presented.

Counterrotating prop-fan simulations which feature a relative-motion multiblock grid decomposition enabling arbitrary time-steps

NASA Technical Reports Server (NTRS)

Janus, J. Mark; Whitfield, David L.

1990-01-01

Improvements are presented of a computer algorithm developed for the time-accurate flow analysis of rotating machines. The flow model is a finite volume method utilizing a high-resolution approximate Riemann solver for interface flux definitions. The numerical scheme is a block LU implicit iterative-refinement method which possesses apparent unconditional stability. Multiblock composite gridding is used to orderly partition the field into a specified arrangement of blocks exhibiting varying degrees of similarity. Block-block relative motion is achieved using local grid distortion to reduce grid skewness and accommodate arbitrary time step selection. A general high-order numerical scheme is applied to satisfy the geometric conservation law. An even-blade-count counterrotating unducted fan configuration is chosen for a computational study comparing solutions resulting from altering parameters such as time step size and iteration count. The solutions are compared with measured data.

A new iterative approach for multi-objective fault detection observer design and its application to a hypersonic vehicle

NASA Astrophysics Data System (ADS)

Huang, Di; Duan, Zhisheng

2018-03-01

This paper addresses the multi-objective fault detection observer design problems for a hypersonic vehicle. Owing to the fact that parameters' variations, modelling errors and disturbances are inevitable in practical situations, system uncertainty is considered in this study. By fully utilising the orthogonal space information of output matrix, some new understandings are proposed for the construction of Lyapunov matrix. Sufficient conditions for the existence of observers to guarantee the fault sensitivity and disturbance robustness in infinite frequency domain are presented. In order to further relax the conservativeness, slack matrices are introduced to fully decouple the observer gain with the Lyapunov matrices in finite frequency range. Iterative linear matrix inequality algorithms are proposed to obtain the solutions. The simulation examples which contain a Monte Carlo campaign illustrate that the new methods can effectively reduce the design conservativeness compared with the existing methods.

The existence of periodic solutions for nonlinear beam equations on Td by a para-differential method

NASA Astrophysics Data System (ADS)

Chen, Bochao; Li, Yong; Gao, Yixian

2018-05-01

This paper focuses on the construction of periodic solutions of nonlinear beam equations on the $d$-dimensional tori. For a large set of frequencies, we demonstrate that an equivalent form of the nonlinear equations can be obtained by a para-differential conjugation. Given the non-resonant conditions on each finite dimensional subspaces, it is shown that the periodic solutions can be constructed for the block diagonal equation by a classical iteration scheme.

Phase retrieval with Fourier-weighted projections.

PubMed

Guizar-Sicairos, Manuel; Fienup, James R

2008-03-01

In coherent lensless imaging, the presence of image sidelobes, which arise as a natural consequence of the finite nature of the detector array, was early recognized as a convergence issue for phase retrieval algorithms that rely on an object support constraint. To mitigate the problem of truncated far-field measurement, a controlled analytic continuation by means of an iterative transform algorithm with weighted projections is proposed and tested. This approach avoids the use of sidelobe reduction windows and achieves full-resolution reconstructions.

Decoupling the Stationary Navier-Stokes-Darcy System with the Beavers-Joseph-Saffman Interface Condition

DOE PAGES

Cao, Yong; Chu, Yuchuan; He, Xiaoming; ...

2013-01-01

This paper proposes a domain decomposition method for the coupled stationary Navier-Stokes and Darcy equations with the Beavers-Joseph-Saffman interface condition in order to improve the efficiency of the finite element method. The physical interface conditions are directly utilized to construct the boundary conditions on the interface and then decouple the Navier-Stokes and Darcy equations. Newton iteration will be used to deal with the nonlinear systems. Numerical results are presented to illustrate the features of the proposed method.

Differential Frequency Hopping (DFH) Modulation for Underwater Acoustic Communications and Networking

DTIC Science & Technology

2009-10-09

trains the coefficients c of a finite impulse response (FIR) filter by gradient descent. The coefficients at iteration k + 1 are computed with the update... absorption . Figure 9 shows the reflection loss as a function of grazing angle for this bottom model. Note that below 30◦ this bottom model predicts...less than 1 dB loss per ray bounce. 11 Figure 9: Jackson bottom reflection loss for sand at 15 kHz Absorption Loss The absorption loss in the medium was

FPGA architecture and implementation of sparse matrix vector multiplication for the finite element method

NASA Astrophysics Data System (ADS)

Elkurdi, Yousef; Fernández, David; Souleimanov, Evgueni; Giannacopoulos, Dennis; Gross, Warren J.

