Common aero vehicle autonomous reentry trajectory optimization satisfying waypoint and no-fly zone constraints

NASA Astrophysics Data System (ADS)

Jorris, Timothy R.

2007-12-01

To support the Air Force's Global Reach concept, a Common Aero Vehicle is being designed to support the Global Strike mission. "Waypoints" are specified for reconnaissance or multiple payload deployments and "no-fly zones" are specified for geopolitical restrictions or threat avoidance. Due to time critical targets and multiple scenario analysis, an autonomous solution is preferred over a time-intensive, manually iterative one. Thus, a real-time or near real-time autonomous trajectory optimization technique is presented to minimize the flight time, satisfy terminal and intermediate constraints, and remain within the specified vehicle heating and control limitations. This research uses the Hypersonic Cruise Vehicle (HCV) as a simplified two-dimensional platform to compare multiple solution techniques. The solution techniques include a unique geometric approach developed herein, a derived analytical dynamic optimization technique, and a rapidly emerging collocation numerical approach. This up-and-coming numerical technique is a direct solution method involving discretization then dualization, with pseudospectral methods and nonlinear programming used to converge to the optimal solution. This numerical approach is applied to the Common Aero Vehicle (CAV) as the test platform for the full three-dimensional reentry trajectory optimization problem. The culmination of this research is the verification of the optimality of this proposed numerical technique, as shown for both the two-dimensional and three-dimensional models. Additionally, user implementation strategies are presented to improve accuracy and enhance solution convergence. Thus, the contributions of this research are the geometric approach, the user implementation strategies, and the determination and verification of a numerical solution technique for the optimal reentry trajectory problem that minimizes time to target while satisfying vehicle dynamics and control limitation, and heating, waypoint, and no-fly zone constraints.

The three-dimensional compressible flow in a radial inflow turbine scroll

NASA Technical Reports Server (NTRS)

Hamed, A.; Tabakoff, W.; Malak, M.

1984-01-01

This work presents the results of an analytical study and an experimental investigation of the three-dimensional flow in a turbine scroll. The finite element method is used in the iterative numerical solution of the locally linearized governing equations for the three-dimensional velocity potential field. The results of the numerical computations are compared with the experimental measurements in the scroll cross sections, which were obtained using laser Doppler velocimetry and hot wire techniques. The results of the computations show a variation in the flow conditions around the rotor periphery which was found to depend on the scroll geometry.

Numerical Solution of the Flow of a Perfect Gas Over A Circular Cylinder at Infinite Mach Number

NASA Technical Reports Server (NTRS)

Hamaker, Frank M.

1959-01-01

A solution for the two-dimensional flow of an inviscid perfect gas over a circular cylinder at infinite Mach number is obtained by numerical methods of analysis. Nonisentropic conditions of curved shock waves and vorticity are included in the solution. The analysis is divided into two distinct regions, the subsonic region which is analyzed by the relaxation method of Southwell and the supersonic region which was treated by the method of characteristics. Both these methods of analysis are inapplicable on the sonic line which is therefore considered separately. The shapes of the sonic line and the shock wave are obtained by iteration techniques. The striking result of the solution is the strong curvature of the sonic line and of the other lines of constant Mach number. Because of this the influence of the supersonic flow on the sonic line is negligible. On comparison with Newtonian flow methods, it is found that the approximate methods show a larger variation of surface pressure than is given by the present solution.

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

Pseudo-time methods for constrained optimization problems governed by PDE

NASA Technical Reports Server (NTRS)

Taasan, Shlomo

1995-01-01

In this paper we present a novel method for solving optimization problems governed by partial differential equations. Existing methods are gradient information in marching toward the minimum, where the constrained PDE is solved once (sometimes only approximately) per each optimization step. Such methods can be viewed as a marching techniques on the intersection of the state and costate hypersurfaces while improving the residuals of the design equations per each iteration. In contrast, the method presented here march on the design hypersurface and at each iteration improve the residuals of the state and costate equations. The new method is usually much less expensive per iteration step since, in most problems of practical interest, the design equation involves much less unknowns that that of either the state or costate equations. Convergence is shown using energy estimates for the evolution equations governing the iterative process. Numerical tests show that the new method allows the solution of the optimization problem in a cost of solving the analysis problems just a few times, independent of the number of design parameters. The method can be applied using single grid iterations as well as with multigrid solvers.

Steady-state protein focusing in carrier ampholyte based isoelectric focusing: Part I-Analytical solution.

PubMed

Shim, Jaesool; Yoo, Kisoo; Dutta, Prashanta

2017-03-01

The determination of an analytical solution to find the steady-state protein concentration distribution in IEF is very challenging due to the nonlinear coupling between mass and charge conservation equations. In this study, approximate analytical solutions are obtained for steady-state protein distribution in carrier ampholyte based IEF. Similar to the work of Svensson, the final concentration profile for proteins is assumed to be Gaussian, but appropriate expressions are presented in order to obtain the effective electric field and pH gradient in the focused protein band region. Analytical results are found from iterative solutions of a system of coupled algebraic equations using only several iterations for IEF separation of three plasma proteins: albumin, cardiac troponin I, and hemoglobin. The analytical results are compared with numerically predicted results for IEF, showing excellent agreement. Analytically obtained electric field and ionic conductivity distributions show significant deviation from their nominal values, which is essential in finding the protein focusing behavior at isoelectric points. These analytical solutions can be used to determine steady-state protein concentration distribution for experiment design of IEF considering any number of proteins and ampholytes. Moreover, the model presented herein can be used to find the conductivity, electric field, and pH field. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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.

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

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.

Numerical Analysis of Coolant Flow and Heat Transfer in ITER Diagnostic First Wall

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

Khodak, A.; Loesser, G.; Zhai, Y.

2015-07-24

We performed numerical simulations of the ITER Diagnostic First Wall (DFW) using ANSYS workbench. During operation DFW will include solid main body as well as liquid coolant. Thus thermal and hydraulic analysis of the DFW was performed using conjugated heat transfer approach, in which heat transfer was resolved in both solid and liquid parts, and simultaneously fluid dynamics analysis was performed only in the liquid part. This approach includes interface between solid and liquid part of the systemAnalysis was performed using ANSYS CFX software. CFX software allows solution of heat transfer equations in solid and liquid part, and solution ofmore » the flow equations in the liquid part. Coolant flow in the DFW was assumed turbulent and was resolved using Reynolds averaged Navier-Stokes equations with Shear Stress Transport turbulence model. Meshing was performed using CFX method available within ANSYS. The data cloud for thermal loading consisting of volumetric heating and surface heating was imported into CFX Volumetric heating source was generated using Attila software. Surface heating was obtained using radiation heat transfer analysis. Our results allowed us to identify areas of excessive heating. Proposals for cooling channel relocation were made. Additional suggestions were made to improve hydraulic performance of the cooling system.« less

Adaptive [theta]-methods for pricing American options

NASA Astrophysics Data System (ADS)

Khaliq, Abdul Q. M.; Voss, David A.; Kazmi, Kamran

2008-12-01

We develop adaptive [theta]-methods for solving the Black-Scholes PDE for American options. By adding a small, continuous term, the Black-Scholes PDE becomes an advection-diffusion-reaction equation on a fixed spatial domain. Standard implementation of [theta]-methods would require a Newton-type iterative procedure at each time step thereby increasing the computational complexity of the methods. Our linearly implicit approach avoids such complications. We establish a general framework under which [theta]-methods satisfy a discrete version of the positivity constraint characteristic of American options, and numerically demonstrate the sensitivity of the constraint. The positivity results are established for the single-asset and independent two-asset models. In addition, we have incorporated and analyzed an adaptive time-step control strategy to increase the computational efficiency. Numerical experiments are presented for one- and two-asset American options, using adaptive exponential splitting for two-asset problems. The approach is compared with an iterative solution of the two-asset problem in terms of computational efficiency.

Image reconstruction algorithms for electrical capacitance tomography based on ROF model using new numerical techniques

NASA Astrophysics Data System (ADS)

Chen, Jiaoxuan; Zhang, Maomao; Liu, Yinyan; Chen, Jiaoliao; Li, Yi

2017-03-01

Electrical capacitance tomography (ECT) is a promising technique applied in many fields. However, the solutions for ECT are not unique and highly sensitive to the measurement noise. To remain a good shape of reconstructed object and endure a noisy data, a Rudin-Osher-Fatemi (ROF) model with total variation regularization is applied to image reconstruction in ECT. Two numerical methods, which are simplified augmented Lagrangian (SAL) and accelerated alternating direction method of multipliers (AADMM), are innovatively introduced to try to solve the above mentioned problems in ECT. The effect of the parameters and the number of iterations for different algorithms, and the noise level in capacitance data are discussed. Both simulation and experimental tests were carried out to validate the feasibility of the proposed algorithms, compared to the Landweber iteration (LI) algorithm. The results show that the SAL and AADMM algorithms can handle a high level of noise and the AADMM algorithm outperforms other algorithms in identifying the object from its background.

Nonlinear equation of the modes in circular slab waveguides and its application.

PubMed

Zhu, Jianxin; Zheng, Jia

2013-11-20

In this paper, circularly curved inhomogeneous waveguides are transformed into straight inhomogeneous waveguides first by a conformal mapping. Then, the differential transfer matrix method is introduced and adopted to deduce the exact dispersion relation for modes. This relation itself is complex and difficult to solve, but it can be approximated by a simpler nonlinear equation in practical applications, which is close to the exact relation and quite easy to analyze. Afterward, optimized asymptotic solutions are obtained and act as initial guesses for the following Newton's iteration. Finally, very accurate solutions are achieved in the numerical experiment.