2008-04-01

The Finite Element Method (FEM) is a computationally intensive scientific and engineering analysis tool that has diverse applications ranging from structural engineering to electromagnetic simulation. The trends in floating-point performance are moving in favor of Field-Programmable Gate Arrays (FPGAs), hence increasing interest has grown in the scientific community to exploit this technology. We present an architecture and implementation of an FPGA-based sparse matrix-vector multiplier (SMVM) for use in the iterative solution of large, sparse systems of equations arising from FEM applications. FEM matrices display specific sparsity patterns that can be exploited to improve the efficiency of hardware designs. Our architecture exploits FEM matrix sparsity structure to achieve a balance between performance and hardware resource requirements by relying on external SDRAM for data storage while utilizing the FPGAs computational resources in a stream-through systolic approach. The architecture is based on a pipelined linear array of processing elements (PEs) coupled with a hardware-oriented matrix striping algorithm and a partitioning scheme which enables it to process arbitrarily big matrices without changing the number of PEs in the architecture. Therefore, this architecture is only limited by the amount of external RAM available to the FPGA. The implemented SMVM-pipeline prototype contains 8 PEs and is clocked at 110 MHz obtaining a peak performance of 1.76 GFLOPS. For 8 GB/s of memory bandwidth typical of recent FPGA systems, this architecture can achieve 1.5 GFLOPS sustained performance. Using multiple instances of the pipeline, linear scaling of the peak and sustained performance can be achieved. Our stream-through architecture provides the added advantage of enabling an iterative implementation of the SMVM computation required by iterative solution techniques such as the conjugate gradient method, avoiding initialization time due to data loading and setup inside the FPGA internal memory.

Project APhiD: A Lorenz-gauged A-Φ decomposition for parallelized computation of ultra-broadband electromagnetic induction in a fully heterogeneous Earth

NASA Astrophysics Data System (ADS)

Weiss, Chester J.

2013-08-01

An essential element for computational hypothesis testing, data inversion and experiment design for electromagnetic geophysics is a robust forward solver, capable of easily and quickly evaluating the electromagnetic response of arbitrary geologic structure. The usefulness of such a solver hinges on the balance among competing desires like ease of use, speed of forward calculation, scalability to large problems or compute clusters, parsimonious use of memory access, accuracy and by necessity, the ability to faithfully accommodate a broad range of geologic scenarios over extremes in length scale and frequency content. This is indeed a tall order. The present study addresses recent progress toward the development of a forward solver with these properties. Based on the Lorenz-gauged Helmholtz decomposition, a new finite volume solution over Cartesian model domains endowed with complex-valued electrical properties is shown to be stable over the frequency range 10-2-1010 Hz and range 10-3-105 m in length scale. Benchmark examples are drawn from magnetotellurics, exploration geophysics, geotechnical mapping and laboratory-scale analysis, showing excellent agreement with reference analytic solutions. Computational efficiency is achieved through use of a matrix-free implementation of the quasi-minimum-residual (QMR) iterative solver, which eliminates explicit storage of finite volume matrix elements in favor of "on the fly" computation as needed by the iterative Krylov sequence. Further efficiency is achieved through sparse coupling matrices between the vector and scalar potentials whose non-zero elements arise only in those parts of the model domain where the conductivity gradient is non-zero. Multi-thread parallelization in the QMR solver through OpenMP pragmas is used to reduce the computational cost of its most expensive step: the single matrix-vector product at each iteration. High-level MPI communicators farm independent processes to available compute nodes for simultaneous computation of multi-frequency or multi-transmitter responses.

WARP3D-Release 10.8: Dynamic Nonlinear Analysis of Solids using a Preconditioned Conjugate Gradient Software Architecture

NASA Technical Reports Server (NTRS)

Koppenhoefer, Kyle C.; Gullerud, Arne S.; Ruggieri, Claudio; Dodds, Robert H., Jr.; Healy, Brian E.

1998-01-01

This report describes theoretical background material and commands necessary to use the WARP3D finite element code. WARP3D is under continuing development as a research code for the solution of very large-scale, 3-D solid models subjected to static and dynamic loads. Specific features in the code oriented toward the investigation of ductile fracture in metals include a robust finite strain formulation, a general J-integral computation facility (with inertia, face loading), an element extinction facility to model crack growth, nonlinear material models including viscoplastic effects, and the Gurson-Tver-gaard dilatant plasticity model for void growth. The nonlinear, dynamic equilibrium equations are solved using an incremental-iterative, implicit formulation with full Newton iterations to eliminate residual nodal forces. The history integration of the nonlinear equations of motion is accomplished with Newmarks Beta method. A central feature of WARP3D involves the use of a linear-preconditioned conjugate gradient (LPCG) solver implemented in an element-by-element format to replace a conventional direct linear equation solver. This software architecture dramatically reduces both the memory requirements and CPU time for very large, nonlinear solid models since formation of the assembled (dynamic) stiffness matrix is avoided. Analyses thus exhibit the numerical stability for large time (load) steps provided by the implicit formulation coupled with the low memory requirements characteristic of an explicit code. In addition to the much lower memory requirements of the LPCG solver, the CPU time required for solution of the linear equations during each Newton iteration is generally one-half or less of the CPU time required for a traditional direct solver. All other computational aspects of the code (element stiffnesses, element strains, stress updating, element internal forces) are implemented in the element-by- element, blocked architecture. This greatly improves vectorization of the code on uni-processor hardware and enables straightforward parallel-vector processing of element blocks on multi-processor hardware.

What's Cooler Than Being Cool? Ice-Sheet Models Using a Fluidity-Based FOSLS Approach to Nonlinear-Stokes Flow

NASA Astrophysics Data System (ADS)

Allen, Jeffery M.

This research involves a few First-Order System Least Squares (FOSLS) formulations of a nonlinear-Stokes flow model for ice sheets. In Glen's flow law, a commonly used constitutive equation for ice rheology, the viscosity becomes infinite as the velocity gradients approach zero. This typically occurs near the ice surface or where there is basal sliding. The computational difficulties associated with the infinite viscosity are often overcome by an arbitrary modification of Glen's law that bounds the maximum viscosity. The FOSLS formulations developed in this thesis are designed to overcome this difficulty. The first FOSLS formulation is just the first-order representation of the standard nonlinear, full-Stokes and is known as the viscosity formulation and suffers from the problem above. To overcome the problem of infinite viscosity, two new formulation exploit the fact that the deviatoric stress, the product of viscosity and strain-rate, approaches zero as the viscosity goes to infinity. Using the deviatoric stress as the basis for a first-order system results in the the basic fluidity system. Augmenting the basic fluidity system with a curl-type equation results in the augmented fluidity system, which is more amenable to the iterative solver, Algebraic MultiGrid (AMG). A Nested Iteration (NI) Newton-FOSLS-AMG approach is used to solve the nonlinear-Stokes problems. Several test problems from the ISMIP set of benchmarks is examined to test the effectiveness of the various formulations. These test show that the viscosity based method is more expensive and less accurate. The basic fluidity system shows optimal finite-element convergence. However, there is not yet an efficient iterative solver for this type of system and this is the topic of future research. Alternatively, AMG performs better on the augmented fluidity system when using specific scaling. Unfortunately, this scaling results in reduced finite-element convergence.

Lateral conduction effects on heat-transfer data obtained with the phase-change paint technique

NASA Technical Reports Server (NTRS)

Maise, G.; Rossi, M. J.

1974-01-01

A computerized tool, CAPE, (Conduction Analysis Program using Eigenvalues) has been developed to account for lateral heat conduction in wind tunnel models in the data reduction of the phase-change paint technique. The tool also accounts for the effects of finite thickness (thin wings) and surface curvature. A special reduction procedure using just one time of melt is also possible on leading edges. A novel iterative numerical scheme was used, with discretized spatial coordinates but analytic integration in time, to solve the inverse conduction problem involved in the data reduction. A yes-no chart is provided which tells the test engineer when various corrections are large enough so that CAPE should be used. The accuracy of the phase-change paint technique in the presence of finite thickness and lateral conduction is also investigated.

A finite element conjugate gradient FFT method for scattering

NASA Technical Reports Server (NTRS)

Collins, Jeffery D.; Zapp, John; Hsa, Chang-Yu; Volakis, John L.

1990-01-01

An extension of a two dimensional formulation is presented for a three dimensional body of revolution. With the introduction of a Fourier expansion of the vector electric and magnetic fields, a coupled two dimensional system is generated and solved via the finite element method. An exact boundary condition is employed to terminate the mesh and the fast fourier transformation (FFT) is used to evaluate the boundary integrals for low O(n) memory demand when an iterative solution algorithm is used. By virtue of the finite element method, the algorithm is applicable to structures of arbitrary material composition. Several improvements to the two dimensional algorithm are also described. These include: (1) modifications for terminating the mesh at circular boundaries without distorting the convolutionality of the boundary integrals; (2) the development of nonproprietary mesh generation routines for two dimensional applications; (3) the development of preprocessors for interfacing SDRC IDEAS with the main algorithm; and (4) the development of post-processing algorithms based on the public domain package GRAFIC to generate two and three dimensional gray level and color field maps.