Determination of gap solution and critical temperature in doped graphene superconductivity

NASA Astrophysics Data System (ADS)

Xu, Chenmei; Yang, Yisong

2017-04-01

It is shown that the gap solution and critical transition temperature are significantly enhanced by doping in a recently developed BCS formalism for graphene superconductivity in such a way that positive gap and transition temperature both occur in arbitrary pairing coupling as far as doping is present. The analytic construction of the BCS gap and transition temperature offers highly effective globally convergent iterative methods for the computation of these quantities. A series of numerical examples are presented as illustrations which are in agreement with the theoretical and experimental results obtained in the physics literature and consolidate the analytic understanding achieved.

High-Order Methods for Incompressible Fluid Flow

NASA Astrophysics Data System (ADS)

Deville, M. O.; Fischer, P. F.; Mund, E. H.

2002-08-01

High-order numerical methods provide an efficient approach to simulating many physical problems. This book considers the range of mathematical, engineering, and computer science topics that form the foundation of high-order numerical methods for the simulation of incompressible fluid flows in complex domains. Introductory chapters present high-order spatial and temporal discretizations for one-dimensional problems. These are extended to multiple space dimensions with a detailed discussion of tensor-product forms, multi-domain methods, and preconditioners for iterative solution techniques. Numerous discretizations of the steady and unsteady Stokes and Navier-Stokes equations are presented, with particular sttention given to enforcement of imcompressibility. Advanced discretizations. implementation issues, and parallel and vector performance are considered in the closing sections. Numerous examples are provided throughout to illustrate the capabilities of high-order methods in actual applications.

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.

Numerical solution of the exterior oblique derivative BVP using the direct BEM formulation

NASA Astrophysics Data System (ADS)

Čunderlík, Róbert; Špir, Róbert; Mikula, Karol

2016-04-01

The fixed gravimetric boundary value problem (FGBVP) represents an exterior oblique derivative problem for the Laplace equation. A direct formulation of the boundary element method (BEM) for the Laplace equation leads to a boundary integral equation (BIE) where a harmonic function is represented as a superposition of the single-layer and double-layer potential. Such a potential representation is applied to obtain a numerical solution of FGBVP. The oblique derivative problem is treated by a decomposition of the gradient of the unknown disturbing potential into its normal and tangential components. Our numerical scheme uses the collocation with linear basis functions. It involves a triangulated discretization of the Earth's surface as our computational domain considering its complicated topography. To achieve high-resolution numerical solutions, parallel implementations using the MPI subroutines as well as an iterative elimination of far zones' contributions are performed. Numerical experiments present a reconstruction of a harmonic function above the Earth's topography given by the spherical harmonic approach, namely by the EGM2008 geopotential model up to degree 2160. The SRTM30 global topography model is used to approximate the Earth's surface by the triangulated discretization. The obtained BEM solution with the resolution 0.05 deg (12,960,002 nodes) is compared with EGM2008. The standard deviation of residuals 5.6 cm indicates a good agreement. The largest residuals are obviously in high mountainous regions. They are negative reaching up to -0.7 m in Himalayas and about -0.3 m in Andes and Rocky Mountains. A local refinement in the area of Slovakia confirms an improvement of the numerical solution in this mountainous region despite of the fact that the Earth's topography is here considered in more details.

An Algorithm for the Mixed Transportation Network Design Problem

PubMed Central

Liu, Xinyu; Chen, Qun

2016-01-01

This paper proposes an optimization algorithm, the dimension-down iterative algorithm (DDIA), for solving a mixed transportation network design problem (MNDP), which is generally expressed as a mathematical programming with equilibrium constraint (MPEC). The upper level of the MNDP aims to optimize the network performance via both the expansion of the existing links and the addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium (UE) problem. The idea of the proposed solution algorithm (DDIA) is to reduce the dimensions of the problem. A group of variables (discrete/continuous) is fixed to optimize another group of variables (continuous/discrete) alternately; then, the problem is transformed into solving a series of CNDPs (continuous network design problems) and DNDPs (discrete network design problems) repeatedly until the problem converges to the optimal solution. The advantage of the proposed algorithm is that its solution process is very simple and easy to apply. Numerical examples show that for the MNDP without budget constraint, the optimal solution can be found within a few iterations with DDIA. For the MNDP with budget constraint, however, the result depends on the selection of initial values, which leads to different optimal solutions (i.e., different local optimal solutions). Some thoughts are given on how to derive meaningful initial values, such as by considering the budgets of new and reconstruction projects separately. PMID:27626803

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.

Development and tests of molybdenum armored copper components for MITICA ion source

NASA Astrophysics Data System (ADS)

Pavei, Mauro; Böswirth, Bernd; Greuner, Henri; Marcuzzi, Diego; Rizzolo, Andrea; Valente, Matteo

2016-02-01

In order to prevent detrimental material erosion of components impinged by back-streaming positive D or H ions in the megavolt ITER injector and concept advancement beam source, a solution based on explosion bonding technique has been identified for producing a 1 mm thick molybdenum armour layer on copper substrate, compatible with ITER requirements. Prototypes have been recently manufactured and tested in the high heat flux test facility Garching Large Divertor Sample Test Facility (GLADIS) to check the capability of the molybdenum-copper interface to withstand several thermal shock cycles at high power density. This paper presents both the numerical fluid-dynamic analyses of the prototypes simulating the test conditions in GLADIS as well as the experimental results.

Development and tests of molybdenum armored copper components for MITICA ion source

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

Pavei, Mauro, E-mail: mauro.pavei@igi.cnr.it; Marcuzzi, Diego; Rizzolo, Andrea

2016-02-15

In order to prevent detrimental material erosion of components impinged by back-streaming positive D or H ions in the megavolt ITER injector and concept advancement beam source, a solution based on explosion bonding technique has been identified for producing a 1 mm thick molybdenum armour layer on copper substrate, compatible with ITER requirements. Prototypes have been recently manufactured and tested in the high heat flux test facility Garching Large Divertor Sample Test Facility (GLADIS) to check the capability of the molybdenum-copper interface to withstand several thermal shock cycles at high power density. This paper presents both the numerical fluid-dynamic analysesmore » of the prototypes simulating the test conditions in GLADIS as well as the experimental results.« less

Development and tests of molybdenum armored copper components for MITICA ion source.

PubMed

Pavei, Mauro; Böswirth, Bernd; Greuner, Henri; Marcuzzi, Diego; Rizzolo, Andrea; Valente, Matteo

2016-02-01

In order to prevent detrimental material erosion of components impinged by back-streaming positive D or H ions in the megavolt ITER injector and concept advancement beam source, a solution based on explosion bonding technique has been identified for producing a 1 mm thick molybdenum armour layer on copper substrate, compatible with ITER requirements. Prototypes have been recently manufactured and tested in the high heat flux test facility Garching Large Divertor Sample Test Facility (GLADIS) to check the capability of the molybdenum-copper interface to withstand several thermal shock cycles at high power density. This paper presents both the numerical fluid-dynamic analyses of the prototypes simulating the test conditions in GLADIS as well as the experimental results.

A Two Colorable Fourth Order Compact Difference Scheme and Parallel Iterative Solution of the 3D Convection Diffusion Equation

NASA Technical Reports Server (NTRS)

Zhang, Jun; Ge, Lixin; Kouatchou, Jules

2000-01-01

A new fourth order compact difference scheme for the three dimensional convection diffusion equation with variable coefficients is presented. The novelty of this new difference scheme is that it Only requires 15 grid points and that it can be decoupled with two colors. The entire computational grid can be updated in two parallel subsweeps with the Gauss-Seidel type iterative method. This is compared with the known 19 point fourth order compact differenCe scheme which requires four colors to decouple the computational grid. Numerical results, with multigrid methods implemented on a shared memory parallel computer, are presented to compare the 15 point and the 19 point fourth order compact schemes.

One-dimensional analysis of unsteady flows due to supercritical heat addition in high speed condensing steam

NASA Astrophysics Data System (ADS)

Malek, N. A.; Hasini, H.; Yusoff, M. Z.

2013-06-01

Unsteadiness in supersonic flow in nozzles can be generated by the release of heat due to spontaneous condensation. The heat released is termed "supercritical" and may be responsible for turbine blades failure in turbine cascade as it causes a supersonic flow to decelerate. When the Mach number is reduced to unity, the flow can no longer sustain the additional heat and becomes unstable. This paper aims to numerically investigate the unsteadiness caused by supercritical heat addition in one-dimensional condensing flows. The governing equations for mass, momentum and energy, coupled with the equations describing the wetness fraction and droplet growth are integrated and solved iteratively to reveal the final solution. Comparison is made with well-established experimental and numerical solution done by previous researchers that shows similar phenomena.

A model reduction approach to numerical inversion for a parabolic partial differential equation

NASA Astrophysics Data System (ADS)

Borcea, Liliana; Druskin, Vladimir; Mamonov, Alexander V.; Zaslavsky, Mikhail

2014-12-01

We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where the unknown is the subsurface electrical resistivity and the data are time resolved surface measurements of the magnetic field. The algorithm presented in this paper considers inversion in one and two dimensions. The reduced model is obtained with rational interpolation in the frequency (Laplace) domain and a rational Krylov subspace projection method. It amounts to a nonlinear mapping from the function space of the unknown resistivity to the small dimensional space of the parameters of the reduced model. We use this mapping as a nonlinear preconditioner for the Gauss-Newton iterative solution of the inverse problem. The advantage of the inversion algorithm is twofold. First, the nonlinear preconditioner resolves most of the nonlinearity of the problem. Thus the iterations are less likely to get stuck in local minima and the convergence is fast. Second, the inversion is computationally efficient because it avoids repeated accurate simulations of the time-domain response. We study the stability of the inversion algorithm for various rational Krylov subspaces, and assess its performance with numerical experiments.

A different approach to estimate nonlinear regression model using numerical methods

NASA Astrophysics Data System (ADS)

Mahaboob, B.; Venkateswarlu, B.; Mokeshrayalu, G.; Balasiddamuni, P.