Partitioned fluid-solid coupling for cardiovascular blood flow: left-ventricular fluid mechanics.

PubMed

Krittian, Sebastian; Janoske, Uwe; Oertel, Herbert; Böhlke, Thomas

2010-04-01

We present a 3D code-coupling approach which has been specialized towards cardiovascular blood flow. For the first time, the prescribed geometry movement of the cardiovascular flow model KaHMo (Karlsruhe Heart Model) has been replaced by a myocardial composite model. Deformation is driven by fluid forces and myocardial response, i.e., both its contractile and constitutive behavior. Whereas the arbitrary Lagrangian-Eulerian formulation (ALE) of the Navier-Stokes equations is discretized by finite volumes (FVM), the solid mechanical finite elasticity equations are discretized by a finite element (FEM) approach. Taking advantage of specialized numerical solution strategies for non-matching fluid and solid domain meshes, an iterative data-exchange guarantees the interface equilibrium of the underlying governing equations. The focus of this work is on left-ventricular fluid-structure interaction based on patient-specific magnetic resonance imaging datasets. Multi-physical phenomena are described by temporal visualization and characteristic FSI numbers. The results gained show flow patterns that are in good agreement with previous observations. A deeper understanding of cavity deformation, blood flow, and their vital interaction can help to improve surgical treatment and clinical therapy planning.

Nonlinear analysis for the response and failure of compression-loaded angle-ply laminates with a hole

NASA Technical Reports Server (NTRS)

Mathison, Steven R.; Herakovich, Carl T.; Pindera, Marek-Jerzy; Shuart, Mark J.

1987-01-01

The objective was to determine the effect of nonlinear material behavior on the response and failure of unnotched and notched angle-ply laminates under uniaxial compressive loading. The endochronic theory was chosen as the constitutive theory to model the AS4/3502 graphite-epoxy material system. Three-dimensional finite element analysis incorporating the endochronic theory was used to determine the stresses and strains in the laminates. An incremental/iterative initial strain algorithm was used in the finite element program. To increase computational efficiency, a 180 deg rotational symmetry relationship was utilized and the finite element program was vectorized to run on a supercomputer. Laminate response was compared to experimentation revealing excellent agreement for both the unnotched and notched angle-ply laminates. Predicted stresses in the region of the hole were examined and are presented, comparing linear elastic analysis to the inelastic endochronic theory analysis. A failure analysis of the unnotched and notched laminates was performed using the quadratic tensor polynomial. Predicted fracture loads compared well with experimentation for the unnotched laminates, but were very conservative in comparison with experiments for the notched laminates.

Possibilities of the particle finite element method for fluid-soil-structure interaction problems

NASA Astrophysics Data System (ADS)

Oñate, Eugenio; Celigueta, Miguel Angel; Idelsohn, Sergio R.; Salazar, Fernando; Suárez, Benjamín

2011-09-01

We present some developments in the particle finite element method (PFEM) for analysis of complex coupled problems in mechanics involving fluid-soil-structure interaction (FSSI). The PFEM uses an updated Lagrangian description to model the motion of nodes (particles) in both the fluid and the solid domains (the later including soil/rock and structures). A mesh connects the particles (nodes) defining the discretized domain where the governing equations for each of the constituent materials are solved as in the standard FEM. The stabilization for dealing with an incompressibility continuum is introduced via the finite calculus method. An incremental iterative scheme for the solution of the non linear transient coupled FSSI problem is described. The procedure to model frictional contact conditions and material erosion at fluid-solid and solid-solid interfaces is described. We present several examples of application of the PFEM to solve FSSI problems such as the motion of rocks by water streams, the erosion of a river bed adjacent to a bridge foundation, the stability of breakwaters and constructions sea waves and the study of landslides.

An Approach for Assessing Delamination Propagation Capabilities in Commercial Finite Element Codes

NASA Technical Reports Server (NTRS)

Krueger, Ronald

2007-01-01

An approach for assessing the delamination propagation capabilities in commercial finite element codes is presented and demonstrated for one code. For this investigation, the Double Cantilever Beam (DCB) specimen and the Single Leg Bending (SLB) specimen were chosen for full three-dimensional finite element simulations. First, benchmark results were created for both specimens. Second, starting from an initially straight front, the delamination was allowed to propagate. Good agreement between the load-displacement relationship obtained from the propagation analysis results and the benchmark results could be achieved by selecting the appropriate input parameters. Selecting the appropriate input parameters, however, was not straightforward and often required an iterative procedure. Qualitatively, the delamination front computed for the DCB specimen did not take the shape of a curved front as expected. However, the analysis of the SLB specimen yielded a curved front as may be expected from the distribution of the energy release rate and the failure index across the width of the specimen. Overall, the results are encouraging but further assessment on a structural level is required.