2017-11-01

This research paper concerns with the computational methods namely the Gauss-Newton method, Gradient algorithm methods (Newton-Raphson method, Steepest Descent or Steepest Ascent algorithm method, the Method of Scoring, the Method of Quadratic Hill-Climbing) based on numerical analysis to estimate parameters of nonlinear regression model in a very different way. Principles of matrix calculus have been used to discuss the Gradient-Algorithm methods. Yonathan Bard [1] discussed a comparison of gradient methods for the solution of nonlinear parameter estimation problems. However this article discusses an analytical approach to the gradient algorithm methods in a different way. This paper describes a new iterative technique namely Gauss-Newton method which differs from the iterative technique proposed by Gorden K. Smyth [2]. Hans Georg Bock et.al [10] proposed numerical methods for parameter estimation in DAE’s (Differential algebraic equation). Isabel Reis Dos Santos et al [11], Introduced weighted least squares procedure for estimating the unknown parameters of a nonlinear regression metamodel. For large-scale non smooth convex minimization the Hager and Zhang (HZ) conjugate gradient Method and the modified HZ (MHZ) method were presented by Gonglin Yuan et al [12].

Recovery of time-dependent volatility in option pricing model

NASA Astrophysics Data System (ADS)

Deng, Zui-Cha; Hon, Y. C.; Isakov, V.

2016-11-01

In this paper we investigate an inverse problem of determining the time-dependent volatility from observed market prices of options with different strikes. Due to the non linearity and sparsity of observations, an analytical solution to the problem is generally not available. Numerical approximation is also difficult to obtain using most of the existing numerical algorithms. Based on our recent theoretical results, we apply the linearisation technique to convert the problem into an inverse source problem from which recovery of the unknown volatility function can be achieved. Two kinds of strategies, namely, the integral equation method and the Landweber iterations, are adopted to obtain the stable numerical solution to the inverse problem. Both theoretical analysis and numerical examples confirm that the proposed approaches are effective. The work described in this paper was partially supported by a grant from the Research Grant Council of the Hong Kong Special Administrative Region (Project No. CityU 101112) and grants from the NNSF of China (Nos. 11261029, 11461039), and NSF grants DMS 10-08902 and 15-14886 and by Emylou Keith and Betty Dutcher Distinguished Professorship at the Wichita State University (USA).

Steady-state configuration and tension calculations of marine cables under complex currents via separated particle swarm optimization

NASA Astrophysics Data System (ADS)

Xu, Xue-song

2014-12-01

Under complex currents, the motion governing equations of marine cables are complex and nonlinear, and the calculations of cable configuration and tension become difficult compared with those under the uniform or simple currents. To obtain the numerical results, the usual Newton-Raphson iteration is often adopted, but its stability depends on the initial guessed solution to the governing equations. To improve the stability of numerical calculation, this paper proposed separated the particle swarm optimization, in which the variables are separated into several groups, and the dimension of search space is reduced to facilitate the particle swarm optimization. Via the separated particle swarm optimization, these governing nonlinear equations can be solved successfully with any initial solution, and the process of numerical calculation is very stable. For the calculations of cable configuration and tension of marine cables under complex currents, the proposed separated swarm particle optimization is more effective than the other particle swarm optimizations.

A family of conjugate gradient methods for large-scale nonlinear equations.

PubMed

Feng, Dexiang; Sun, Min; Wang, Xueyong

2017-01-01

In this paper, we present a family of conjugate gradient projection methods for solving large-scale nonlinear equations. At each iteration, it needs low storage and the subproblem can be easily solved. Compared with the existing solution methods for solving the problem, its global convergence is established without the restriction of the Lipschitz continuity on the underlying mapping. Preliminary numerical results are reported to show the efficiency of the proposed method.

Limited-memory trust-region methods for sparse relaxation

NASA Astrophysics Data System (ADS)

Adhikari, Lasith; DeGuchy, Omar; Erway, Jennifer B.; Lockhart, Shelby; Marcia, Roummel F.

2017-08-01

In this paper, we solve the l2-l1 sparse recovery problem by transforming the objective function of this problem into an unconstrained differentiable function and applying a limited-memory trust-region method. Unlike gradient projection-type methods, which uses only the current gradient, our approach uses gradients from previous iterations to obtain a more accurate Hessian approximation. Numerical experiments show that our proposed approach eliminates spurious solutions more effectively while improving computational time.

A Fixed-point Scheme for the Numerical Construction of Magnetohydrostatic Atmospheres in Three Dimensions

NASA Astrophysics Data System (ADS)

Gilchrist, S. A.; Braun, D. C.; Barnes, G.

2016-12-01

Magnetohydrostatic models of the solar atmosphere are often based on idealized analytic solutions because the underlying equations are too difficult to solve in full generality. Numerical approaches, too, are often limited in scope and have tended to focus on the two-dimensional problem. In this article we develop a numerical method for solving the nonlinear magnetohydrostatic equations in three dimensions. Our method is a fixed-point iteration scheme that extends the method of Grad and Rubin ( Proc. 2nd Int. Conf. on Peaceful Uses of Atomic Energy 31, 190, 1958) to include a finite gravity force. We apply the method to a test case to demonstrate the method in general and our implementation in code in particular.

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.

A Numerical, Literal, and Converged Perturbation Algorithm

NASA Astrophysics Data System (ADS)

Wiesel, William E.

2017-09-01

The KAM theorem and von Ziepel's method are applied to a perturbed harmonic oscillator, and it is noted that the KAM methodology does not allow for necessary frequency or angle corrections, while von Ziepel does. The KAM methodology can be carried out with purely numerical methods, since its generating function does not contain momentum dependence. The KAM iteration is extended to allow for frequency and angle changes, and in the process apparently can be successfully applied to degenerate systems normally ruled out by the classical KAM theorem. Convergence is observed to be geometric, not exponential, but it does proceed smoothly to machine precision. The algorithm produces a converged perturbation solution by numerical methods, while still retaining literal variable dependence, at least in the vicinity of a given trajectory.

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.

The CMC:3DPNS computer program for prediction of three-dimensional, subsonic, turbulent aerodynamic juncture region flow. Volume 1: Theoretical

NASA Technical Reports Server (NTRS)

Baker, A. J.

1982-01-01

An order-of-magnitude analysis of the subsonic three dimensional steady time averaged Navier-Stokes equations, for semibounded aerodynamic juncture geometries, yields the parabolic Navier-Stokes simplification. The numerical solution of the resultant pressure Poisson equation is cast into complementary and particular parts, yielding an iterative interaction algorithm with an exterior three dimensional potential flow solution. A parabolic transverse momentum equation set is constructed, wherein robust enforcement of first order continuity effects is accomplished using a penalty differential constraint concept within a finite element solution algorithm. A Reynolds stress constitutive equation, with low turbulence Reynolds number wall functions, is employed for closure, using parabolic forms of the two-equation turbulent kinetic energy-dissipation equation system. Numerical results document accuracy, convergence, and utility of the developed finite element algorithm, and the CMC:3DPNS computer code applied to an idealized wing-body juncture region. Additional results document accuracy aspects of the algorithm turbulence closure model.

An interaction algorithm for prediction of mean and fluctuating velocities in two-dimensional aerodynamic wake flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Orzechowski, J. A.

1980-01-01

A theoretical analysis is presented yielding sets of partial differential equations for determination of turbulent aerodynamic flowfields in the vicinity of an airfoil trailing edge. A four phase interaction algorithm is derived to complete the analysis. Following input, the first computational phase is an elementary viscous corrected two dimensional potential flow solution yielding an estimate of the inviscid-flow induced pressure distribution. Phase C involves solution of the turbulent two dimensional boundary layer equations over the trailing edge, with transition to a two dimensional parabolic Navier-Stokes equation system describing the near-wake merging of the upper and lower surface boundary layers. An iteration provides refinement of the potential flow induced pressure coupling to the viscous flow solutions. The final phase is a complete two dimensional Navier-Stokes analysis of the wake flow in the vicinity of a blunt-bases airfoil. A finite element numerical algorithm is presented which is applicable to solution of all partial differential equation sets of inviscid-viscous aerodynamic interaction algorithm. Numerical results are discussed.

Exact and approximate Fourier rebinning algorithms for the solution of the data truncation problem in 3-D PET.

PubMed

Bouallègue, Fayçal Ben; Crouzet, Jean-François; Comtat, Claude; Fourcade, Marjolaine; Mohammadi, Bijan; Mariano-Goulart, Denis

2007-07-01

This paper presents an extended 3-D exact rebinning formula in the Fourier space that leads to an iterative reprojection algorithm (iterative FOREPROJ), which enables the estimation of unmeasured oblique projection data on the basis of the whole set of measured data. In first approximation, this analytical formula also leads to an extended Fourier rebinning equation that is the basis for an approximate reprojection algorithm (extended FORE). These algorithms were evaluated on numerically simulated 3-D positron emission tomography (PET) data for the solution of the truncation problem, i.e., the estimation of the missing portions in the oblique projection data, before the application of algorithms that require complete projection data such as some rebinning methods (FOREX) or 3-D reconstruction algorithms (3DRP or direct Fourier methods). By taking advantage of all the 3-D data statistics, the iterative FOREPROJ reprojection provides a reliable alternative to the classical FOREPROJ method, which only exploits the low-statistics nonoblique data. It significantly improves the quality of the external reconstructed slices without loss of spatial resolution. As for the approximate extended FORE algorithm, it clearly exhibits limitations due to axial interpolations, but will require clinical studies with more realistic measured data in order to decide on its pertinence.

A Bee Evolutionary Guiding Nondominated Sorting Genetic Algorithm II for Multiobjective Flexible Job-Shop Scheduling.