A nonlinear dynamic finite element approach for simulating muscular hydrostats.

PubMed

Vavourakis, V; Kazakidi, A; Tsakiris, D P; Ekaterinaris, J A

2014-01-01

An implicit nonlinear finite element model for simulating biological muscle mechanics is developed. The numerical method is suitable for dynamic simulations of three-dimensional, nonlinear, nearly incompressible, hyperelastic materials that undergo large deformations. These features characterise biological muscles, which consist of fibres and connective tissues. It can be assumed that the stress distribution inside the muscles is the superposition of stresses along the fibres and the connective tissues. The mechanical behaviour of the surrounding tissues is determined by adopting a Mooney-Rivlin constitutive model, while the mechanical description of fibres is considered to be the sum of active and passive stresses. Due to the nonlinear nature of the problem, evaluation of the Jacobian matrix is carried out in order to subsequently utilise the standard Newton-Raphson iterative procedure and to carry out time integration with an implicit scheme. The proposed methodology is implemented into our in-house, open source, finite element software, which is validated by comparing numerical results with experimental measurements and other numerical results. Finally, the numerical procedure is utilised to simulate primitive octopus arm manoeuvres, such as bending and reaching.

An Approach to Assess Delamination Propagation Simulation Capabilities in Commercial Finite Element Codes

NASA Technical Reports Server (NTRS)

Krueger, Ronald

2008-01-01

An approach for assessing the delamination propagation simulation capabilities in commercial finite element codes is presented and demonstrated. For this investigation, the Double Cantilever Beam (DCB) specimen and the Single Leg Bending (SLB) specimen were chosen for full three-dimensional finite element simulations. First, benchmark results were created for both specimens. Second, starting from an initially straight front, the delamination was allowed to propagate. The load-displacement relationship and the total strain energy obtained from the propagation analysis results and the benchmark results were compared and good agreements could be achieved by selecting the appropriate input parameters. Selecting the appropriate input parameters, however, was not straightforward and often required an iterative procedure. Qualitatively, the delamination front computed for the DCB specimen did not take the shape of a curved front as expected. However, the analysis of the SLB specimen yielded a curved front as was expected from the distribution of the energy release rate and the failure index across the width of the specimen. Overall, the results are encouraging but further assessment on a structural level is required.

Aeroelastic Stability of Rotor Blades Using Finite Element Analysis

NASA Technical Reports Server (NTRS)

Chopra, I.; Sivaneri, N.

1982-01-01

The flutter stability of flap bending, lead-lag bending, and torsion of helicopter rotor blades in hover is investigated using a finite element formulation based on Hamilton's principle. The blade is divided into a number of finite elements. Quasi-steady strip theory is used to evaluate the aerodynamic loads. The nonlinear equations of motion are solved for steady-state blade deflections through an iterative procedure. The equations of motion are linearized assuming blade motion to be a small perturbation about the steady deflected shape. The normal mode method based on the coupled rotating natural modes is used to reduce the number of equations in the flutter analysis. First the formulation is applied to single-load-path blades (articulated and hingeless blades). Numerical results show very good agreement with existing results obtained using the modal approach. The second part of the application concerns multiple-load-path blades, i.e. bearingless blades. Numerical results are presented for several analytical models of the bearingless blade. Results are also obtained using an equivalent beam approach wherein a bearingless blade is modelled as a single beam with equivalent properties. Results show the equivalent beam model.

Development of new vibration energy flow analysis software and its applications to vehicle systems

NASA Astrophysics Data System (ADS)

Kim, D.-J.; Hong, S.-Y.; Park, Y.-H.

2005-09-01

The Energy flow analysis (EFA) offers very promising results in predicting the noise and vibration responses of system structures in medium-to-high frequency ranges. We have developed the Energy flow finite element method (EFFEM) based software, EFADSC++ R4, for the vibration analysis. The software can analyze the system structures composed of beam, plate, spring-damper, rigid body elements and many other components developed, and has many useful functions in analysis. For convenient use of the software, the main functions of the whole software are modularized into translator, model-converter, and solver. The translator module makes it possible to use finite element (FE) model for the vibration analysis. The model-converter module changes FE model into energy flow finite element (EFFE) model, and generates joint elements to cover the vibrational attenuation in the complex structures composed of various elements and can solve the joint element equations by using the wave tra! nsmission approach very quickly. The solver module supports the various direct and iterative solvers for multi-DOF structures. The predictions of vibration for real vehicles by using the developed software were performed successfully.

A parallel algorithm for the two-dimensional time fractional diffusion equation with implicit difference method.

PubMed

Gong, Chunye; Bao, Weimin; Tang, Guojian; Jiang, Yuewen; Liu, Jie

2014-01-01

It is very time consuming to solve fractional differential equations. The computational complexity of two-dimensional fractional differential equation (2D-TFDE) with iterative implicit finite difference method is O(M(x)M(y)N(2)). In this paper, we present a parallel algorithm for 2D-TFDE and give an in-depth discussion about this algorithm. A task distribution model and data layout with virtual boundary are designed for this parallel algorithm. The experimental results show that the parallel algorithm compares well with the exact solution. The parallel algorithm on single Intel Xeon X5540 CPU runs 3.16-4.17 times faster than the serial algorithm on single CPU core. The parallel efficiency of 81 processes is up to 88.24% compared with 9 processes on a distributed memory cluster system. We do think that the parallel computing technology will become a very basic method for the computational intensive fractional applications in the near future.

A transonic interactive boundary-layer theory for laminar and turbulent flow over swept wings

NASA Technical Reports Server (NTRS)

Woodson, Shawn H.; Dejarnette, Fred R.

1988-01-01

A 3-D laminar and turbulent boundary-layer method is developed for compressible flow over swept wings. The governing equations and curvature terms are derived in detail for a nonorthogonal, curvilinear coordinate system. Reynolds shear-stress terms are modeled by the Cebeci-Smith eddy-viscosity formulation. The governing equations are descretized using the second-order accurate, predictor-corrector finite-difference technique of Matsuno, which has the advantage that the crossflow difference formulas are formed independent of the sign of the crossflow velocity component. The method is coupled with a full potential wing/body inviscid code (FLO-30) and the inviscid-viscous interaction is performed by updating the original wing surface with the viscous displacement surface calculated by the boundary-layer code. The number of these global iterations ranged from five to twelve depending on Mach number, sweep angle, and angle of attack. Several test cases are computed by this method and the results are compared with another inviscid-viscous interaction method (TAWFIVE) and with experimental data.

Two-Level Chebyshev Filter Based Complementary Subspace Method: Pushing the Envelope of Large-Scale Electronic Structure Calculations.

PubMed

Banerjee, Amartya S; Lin, Lin; Suryanarayana, Phanish; Yang, Chao; Pask, John E

2018-06-12

We describe a novel iterative strategy for Kohn-Sham density functional theory calculations aimed at large systems (>1,000 electrons), applicable to metals and insulators alike. In lieu of explicit diagonalization of the Kohn-Sham Hamiltonian on every self-consistent field (SCF) iteration, we employ a two-level Chebyshev polynomial filter based complementary subspace strategy to (1) compute a set of vectors that span the occupied subspace of the Hamiltonian; (2) reduce subspace diagonalization to just partially occupied states; and (3) obtain those states in an efficient, scalable manner via an inner Chebyshev filter iteration. By reducing the necessary computation to just partially occupied states and obtaining these through an inner Chebyshev iteration, our approach reduces the cost of large metallic calculations significantly, while eliminating subspace diagonalization for insulating systems altogether. We describe the implementation of the method within the framework of the discontinuous Galerkin (DG) electronic structure method and show that this results in a computational scheme that can effectively tackle bulk and nano systems containing tens of thousands of electrons, with chemical accuracy, within a few minutes or less of wall clock time per SCF iteration on large-scale computing platforms. We anticipate that our method will be instrumental in pushing the envelope of large-scale ab initio molecular dynamics. As a demonstration of this, we simulate a bulk silicon system containing 8,000 atoms at finite temperature, and obtain an average SCF step wall time of 51 s on 34,560 processors; thus allowing us to carry out 1.0 ps of ab initio molecular dynamics in approximately 28 h (of wall time).