PubMed

Deng, Qianwang; Gong, Guiliang; Gong, Xuran; Zhang, Like; Liu, Wei; Ren, Qinghua

2017-01-01

Flexible job-shop scheduling problem (FJSP) is an NP-hard puzzle which inherits the job-shop scheduling problem (JSP) characteristics. This paper presents a bee evolutionary guiding nondominated sorting genetic algorithm II (BEG-NSGA-II) for multiobjective FJSP (MO-FJSP) with the objectives to minimize the maximal completion time, the workload of the most loaded machine, and the total workload of all machines. It adopts a two-stage optimization mechanism during the optimizing process. In the first stage, the NSGA-II algorithm with T iteration times is first used to obtain the initial population N , in which a bee evolutionary guiding scheme is presented to exploit the solution space extensively. In the second stage, the NSGA-II algorithm with GEN iteration times is used again to obtain the Pareto-optimal solutions. In order to enhance the searching ability and avoid the premature convergence, an updating mechanism is employed in this stage. More specifically, its population consists of three parts, and each of them changes with the iteration times. What is more, numerical simulations are carried out which are based on some published benchmark instances. Finally, the effectiveness of the proposed BEG-NSGA-II algorithm is shown by comparing the experimental results and the results of some well-known algorithms already existed.

A Bee Evolutionary Guiding Nondominated Sorting Genetic Algorithm II for Multiobjective Flexible Job-Shop Scheduling

PubMed Central

Deng, Qianwang; Gong, Xuran; Zhang, Like; Liu, Wei; Ren, Qinghua

2017-01-01

Flexible job-shop scheduling problem (FJSP) is an NP-hard puzzle which inherits the job-shop scheduling problem (JSP) characteristics. This paper presents a bee evolutionary guiding nondominated sorting genetic algorithm II (BEG-NSGA-II) for multiobjective FJSP (MO-FJSP) with the objectives to minimize the maximal completion time, the workload of the most loaded machine, and the total workload of all machines. It adopts a two-stage optimization mechanism during the optimizing process. In the first stage, the NSGA-II algorithm with T iteration times is first used to obtain the initial population N, in which a bee evolutionary guiding scheme is presented to exploit the solution space extensively. In the second stage, the NSGA-II algorithm with GEN iteration times is used again to obtain the Pareto-optimal solutions. In order to enhance the searching ability and avoid the premature convergence, an updating mechanism is employed in this stage. More specifically, its population consists of three parts, and each of them changes with the iteration times. What is more, numerical simulations are carried out which are based on some published benchmark instances. Finally, the effectiveness of the proposed BEG-NSGA-II algorithm is shown by comparing the experimental results and the results of some well-known algorithms already existed. PMID:28458687

New algorithms to compute the nearness symmetric solution of the matrix equation.

PubMed

Peng, Zhen-Yun; Fang, Yang-Zhi; Xiao, Xian-Wei; Du, Dan-Dan

2016-01-01

In this paper we consider the nearness symmetric solution of the matrix equation AXB = C to a given matrix [Formula: see text] in the sense of the Frobenius norm. By discussing equivalent form of the considered problem, we derive some necessary and sufficient conditions for the matrix [Formula: see text] is a solution of the considered problem. Based on the idea of the alternating variable minimization with multiplier method, we propose two iterative methods to compute the solution of the considered problem, and analyze the global convergence results of the proposed algorithms. Numerical results illustrate the proposed methods are more effective than the existing two methods proposed in Peng et al. (Appl Math Comput 160:763-777, 2005) and Peng (Int J Comput Math 87: 1820-1830, 2010).

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.

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.

Second-order Poisson Nernst-Planck solver for ion channel transport

PubMed Central

Zheng, Qiong; Chen, Duan; Wei, Guo-Wei

2010-01-01

The Poisson Nernst-Planck (PNP) theory is a simplified continuum model for a wide variety of chemical, physical and biological applications. Its ability of providing quantitative explanation and increasingly qualitative predictions of experimental measurements has earned itself much recognition in the research community. Numerous computational algorithms have been constructed for the solution of the PNP equations. However, in the realistic ion-channel context, no second order convergent PNP algorithm has ever been reported in the literature, due to many numerical obstacles, including discontinuous coefficients, singular charges, geometric singularities, and nonlinear couplings. The present work introduces a number of numerical algorithms to overcome the abovementioned numerical challenges and constructs the first second-order convergent PNP solver in the ion-channel context. First, a Dirichlet to Neumann mapping (DNM) algorithm is designed to alleviate the charge singularity due to the protein structure. Additionally, the matched interface and boundary (MIB) method is reformulated for solving the PNP equations. The MIB method systematically enforces the interface jump conditions and achieves the second order accuracy in the presence of complex geometry and geometric singularities of molecular surfaces. Moreover, two iterative schemes are utilized to deal with the coupled nonlinear equations. Furthermore, extensive and rigorous numerical validations are carried out over a number of geometries, including a sphere, two proteins and an ion channel, to examine the numerical accuracy and convergence order of the present numerical algorithms. Finally, application is considered to a real transmembrane protein, the Gramicidin A channel protein. The performance of the proposed numerical techniques is tested against a number of factors, including mesh sizes, diffusion coefficient profiles, iterative schemes, ion concentrations, and applied voltages. Numerical predictions are compared with experimental measurements. PMID:21552336

A stepladder approach to a tokamak fusion power plant

NASA Astrophysics Data System (ADS)

Zohm, H.; Träuble, F.; Biel, W.; Fable, E.; Kemp, R.; Lux, H.; Siccinio, M.; Wenninger, R.

2017-08-01

We present an approach to design in a consistent way a stepladder connecting ITER, DEMO and an FPP, starting from an attractive FPP and then locating DEMO such that main similarity parameters for the core scenario are constant. The approach presented suggests how to use ITER such that DEMO can be extrapolated with maximum confidence and a development path for plasma scenarios in ITER follows from our approach, moving from low β N and q typical for the present Q  =  10 scenario to higher values needed for steady state. A numerical example is given, indicative of the feasibility of the approach, and it is backed up by more detailed 1.5-D calculation using the ASTRA code. We note that ideal MHD stability analysis of the DEMO operating point indicates that it is located between the no-wall and the ideal wall β-limit, which may require active stabilization. The DEMO design could also be a pulsed fallback solution should a stationary operation turn out to be impossible.

Acoustic scattering by arbitrary distributions of disjoint, homogeneous cylinders or spheres.

PubMed

Hesford, Andrew J; Astheimer, Jeffrey P; Waag, Robert C

2010-05-01

A T-matrix formulation is presented to compute acoustic scattering from arbitrary, disjoint distributions of cylinders or spheres, each with arbitrary, uniform acoustic properties. The generalized approach exploits the similarities in these scattering problems to present a single system of equations that is easily specialized to cylindrical or spherical scatterers. By employing field expansions based on orthogonal harmonic functions, continuity of pressure and normal particle velocity are directly enforced at each scatterer using diagonal, analytic expressions to eliminate the need for integral equations. The effect of a cylinder or sphere that encloses all other scatterers is simulated with an outer iterative procedure that decouples the inner-object solution from the effect of the enclosing object to improve computational efficiency when interactions among the interior objects are significant. Numerical results establish the validity and efficiency of the outer iteration procedure for nested objects. Two- and three-dimensional methods that employ this outer iteration are used to measure and characterize the accuracy of two-dimensional approximations to three-dimensional scattering of elevation-focused beams.

An iterative kernel based method for fourth order nonlinear equation with nonlinear boundary condition

NASA Astrophysics Data System (ADS)

Azarnavid, Babak; Parand, Kourosh; Abbasbandy, Saeid

2018-06-01

This article discusses an iterative reproducing kernel method with respect to its effectiveness and capability of solving a fourth-order boundary value problem with nonlinear boundary conditions modeling beams on elastic foundations. Since there is no method of obtaining reproducing kernel which satisfies nonlinear boundary conditions, the standard reproducing kernel methods cannot be used directly to solve boundary value problems with nonlinear boundary conditions as there is no knowledge about the existence and uniqueness of the solution. The aim of this paper is, therefore, to construct an iterative method by the use of a combination of reproducing kernel Hilbert space method and a shooting-like technique to solve the mentioned problems. Error estimation for reproducing kernel Hilbert space methods for nonlinear boundary value problems have yet to be discussed in the literature. In this paper, we present error estimation for the reproducing kernel method to solve nonlinear boundary value problems probably for the first time. Some numerical results are given out to demonstrate the applicability of the method.

Gyrokinetic equations and full f solution method based on Dirac's constrained Hamiltonian and inverse Kruskal iteration

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

Heikkinen, J. A.; Nora, M.

2011-02-15

Gyrokinetic equations of motion, Poisson equation, and energy and momentum conservation laws are derived based on the reduced-phase-space Lagrangian and inverse Kruskal iteration introduced by Pfirsch and Correa-Restrepo [J. Plasma Phys. 70, 719 (2004)]. This formalism, together with the choice of the adiabatic invariant J= as one of the averaging coordinates in phase space, provides an alternative to the standard gyrokinetics. Within second order in gyrokinetic parameter, the new equations do not show explicit ponderomotivelike or polarizationlike terms. Pullback of particle information with an iterated gyrophase and field dependent gyroradius function from the gyrocenter position defined by gyroaveraged coordinates allowsmore » direct numerical integration of the gyrokinetic equations in particle simulation of the field and particles with full distribution function. As an example, gyrokinetic systems with polarization drift either present or absent in the equations of motion are considered.« less

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.

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.

Full-order optimal compensators for flow control: the multiple inputs case

NASA Astrophysics Data System (ADS)

Semeraro, Onofrio; Pralits, Jan O.

2018-03-01

Flow control has been the subject of numerous experimental and theoretical works. We analyze full-order, optimal controllers for large dynamical systems in the presence of multiple actuators and sensors. The full-order controllers do not require any preliminary model reduction or low-order approximation: this feature allows us to assess the optimal performance of an actuated flow without relying on any estimation process or further hypothesis on the disturbances. We start from the original technique proposed by Bewley et al. (Meccanica 51(12):2997-3014, 2016. https://doi.org/10.1007/s11012-016-0547-3), the adjoint of the direct-adjoint (ADA) algorithm. The algorithm is iterative and allows bypassing the solution of the algebraic Riccati equation associated with the optimal control problem, typically infeasible for large systems. In this numerical work, we extend the ADA iteration into a more general framework that includes the design of controllers with multiple, coupled inputs and robust controllers (H_{∞} methods). First, we demonstrate our results by showing the analytical equivalence between the full Riccati solutions and the ADA approximations in the multiple inputs case. In the second part of the article, we analyze the performance of the algorithm in terms of convergence of the solution, by comparing it with analogous techniques. We find an excellent scalability with the number of inputs (actuators), making the method a viable way for full-order control design in complex settings. Finally, the applicability of the algorithm to fluid mechanics problems is shown using the linearized Kuramoto-Sivashinsky equation and the Kármán vortex street past a two-dimensional cylinder.