Optimal vibration control of a rotating plate with self-sensing active constrained layer damping

NASA Astrophysics Data System (ADS)

Xie, Zhengchao; Wong, Pak Kin; Lo, Kin Heng

2012-04-01

This paper proposes a finite element model for optimally controlled constrained layer damped (CLD) rotating plate with self-sensing technique and frequency-dependent material property in both the time and frequency domain. Constrained layer damping with viscoelastic material can effectively reduce the vibration in rotating structures. However, most existing research models use complex modulus approach to model viscoelastic material, and an additional iterative approach which is only available in frequency domain has to be used to include the material's frequency dependency. It is meaningful to model the viscoelastic damping layer in rotating part by using the anelastic displacement fields (ADF) in order to include the frequency dependency in both the time and frequency domain. Also, unlike previous ones, this finite element model treats all three layers as having the both shear and extension strains, so all types of damping are taken into account. Thus, in this work, a single layer finite element is adopted to model a three-layer active constrained layer damped rotating plate in which the constraining layer is made of piezoelectric material to work as both the self-sensing sensor and actuator under an linear quadratic regulation (LQR) controller. After being compared with verified data, this newly proposed finite element model is validated and could be used for future research.

Fitted hyperelastic parameters for Human brain tissue from reported tension, compression, and shear tests.

PubMed

Moran, Richard; Smith, Joshua H; García, José J

2014-11-28

The mechanical properties of human brain tissue are the subject of interest because of their use in understanding brain trauma and in developing therapeutic treatments and procedures. To represent the behavior of the tissue, we have developed hyperelastic mechanical models whose parameters are fitted in accordance with experimental test results. However, most studies available in the literature have fitted parameters with data of a single type of loading, such as tension, compression, or shear. Recently, Jin et al. (Journal of Biomechanics 46:2795-2801, 2013) reported data from ex vivo tests of human brain tissue under tension, compression, and shear loading using four strain rates and four different brain regions. However, they do not report parameters of energy functions that can be readily used in finite element simulations. To represent the tissue behavior for the quasi-static loading conditions, we aimed to determine the best fit of the hyperelastic parameters of the hyperfoam, Ogden, and polynomial strain energy functions available in ABAQUS for the low strain rate data, while simultaneously considering all three loading modes. We used an optimization process conducted in MATLAB, calling iteratively three finite element models developed in ABAQUS that represent the three loadings. Results showed a relatively good fit to experimental data in all loading modes using two terms in the energy functions. Values for the shear modulus obtained in this analysis (897-1653Pa) are in the range of those presented in other studies. These energy-function parameters can be used in brain tissue simulations using finite element models. Copyright © 2014 Elsevier Ltd. All rights reserved.

Stability analysis of a deterministic dose calculation for MRI-guided radiotherapy.

PubMed

Zelyak, O; Fallone, B G; St-Aubin, J

2017-12-14

Modern effort in radiotherapy to address the challenges of tumor localization and motion has led to the development of MRI guided radiotherapy technologies. Accurate dose calculations must properly account for the effects of the MRI magnetic fields. Previous work has investigated the accuracy of a deterministic linear Boltzmann transport equation (LBTE) solver that includes magnetic field, but not the stability of the iterative solution method. In this work, we perform a stability analysis of this deterministic algorithm including an investigation of the convergence rate dependencies on the magnetic field, material density, energy, and anisotropy expansion. The iterative convergence rate of the continuous and discretized LBTE including magnetic fields is determined by analyzing the spectral radius using Fourier analysis for the stationary source iteration (SI) scheme. The spectral radius is calculated when the magnetic field is included (1) as a part of the iteration source, and (2) inside the streaming-collision operator. The non-stationary Krylov subspace solver GMRES is also investigated as a potential method to accelerate the iterative convergence, and an angular parallel computing methodology is investigated as a method to enhance the efficiency of the calculation. SI is found to be unstable when the magnetic field is part of the iteration source, but unconditionally stable when the magnetic field is included in the streaming-collision operator. The discretized LBTE with magnetic fields using a space-angle upwind stabilized discontinuous finite element method (DFEM) was also found to be unconditionally stable, but the spectral radius rapidly reaches unity for very low-density media and increasing magnetic field strengths indicating arbitrarily slow convergence rates. However, GMRES is shown to significantly accelerate the DFEM convergence rate showing only a weak dependence on the magnetic field. In addition, the use of an angular parallel computing strategy is shown to potentially increase the efficiency of the dose calculation.

Stability analysis of a deterministic dose calculation for MRI-guided radiotherapy

NASA Astrophysics Data System (ADS)

Zelyak, O.; Fallone, B. G.; St-Aubin, J.