Measurement Uncertainty of Dew-Point Temperature in a Two-Pressure Humidity Generator

NASA Astrophysics Data System (ADS)

Martins, L. Lages; Ribeiro, A. Silva; Alves e Sousa, J.; Forbes, Alistair B.

2012-09-01

This article describes the measurement uncertainty evaluation of the dew-point temperature when using a two-pressure humidity generator as a reference standard. The estimation of the dew-point temperature involves the solution of a non-linear equation for which iterative solution techniques, such as the Newton-Raphson method, are required. Previous studies have already been carried out using the GUM method and the Monte Carlo method but have not discussed the impact of the approximate numerical method used to provide the temperature estimation. One of the aims of this article is to take this approximation into account. Following the guidelines presented in the GUM Supplement 1, two alternative approaches can be developed: the forward measurement uncertainty propagation by the Monte Carlo method when using the Newton-Raphson numerical procedure; and the inverse measurement uncertainty propagation by Bayesian inference, based on prior available information regarding the usual dispersion of values obtained by the calibration process. The measurement uncertainties obtained using these two methods can be compared with previous results. Other relevant issues concerning this research are the broad application to measurements that require hygrometric conditions obtained from two-pressure humidity generators and, also, the ability to provide a solution that can be applied to similar iterative models. The research also studied the factors influencing both the use of the Monte Carlo method (such as the seed value and the convergence parameter) and the inverse uncertainty propagation using Bayesian inference (such as the pre-assigned tolerance, prior estimate, and standard deviation) in terms of their accuracy and adequacy.

Self-adaptive difference method for the effective solution of computationally complex problems of boundary layer theory

NASA Technical Reports Server (NTRS)

Schoenauer, W.; Daeubler, H. G.; Glotz, G.; Gruening, J.

1986-01-01

An implicit difference procedure for the solution of equations for a chemically reacting hypersonic boundary layer is described. Difference forms of arbitrary error order in the x and y coordinate plane were used to derive estimates for discretization error. Computational complexity and time were minimized by the use of this difference method and the iteration of the nonlinear boundary layer equations was regulated by discretization error. Velocity and temperature profiles are presented for Mach 20.14 and Mach 18.5; variables are velocity profiles, temperature profiles, mass flow factor, Stanton number, and friction drag coefficient; three figures include numeric data.

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.

Some estimation formulae for continuous time-invariant linear systems

NASA Technical Reports Server (NTRS)

Bierman, G. J.; Sidhu, G. S.

1975-01-01

In this brief paper we examine a Riccati equation decomposition due to Reid and Lainiotis and apply the result to the continuous time-invariant linear filtering problem. Exploitation of the time-invariant structure leads to integration-free covariance recursions which are of use in covariance analyses and in filter implementations. A super-linearly convergent iterative solution to the algebraic Riccati equation (ARE) is developed. The resulting algorithm, arranged in a square-root form, is thought to be numerically stable and competitive with other ARE solution methods. Certain covariance relations that are relevant to the fixed-point and fixed-lag smoothing problems are also discussed.

Optimal startup control of a jacketed tubular reactor.

NASA Technical Reports Server (NTRS)

Hahn, D. R.; Fan, L. T.; Hwang, C. L.

1971-01-01

The optimal startup policy of a jacketed tubular reactor, in which a first-order, reversible, exothermic reaction takes place, is presented. A distributed maximum principle is presented for determining weak necessary conditions for optimality of a diffusional distributed parameter system. A numerical technique is developed for practical implementation of the distributed maximum principle. This involves the sequential solution of the state and adjoint equations, in conjunction with a functional gradient technique for iteratively improving the control function.

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.

FAST TRACK PAPER: Non-iterative multiple-attenuation methods: linear inverse solutions to non-linear inverse problems - II. BMG approximation

NASA Astrophysics Data System (ADS)

Ikelle, Luc T.; Osen, Are; Amundsen, Lasse; Shen, Yunqing

2004-12-01

The classical linear solutions to the problem of multiple attenuation, like predictive deconvolution, τ-p filtering, or F-K filtering, are generally fast, stable, and robust compared to non-linear solutions, which are generally either iterative or in the form of a series with an infinite number of terms. These qualities have made the linear solutions more attractive to seismic data-processing practitioners. However, most linear solutions, including predictive deconvolution or F-K filtering, contain severe assumptions about the model of the subsurface and the class of free-surface multiples they can attenuate. These assumptions limit their usefulness. In a recent paper, we described an exception to this assertion for OBS data. We showed in that paper that a linear and non-iterative solution to the problem of attenuating free-surface multiples which is as accurate as iterative non-linear solutions can be constructed for OBS data. We here present a similar linear and non-iterative solution for attenuating free-surface multiples in towed-streamer data. For most practical purposes, this linear solution is as accurate as the non-linear ones.

Optimization-based additive decomposition of weakly coercive problems with applications

DOE PAGES

Bochev, Pavel B.; Ridzal, Denis

2016-01-27

In this study, we present an abstract mathematical framework for an optimization-based additive decomposition of a large class of variational problems into a collection of concurrent subproblems. The framework replaces a given monolithic problem by an equivalent constrained optimization formulation in which the subproblems define the optimization constraints and the objective is to minimize the mismatch between their solutions. The significance of this reformulation stems from the fact that one can solve the resulting optimality system by an iterative process involving only solutions of the subproblems. Consequently, assuming that stable numerical methods and efficient solvers are available for every subproblem,more » our reformulation leads to robust and efficient numerical algorithms for a given monolithic problem by breaking it into subproblems that can be handled more easily. An application of the framework to the Oseen equations illustrates its potential.« less

A Multi-Verse Optimizer with Levy Flights for Numerical Optimization and Its Application in Test Scheduling for Network-on-Chip.

PubMed

Hu, Cong; Li, Zhi; Zhou, Tian; Zhu, Aijun; Xu, Chuanpei

2016-01-01

We propose a new meta-heuristic algorithm named Levy flights multi-verse optimizer (LFMVO), which incorporates Levy flights into multi-verse optimizer (MVO) algorithm to solve numerical and engineering optimization problems. The Original MVO easily falls into stagnation when wormholes stochastically re-span a number of universes (solutions) around the best universe achieved over the course of iterations. Since Levy flights are superior in exploring unknown, large-scale search space, they are integrated into the previous best universe to force MVO out of stagnation. We test this method on three sets of 23 well-known benchmark test functions and an NP complete problem of test scheduling for Network-on-Chip (NoC). Experimental results prove that the proposed LFMVO is more competitive than its peers in both the quality of the resulting solutions and convergence speed.

A Multi-Verse Optimizer with Levy Flights for Numerical Optimization and Its Application in Test Scheduling for Network-on-Chip

PubMed Central

Hu, Cong; Li, Zhi; Zhou, Tian; Zhu, Aijun; Xu, Chuanpei

2016-01-01

We propose a new meta-heuristic algorithm named Levy flights multi-verse optimizer (LFMVO), which incorporates Levy flights into multi-verse optimizer (MVO) algorithm to solve numerical and engineering optimization problems. The Original MVO easily falls into stagnation when wormholes stochastically re-span a number of universes (solutions) around the best universe achieved over the course of iterations. Since Levy flights are superior in exploring unknown, large-scale search space, they are integrated into the previous best universe to force MVO out of stagnation. We test this method on three sets of 23 well-known benchmark test functions and an NP complete problem of test scheduling for Network-on-Chip (NoC). Experimental results prove that the proposed LFMVO is more competitive than its peers in both the quality of the resulting solutions and convergence speed. PMID:27926946

Acoustic coupled fluid-structure interactions using a unified fast multipole boundary element method.

PubMed

Wilkes, Daniel R; Duncan, Alec J

2015-04-01

This paper presents a numerical model for the acoustic coupled fluid-structure interaction (FSI) of a submerged finite elastic body using the fast multipole boundary element method (FMBEM). The Helmholtz and elastodynamic boundary integral equations (BIEs) are, respectively, employed to model the exterior fluid and interior solid domains, and the pressure and displacement unknowns are coupled between conforming meshes at the shared boundary interface to achieve the acoustic FSI. The low frequency FMBEM is applied to both BIEs to reduce the algorithmic complexity of the iterative solution from O(N(2)) to O(N(1.5)) operations per matrix-vector product for N boundary unknowns. Numerical examples are presented to demonstrate the algorithmic and memory complexity of the method, which are shown to be in good agreement with the theoretical estimates, while the solution accuracy is comparable to that achieved by a conventional finite element-boundary element FSI model.

An accelerated lambda iteration method for multilevel radiative transfer. I - Non-overlapping lines with background continuum

NASA Technical Reports Server (NTRS)

Rybicki, G. B.; Hummer, D. G.

1991-01-01

A method is presented for solving multilevel transfer problems when nonoverlapping lines and background continuum are present and active continuum transfer is absent. An approximate lambda operator is employed to derive linear, 'preconditioned', statistical-equilibrium equations. A method is described for finding the diagonal elements of the 'true' numerical lambda operator, and therefore for obtaining the coefficients of the equations. Iterations of the preconditioned equations, in conjunction with the transfer equation's formal solution, are used to solve linear equations. Some multilevel problems are considered, including an eleven-level neutral helium atom. Diagonal and tridiagonal approximate lambda operators are utilized in the problems to examine the convergence properties of the method, and it is found to be effective for the line transfer problems.

Spectral iterative method and convergence analysis for solving nonlinear fractional differential equation

NASA Astrophysics Data System (ADS)

Yarmohammadi, M.; Javadi, S.; Babolian, E.

2018-04-01

In this study a new spectral iterative method (SIM) based on fractional interpolation is presented for solving nonlinear fractional differential equations (FDEs) involving Caputo derivative. This method is equipped with a pre-algorithm to find the singularity index of solution of the problem. This pre-algorithm gives us a real parameter as the index of the fractional interpolation basis, for which the SIM achieves the highest order of convergence. In comparison with some recent results about the error estimates for fractional approximations, a more accurate convergence rate has been attained. We have also proposed the order of convergence for fractional interpolation error under the L2-norm. Finally, general error analysis of SIM has been considered. The numerical results clearly demonstrate the capability of the proposed method.

Solution of elliptic partial differential equations by fast Poisson solvers using a local relaxation factor. 1: One-step method

NASA Technical Reports Server (NTRS)

Chang, S. C.

1986-01-01

An algorithm for solving a large class of two- and three-dimensional nonseparable elliptic partial differential equations (PDE's) is developed and tested. It uses a modified D'Yakanov-Gunn iterative procedure in which the relaxation factor is grid-point dependent. It is easy to implement and applicable to a variety of boundary conditions. It is also computationally efficient, as indicated by the results of numerical comparisons with other established methods. Furthermore, the current algorithm has the advantage of possessing two important properties which the traditional iterative methods lack; that is: (1) the convergence rate is relatively insensitive to grid-cell size and aspect ratio, and (2) the convergence rate can be easily estimated by using the coefficient of the PDE being solved.

A novel approach to calibrate the hemodynamic model using functional Magnetic Resonance Imaging (fMRI) measurements.

PubMed

Khoram, Nafiseh; Zayane, Chadia; Djellouli, Rabia; Laleg-Kirati, Taous-Meriem

2016-03-15

The calibration of the hemodynamic model that describes changes in blood flow and blood oxygenation during brain activation is a crucial step for successfully monitoring and possibly predicting brain activity. This in turn has the potential to provide diagnosis and treatment of brain diseases in early stages. We propose an efficient numerical procedure for calibrating the hemodynamic model using some fMRI measurements. The proposed solution methodology is a regularized iterative method equipped with a Kalman filtering-type procedure. The Newton component of the proposed method addresses the nonlinear aspect of the problem. The regularization feature is used to ensure the stability of the algorithm. The Kalman filter procedure is incorporated here to address the noise in the data. Numerical results obtained with synthetic data as well as with real fMRI measurements are presented to illustrate the accuracy, robustness to the noise, and the cost-effectiveness of the proposed method. We present numerical results that clearly demonstrate that the proposed method outperforms the Cubature Kalman Filter (CKF), one of the most prominent existing numerical methods. We have designed an iterative numerical technique, called the TNM-CKF algorithm, for calibrating the mathematical model that describes the single-event related brain response when fMRI measurements are given. The method appears to be highly accurate and effective in reconstructing the BOLD signal even when the measurements are tainted with high noise level (as high as 30%). Published by Elsevier B.V.

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.

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.

Efficient numerical method for investigating diatomic molecules with single active electron subjected to intense and ultrashort laser fields

NASA Astrophysics Data System (ADS)

Kiss, Gellért Zsolt; Borbély, Sándor; Nagy, Ladislau

2017-12-01

We have presented here an efficient numerical approach for the ab initio numerical solution of the time-dependent Schrödinger Equation describing diatomic molecules, which interact with ultrafast laser pulses. During the construction of the model we have assumed a frozen nuclear configuration and a single active electron. In order to increase efficiency our system was described using prolate spheroidal coordinates, where the wave function was discretized using the finite-element discrete variable representation (FE-DVR) method. The discretized wave functions were efficiently propagated in time using the short-iterative Lanczos algorithm. As a first test we have studied here how the laser induced bound state dynamics in H2+ is influenced by the strength of the driving laser field.

An extended GS method for dense linear systems

NASA Astrophysics Data System (ADS)

Niki, Hiroshi; Kohno, Toshiyuki; Abe, Kuniyoshi

2009-09-01

Davey and Rosindale [K. Davey, I. Rosindale, An iterative solution scheme for systems of boundary element equations, Internat. J. Numer. Methods Engrg. 37 (1994) 1399-1411] derived the GSOR method, which uses an upper triangular matrix [Omega] in order to solve dense linear systems. By applying functional analysis, the authors presented an expression for the optimum [Omega]. Moreover, Davey and Bounds [K. Davey, S. Bounds, A generalized SOR method for dense linear systems of boundary element equations, SIAM J. Comput. 19 (1998) 953-967] also introduced further interesting results. In this note, we employ a matrix analysis approach to investigate these schemes, and derive theorems that compare these schemes with existing preconditioners for dense linear systems. We show that the convergence rate of the Gauss-Seidel method with preconditioner PG is superior to that of the GSOR method. Moreover, we define some splittings associated with the iterative schemes. Some numerical examples are reported to confirm the theoretical analysis. We show that the EGS method with preconditioner produces an extremely small spectral radius in comparison with the other schemes considered.

An Efficient Non-iterative Bulk Parametrization of Surface Fluxes for Stable Atmospheric Conditions Over Polar Sea-Ice

NASA Astrophysics Data System (ADS)

Gryanik, Vladimir M.; Lüpkes, Christof

2018-02-01

In climate and weather prediction models the near-surface turbulent fluxes of heat and momentum and related transfer coefficients are usually parametrized on the basis of Monin-Obukhov similarity theory (MOST). To avoid iteration, required for the numerical solution of the MOST equations, many models apply parametrizations of the transfer coefficients based on an approach relating these coefficients to the bulk Richardson number Rib. However, the parametrizations that are presently used in most climate models are valid only for weaker stability and larger surface roughnesses than those documented during the Surface Heat Budget of the Arctic Ocean campaign (SHEBA). The latter delivered a well-accepted set of turbulence data in the stable surface layer over polar sea-ice. Using stability functions based on the SHEBA data, we solve the MOST equations applying a new semi-analytic approach that results in transfer coefficients as a function of Rib and roughness lengths for momentum and heat. It is shown that the new coefficients reproduce the coefficients obtained by the numerical iterative method with a good accuracy in the most relevant range of stability and roughness lengths. For small Rib, the new bulk transfer coefficients are similar to the traditional coefficients, but for large Rib they are much smaller than currently used coefficients. Finally, a possible adjustment of the latter and the implementation of the new proposed parametrizations in models are discussed.

State Transition Matrix for Perturbed Orbital Motion Using Modified Chebyshev Picard Iteration

NASA Astrophysics Data System (ADS)

Read, Julie L.; Younes, Ahmad Bani; Macomber, Brent; Turner, James; Junkins, John L.

2015-06-01

The Modified Chebyshev Picard Iteration (MCPI) method has recently proven to be highly efficient for a given accuracy compared to several commonly adopted numerical integration methods, as a means to solve for perturbed orbital motion. This method utilizes Picard iteration, which generates a sequence of path approximations, and Chebyshev Polynomials, which are orthogonal and also enable both efficient and accurate function approximation. The nodes consistent with discrete Chebyshev orthogonality are generated using cosine sampling; this strategy also reduces the Runge effect and as a consequence of orthogonality, there is no matrix inversion required to find the basis function coefficients. The MCPI algorithms considered herein are parallel-structured so that they are immediately well-suited for massively parallel implementation with additional speedup. MCPI has a wide range of applications beyond ephemeris propagation, including the propagation of the State Transition Matrix (STM) for perturbed two-body motion. A solution is achieved for a spherical harmonic series representation of earth gravity (EGM2008), although the methodology is suitable for application to any gravity model. Included in this representation the normalized, Associated Legendre Functions are given and verified numerically. Modifications of the classical algorithm techniques, such as rewriting the STM equations in a second-order cascade formulation, gives rise to additional speedup. Timing results for the baseline formulation and this second-order formulation are given.

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).

The application of contraction theory to an iterative formulation of electromagnetic scattering

NASA Technical Reports Server (NTRS)

Brand, J. C.; Kauffman, J. F.

1985-01-01

Contraction theory is applied to an iterative formulation of electromagnetic scattering from periodic structures and a computational method for insuring convergence is developed. A short history of spectral (or k-space) formulation is presented with an emphasis on application to periodic surfaces. To insure a convergent solution of the iterative equation, a process called the contraction corrector method is developed. Convergence properties of previously presented iterative solutions to one-dimensional problems are examined utilizing contraction theory and the general conditions for achieving a convergent solution are explored. The contraction corrector method is then applied to several scattering problems including an infinite grating of thin wires with the solution data compared to previous works.

Numerical Solution of 3D Poisson-Nernst-Planck Equations Coupled with Classical Density Functional Theory for Modeling Ion and Electron Transport in a Confined Environment

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

Meng, Da; Zheng, Bin; Lin, Guang

2014-08-29

We have developed efficient numerical algorithms for the solution of 3D steady-state Poisson-Nernst-Planck equations (PNP) with excess chemical potentials described by the classical density functional theory (cDFT). The coupled PNP equations are discretized by finite difference scheme and solved iteratively by Gummel method with relaxation. The Nernst-Planck equations are transformed into Laplace equations through the Slotboom transformation. Algebraic multigrid method is then applied to efficiently solve the Poisson equation and the transformed Nernst-Planck equations. A novel strategy for calculating excess chemical potentials through fast Fourier transforms is proposed which reduces computational complexity from O(N2) to O(NlogN) where N is themore » number of grid points. Integrals involving Dirac delta function are evaluated directly by coordinate transformation which yields more accurate result compared to applying numerical quadrature to an approximated delta function. Numerical results for ion and electron transport in solid electrolyte for Li ion batteries are shown to be in good agreement with the experimental data and the results from previous studies.« less

An efficient transport solver for tokamak plasmas

DOE PAGES

Park, Jin Myung; Murakami, Masanori; St. John, H. E.; ...