2018-01-01

Modern effort in radiotherapy to address the challenges of tumor localization and motion has led to the development of MRI guided radiotherapy technologies. Accurate dose calculations must properly account for the effects of the MRI magnetic fields. Previous work has investigated the accuracy of a deterministic linear Boltzmann transport equation (LBTE) solver that includes magnetic field, but not the stability of the iterative solution method. In this work, we perform a stability analysis of this deterministic algorithm including an investigation of the convergence rate dependencies on the magnetic field, material density, energy, and anisotropy expansion. The iterative convergence rate of the continuous and discretized LBTE including magnetic fields is determined by analyzing the spectral radius using Fourier analysis for the stationary source iteration (SI) scheme. The spectral radius is calculated when the magnetic field is included (1) as a part of the iteration source, and (2) inside the streaming-collision operator. The non-stationary Krylov subspace solver GMRES is also investigated as a potential method to accelerate the iterative convergence, and an angular parallel computing methodology is investigated as a method to enhance the efficiency of the calculation. SI is found to be unstable when the magnetic field is part of the iteration source, but unconditionally stable when the magnetic field is included in the streaming-collision operator. The discretized LBTE with magnetic fields using a space-angle upwind stabilized discontinuous finite element method (DFEM) was also found to be unconditionally stable, but the spectral radius rapidly reaches unity for very low-density media and increasing magnetic field strengths indicating arbitrarily slow convergence rates. However, GMRES is shown to significantly accelerate the DFEM convergence rate showing only a weak dependence on the magnetic field. In addition, the use of an angular parallel computing strategy is shown to potentially increase the efficiency of the dose calculation.

Corrigendum to "Stability analysis of a deterministic dose calculation for MRI-guided radiotherapy".

PubMed

Zelyak, Oleksandr; Fallone, B Gino; St-Aubin, Joel

2018-03-12

Modern effort in radiotherapy to address the challenges of tumor localization and motion has led to the development of MRI guided radiotherapy technologies. Accurate dose calculations must properly account for the effects of the MRI magnetic fields. Previous work has investigated the accuracy of a deterministic linear Boltzmann transport equation (LBTE) solver that includes magnetic field, but not the stability of the iterative solution method. In this work, we perform a stability analysis of this deterministic algorithm including an investigation of the convergence rate dependencies on the magnetic field, material density, energy, and anisotropy expansion. The iterative convergence rate of the continuous and discretized LBTE including magnetic fields is determined by analyzing the spectral radius using Fourier analysis for the stationary source iteration (SI) scheme. The spectral radius is calculated when the magnetic field is included (1) as a part of the iteration source, and (2) inside the streaming-collision operator. The non-stationary Krylov subspace solver GMRES is also investigated as a potential method to accelerate the iterative convergence, and an angular parallel computing methodology is investigated as a method to enhance the efficiency of the calculation. SI is found to be unstable when the magnetic field is part of the iteration source, but unconditionally stable when the magnetic field is included in the streaming-collision operator. The discretized LBTE with magnetic fields using a space-angle upwind stabilized discontinuous finite element method (DFEM) was also found to be unconditionally stable, but the spectral radius rapidly reaches unity for very low density media and increasing magnetic field strengths indicating arbitrarily slow convergence rates. However, GMRES is shown to significantly accelerate the DFEM convergence rate showing only a weak dependence on the magnetic field. In addition, the use of an angular parallel computing strategy is shown to potentially increase the efficiency of the dose calculation. © 2018 Institute of Physics and Engineering in Medicine.

A machine learning approach as a surrogate of finite element analysis-based inverse method to estimate the zero-pressure geometry of human thoracic aorta.

PubMed

Liang, Liang; Liu, Minliang; Martin, Caitlin; Sun, Wei

2018-05-09

Advances in structural finite element analysis (FEA) and medical imaging have made it possible to investigate the in vivo biomechanics of human organs such as blood vessels, for which organ geometries at the zero-pressure level need to be recovered. Although FEA-based inverse methods are available for zero-pressure geometry estimation, these methods typically require iterative computation, which are time-consuming and may be not suitable for time-sensitive clinical applications. In this study, by using machine learning (ML) techniques, we developed an ML model to estimate the zero-pressure geometry of human thoracic aorta given 2 pressurized geometries of the same patient at 2 different blood pressure levels. For the ML model development, a FEA-based method was used to generate a dataset of aorta geometries of 3125 virtual patients. The ML model, which was trained and tested on the dataset, is capable of recovering zero-pressure geometries consistent with those generated by the FEA-based method. Thus, this study demonstrates the feasibility and great potential of using ML techniques as a fast surrogate of FEA-based inverse methods to recover zero-pressure geometries of human organs. Copyright © 2018 John Wiley & Sons, Ltd.