2017-01-03

A simple approach to efficiently solve a coupled set of 1-D diffusion-type transport equations with a stiff transport model for tokamak plasmas is presented based on the 4th order accurate Interpolated Differential Operator scheme along with a nonlinear iteration method derived from a root-finding algorithm. Here, numerical tests using the Trapped Gyro-Landau-Fluid model show that the presented high order method provides an accurate transport solution using a small number of grid points with robust nonlinear convergence.

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.

Efficient Numerical Methods for Nonequilibrium Re-Entry Flows

DTIC Science & Technology

2014-01-14

right-hand side is the only quadratic operation). The number of sub- iterations , kmax, used in this update needs to be chosen for optimal convergence and...Upper Symmetric Gauss - Seidel Method for the Euler and Navier-Stokes Equations,”, AIAA Journal, Vol. 26, No. 9, pp. 1025-1026, Sept. 1988. 11Edwards, J.R...Candler, “The Solution of the Navier-Stokes Equations Using Gauss - Seidel Line Relaxation,” Computers and Fluids, Vol. 17, No. 1, pp. 135-150, 1989

Prediction of overall and blade-element performance for axial-flow pump configurations

NASA Technical Reports Server (NTRS)

Serovy, G. K.; Kavanagh, P.; Okiishi, T. H.; Miller, M. J.

1973-01-01

A method and a digital computer program for prediction of the distributions of fluid velocity and properties in axial flow pump configurations are described and evaluated. The method uses the blade-element flow model and an iterative numerical solution of the radial equilbrium and continuity conditions. Correlated experimental results are used to generate alternative methods for estimating blade-element turning and loss characteristics. Detailed descriptions of the computer program are included, with example input and typical computed results.

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.

Multiple control strategies for prevention of avian influenza pandemic.

PubMed

Ullah, Roman; Zaman, Gul; Islam, Saeed

2014-01-01

We present the prevention of avian influenza pandemic by adjusting multiple control functions in the human-to-human transmittable avian influenza model. First we show the existence of the optimal control problem; then by using both analytical and numerical techniques, we investigate the cost-effective control effects for the prevention of transmission of disease. To do this, we use three control functions, the effort to reduce the number of contacts with human infected with mutant avian influenza, the antiviral treatment of infected individuals, and the effort to reduce the number of infected birds. We completely characterized the optimal control and compute numerical solution of the optimality system by using an iterative method.

Compliance matrices for cracked bodies

NASA Technical Reports Server (NTRS)

Ballarini, R.

1986-01-01

An algorithm is developed to construct the compliance matrix for a cracked solid in the integral-equation formulation of two-dimensional linear-elastic fracture mechanics. The integral equation is reduced to a system of algebraic equations for unknown values of the dislocation-density function at discrete points on the interval from -1 to 1, using the numerical procedure described by Gerasoulis (1982). Sample numerical results are presented, and it is suggested that the algorithm is especially useful in cases where iterative solutions are required; e.g., models of fiber-reinforced concrete, rocks, or ceramics where microcracking, fiber bridging, and other nonlinear effects are treated as nonlinear springs along the crack surfaces (Ballarini et al., 1984).

Numerical solution of the Black-Scholes equation using cubic spline wavelets

NASA Astrophysics Data System (ADS)

Černá, Dana

2016-12-01

The Black-Scholes equation is used in financial mathematics for computation of market values of options at a given time. We use the θ-scheme for time discretization and an adaptive scheme based on wavelets for discretization on the given time level. Advantages of the proposed method are small number of degrees of freedom, high-order accuracy with respect to variables representing prices and relatively small number of iterations needed to resolve the problem with a desired accuracy. We use several cubic spline wavelet and multi-wavelet bases and discuss their advantages and disadvantages. We also compare an isotropic and anisotropic approach. Numerical experiments are presented for the two-dimensional Black-Scholes equation.

Steady axisymmetric vortex flows with swirl and shear

NASA Astrophysics Data System (ADS)

Elcrat, Alan R.; Fornberg, Bengt; Miller, Kenneth G.

A general procedure is presented for computing axisymmetric swirling vortices which are steady with respect to an inviscid flow that is either uniform at infinity or includes shear. We consider cases both with and without a spherical obstacle. Choices of numerical parameters are given which yield vortex rings with swirl, attached vortices with swirl analogous to spherical vortices found by Moffatt, tubes of vorticity extending to infinity and Beltrami flows. When there is a spherical obstacle we have found multiple solutions for each set of parameters. Flows are found by numerically solving the Bragg-Hawthorne equation using a non-Newton-based iterative procedure which is robust in its dependence on an initial guess.

Scalable Nonlinear Solvers for Fully Implicit Coupled Nuclear Fuel Modeling. Final Report

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

Cai, Xiao-Chuan; Keyes, David; Yang, Chao

2014-09-29

The focus of the project is on the development and customization of some highly scalable domain decomposition based preconditioning techniques for the numerical solution of nonlinear, coupled systems of partial differential equations (PDEs) arising from nuclear fuel simulations. These high-order PDEs represent multiple interacting physical fields (for example, heat conduction, oxygen transport, solid deformation), each is modeled by a certain type of Cahn-Hilliard and/or Allen-Cahn equations. Most existing approaches involve a careful splitting of the fields and the use of field-by-field iterations to obtain a solution of the coupled problem. Such approaches have many advantages such as ease of implementationmore » since only single field solvers are needed, but also exhibit disadvantages. For example, certain nonlinear interactions between the fields may not be fully captured, and for unsteady problems, stable time integration schemes are difficult to design. In addition, when implemented on large scale parallel computers, the sequential nature of the field-by-field iterations substantially reduces the parallel efficiency. To overcome the disadvantages, fully coupled approaches have been investigated in order to obtain full physics simulations.« less

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

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

Gauss-Seidel and Successive Overrelaxation Methods for Radiative Transfer with Partial Frequency Redistribution

NASA Astrophysics Data System (ADS)

Sampoorna, M.; Trujillo Bueno, J.

2010-04-01

The linearly polarized solar limb spectrum that is produced by scattering processes contains a wealth of information on the physical conditions and magnetic fields of the solar outer atmosphere, but the modeling of many of its strongest spectral lines requires solving an involved non-local thermodynamic equilibrium radiative transfer problem accounting for partial redistribution (PRD) effects. Fast radiative transfer methods for the numerical solution of PRD problems are also needed for a proper treatment of hydrogen lines when aiming at realistic time-dependent magnetohydrodynamic simulations of the solar chromosphere. Here we show how the two-level atom PRD problem with and without polarization can be solved accurately and efficiently via the application of highly convergent iterative schemes based on the Gauss-Seidel and successive overrelaxation (SOR) radiative transfer methods that had been previously developed for the complete redistribution case. Of particular interest is the Symmetric SOR method, which allows us to reach the fully converged solution with an order of magnitude of improvement in the total computational time with respect to the Jacobi-based local accelerated lambda iteration method.

A Lagrange multiplier and Hopfield-type barrier function method for the traveling salesman problem.

PubMed

Dang, Chuangyin; Xu, Lei

2002-02-01

A Lagrange multiplier and Hopfield-type barrier function method is proposed for approximating a solution of the traveling salesman problem. The method is derived from applications of Lagrange multipliers and a Hopfield-type barrier function and attempts to produce a solution of high quality by generating a minimum point of a barrier problem for a sequence of descending values of the barrier parameter. For any given value of the barrier parameter, the method searches for a minimum point of the barrier problem in a feasible descent direction, which has a desired property that lower and upper bounds on variables are always satisfied automatically if the step length is a number between zero and one. At each iteration, the feasible descent direction is found by updating Lagrange multipliers with a globally convergent iterative procedure. For any given value of the barrier parameter, the method converges to a stationary point of the barrier problem without any condition on the objective function. Theoretical and numerical results show that the method seems more effective and efficient than the softassign algorithm.

A New Homotopy Perturbation Scheme for Solving Singular Boundary Value Problems Arising in Various Physical Models

NASA Astrophysics Data System (ADS)

Roul, Pradip; Warbhe, Ujwal

2017-08-01

The classical homotopy perturbation method proposed by J. H. He, Comput. Methods Appl. Mech. Eng. 178, 257 (1999) is useful for obtaining the approximate solutions for a wide class of nonlinear problems in terms of series with easily calculable components. However, in some cases, it has been found that this method results in slowly convergent series. To overcome the shortcoming, we present a new reliable algorithm called the domain decomposition homotopy perturbation method (DDHPM) to solve a class of singular two-point boundary value problems with Neumann and Robin-type boundary conditions arising in various physical models. Five numerical examples are presented to demonstrate the accuracy and applicability of our method, including thermal explosion, oxygen-diffusion in a spherical cell and heat conduction through a solid with heat generation. A comparison is made between the proposed technique and other existing seminumerical or numerical techniques. Numerical results reveal that only two or three iterations lead to high accuracy of the solution and this newly improved technique introduces a powerful improvement for solving nonlinear singular boundary value problems (SBVPs).

A stopping criterion for the iterative solution of partial differential equations

NASA Astrophysics Data System (ADS)

Rao, Kaustubh; Malan, Paul; Perot, J. Blair

2018-01-01

A stopping criterion for iterative solution methods is presented that accurately estimates the solution error using low computational overhead. The proposed criterion uses information from prior solution changes to estimate the error. When the solution changes are noisy or stagnating it reverts to a less accurate but more robust, low-cost singular value estimate to approximate the error given the residual. This estimator can also be applied to iterative linear matrix solvers such as Krylov subspace or multigrid methods. Examples of the stopping criterion's ability to accurately estimate the non-linear and linear solution error are provided for a number of different test cases in incompressible fluid dynamics.

A STRICTLY CONTRACTIVE PEACEMAN-RACHFORD SPLITTING METHOD FOR CONVEX PROGRAMMING.

PubMed

Bingsheng, He; Liu, Han; Wang, Zhaoran; Yuan, Xiaoming

2014-07-01

In this paper, we focus on the application of the Peaceman-Rachford splitting method (PRSM) to a convex minimization model with linear constraints and a separable objective function. Compared to the Douglas-Rachford splitting method (DRSM), another splitting method from which the alternating direction method of multipliers originates, PRSM requires more restrictive assumptions to ensure its convergence, while it is always faster whenever it is convergent. We first illustrate that the reason for this difference is that the iterative sequence generated by DRSM is strictly contractive, while that generated by PRSM is only contractive with respect to the solution set of the model. With only the convexity assumption on the objective function of the model under consideration, the convergence of PRSM is not guaranteed. But for this case, we show that the first t iterations of PRSM still enable us to find an approximate solution with an accuracy of O (1/ t ). A worst-case O (1/ t ) convergence rate of PRSM in the ergodic sense is thus established under mild assumptions. After that, we suggest attaching an underdetermined relaxation factor with PRSM to guarantee the strict contraction of its iterative sequence and thus propose a strictly contractive PRSM. A worst-case O (1/ t ) convergence rate of this strictly contractive PRSM in a nonergodic sense is established. We show the numerical efficiency of the strictly contractive PRSM by some applications in statistical learning and image processing.

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.

Equivalent charge source model based iterative maximum neighbor weight for sparse EEG source localization.

PubMed

Xu, Peng; Tian, Yin; Lei, Xu; Hu, Xiao; Yao, Dezhong

2008-12-01

How to localize the neural electric activities within brain effectively and precisely from the scalp electroencephalogram (EEG) recordings is a critical issue for current study in clinical neurology and cognitive neuroscience. In this paper, based on the charge source model and the iterative re-weighted strategy, proposed is a new maximum neighbor weight based iterative sparse source imaging method, termed as CMOSS (Charge source model based Maximum neighbOr weight Sparse Solution). Different from the weight used in focal underdetermined system solver (FOCUSS) where the weight for each point in the discrete solution space is independently updated in iterations, the new designed weight for each point in each iteration is determined by the source solution of the last iteration at both the point and its neighbors. Using such a new weight, the next iteration may have a bigger chance to rectify the local source location bias existed in the previous iteration solution. The simulation studies with comparison to FOCUSS and LORETA for various source configurations were conducted on a realistic 3-shell head model, and the results confirmed the validation of CMOSS for sparse EEG source localization. Finally, CMOSS was applied to localize sources elicited in a visual stimuli experiment, and the result was consistent with those source areas involved in visual processing reported in previous studies.

On the convergence of an iterative formulation of the electromagnetic scattering from an infinite grating of thin wires

NASA Technical Reports Server (NTRS)

Brand, J. C.

1985-01-01

Contraction theory is applied to an iterative formulation of electromagnetic scattering from periodic structures and a computational method for insuring convergence is developed. A short history of spectral (or k-space) formulation is presented with an emphasis on application to periodic surfaces. The mathematical background for formulating an iterative equation is covered using straightforward single variable examples including an extension to vector spaces. To insure a convergent solution of the iterative equation, a process called the contraction corrector method is developed. Convergence properties of previously presented iterative solutions to one-dimensional problems are examined utilizing contraction theory and the general conditions for achieving a convergent solution are explored. The contraction corrector method is then applied to several scattering problems including an infinite grating of thin wires with the solution data compared to previous works.

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

An explicit solution to the exoatmospheric powered flight guidance and trajectory optimization problem for rocket propelled vehicles

NASA Technical Reports Server (NTRS)

Jaggers, R. F.

1977-01-01

A derivation of an explicit solution to the two point boundary-value problem of exoatmospheric guidance and trajectory optimization is presented. Fixed initial conditions and continuous burn, multistage thrusting are assumed. Any number of end conditions from one to six (throttling is required in the case of six) can be satisfied in an explicit and practically optimal manner. The explicit equations converge for off nominal conditions such as engine failure, abort, target switch, etc. The self starting, predictor/corrector solution involves no Newton-Rhapson iterations, numerical integration, or first guess values, and converges rapidly if physically possible. A form of this algorithm has been chosen for onboard guidance, as well as real time and preflight ground targeting and trajectory shaping for the NASA Space Shuttle Program.

Approximate solution of space and time fractional higher order phase field equation

NASA Astrophysics Data System (ADS)

Shamseldeen, S.

2018-03-01

This paper is concerned with a class of space and time fractional partial differential equation (STFDE) with Riesz derivative in space and Caputo in time. The proposed STFDE is considered as a generalization of a sixth-order partial phase field equation. We describe the application of the optimal homotopy analysis method (OHAM) to obtain an approximate solution for the suggested fractional initial value problem. An averaged-squared residual error function is defined and used to determine the optimal convergence control parameter. Two numerical examples are studied, considering periodic and non-periodic initial conditions, to justify the efficiency and the accuracy of the adopted iterative approach. The dependence of the solution on the order of the fractional derivative in space and time and model parameters is investigated.

The wide-angle equation and its solution through the short-time iterative Lanczos method.

PubMed

Campos-Martínez, José; Coalson, Rob D

2003-03-20

Properties of the wide-angle equation (WAEQ), a nonparaxial scalar wave equation used to propagate light through media characterized by inhomogeneous refractive-index profiles, are studied. In particular, it is shown that the WAEQ is not equivalent to the more complicated but more fundamental Helmholtz equation (HEQ) when the index of refraction profile depends on the position along the propagation axis. This includes all nonstraight waveguides. To study the quality of the WAEQ approximation, we present a novel method for computing solutions to the WAEQ. This method, based on a short-time iterative Lanczos (SIL) algorithm, can be applied directly to the full three-dimensional case, i.e., systems consisting of the propagation axis coordinate and two transverse coordinates. Furthermore, the SIL method avoids series-expansion procedures (e.g., Padé approximants) and thus convergence problems associated with such procedures. Detailed comparisons of solutions to the HEQ, WAEQ, and the paraxial equation (PEQ) are presented for two cases in which numerically exact solutions to the HEQ can be obtained by independent analysis, namely, (i) propagation in a uniform dielectric medium and (ii) propagation along a straight waveguide that has been tilted at an angle to the propagation axis. The quality of WAEQ and PEQ, compared with exact HEQ results, is investigated. Cases are found for which the WAEQ actually performs worse than the PEQ.

A global stochastic programming approach for the optimal placement of gas detectors with nonuniform unavailabilities

DOE PAGES

Liu, Jianfeng; Laird, Carl Damon

2017-09-22

Optimal design of a gas detection systems is challenging because of the numerous sources of uncertainty, including weather and environmental conditions, leak location and characteristics, and process conditions. Rigorous CFD simulations of dispersion scenarios combined with stochastic programming techniques have been successfully applied to the problem of optimal gas detector placement; however, rigorous treatment of sensor failure and nonuniform unavailability has received less attention. To improve reliability of the design, this paper proposes a problem formulation that explicitly considers nonuniform unavailabilities and all backup detection levels. The resulting sensor placement problem is a large-scale mixed-integer nonlinear programming (MINLP) problem thatmore » requires a tailored solution approach for efficient solution. We have developed a multitree method which depends on iteratively solving a sequence of upper-bounding master problems and lower-bounding subproblems. The tailored global solution strategy is tested on a real data problem and the encouraging numerical results indicate that our solution framework is promising in solving sensor placement problems. This study was selected for the special issue in JLPPI from the 2016 International Symposium of the MKO Process Safety Center.« less

Finite element modeling of borehole heat exchanger systems. Part 1. Fundamentals

NASA Astrophysics Data System (ADS)

Diersch, H.-J. G.; Bauer, D.; Heidemann, W.; Rühaak, W.; Schätzl, P.

2011-08-01

Single borehole heat exchanger (BHE) and arrays of BHE are modeled by using the finite element method. The first part of the paper derives the fundamental equations for BHE systems and their finite element representations, where the thermal exchange between the borehole components is modeled via thermal transfer relations. For this purpose improved relationships for thermal resistances and capacities of BHE are introduced. Pipe-to-grout thermal transfer possesses multiple grout points for double U-shape and single U-shape BHE to attain a more accurate modeling. The numerical solution of the final 3D problems is performed via a widely non-sequential (essentially non-iterative) coupling strategy for the BHE and porous medium discretization. Four types of vertical BHE are supported: double U-shape (2U) pipe, single U-shape (1U) pipe, coaxial pipe with annular (CXA) and centred (CXC) inlet. Two computational strategies are used: (1) The analytical BHE method based on Eskilson and Claesson's (1988) solution, (2) numerical BHE method based on Al-Khoury et al.'s (2005) solution. The second part of the paper focusses on BHE meshing aspects, the validation of BHE solutions and practical applications for borehole thermal energy store systems.

A global stochastic programming approach for the optimal placement of gas detectors with nonuniform unavailabilities

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

Liu, Jianfeng; Laird, Carl Damon

Optimal design of a gas detection systems is challenging because of the numerous sources of uncertainty, including weather and environmental conditions, leak location and characteristics, and process conditions. Rigorous CFD simulations of dispersion scenarios combined with stochastic programming techniques have been successfully applied to the problem of optimal gas detector placement; however, rigorous treatment of sensor failure and nonuniform unavailability has received less attention. To improve reliability of the design, this paper proposes a problem formulation that explicitly considers nonuniform unavailabilities and all backup detection levels. The resulting sensor placement problem is a large-scale mixed-integer nonlinear programming (MINLP) problem thatmore » requires a tailored solution approach for efficient solution. We have developed a multitree method which depends on iteratively solving a sequence of upper-bounding master problems and lower-bounding subproblems. The tailored global solution strategy is tested on a real data problem and the encouraging numerical results indicate that our solution framework is promising in solving sensor placement problems. This study was selected for the special issue in JLPPI from the 2016 International Symposium of the MKO Process Safety Center.« less

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

Rasouli, C.; Abbasi Davani, F.; Rokrok, B.

Plasma confinement using external magnetic field is one of the successful ways leading to the controlled nuclear fusion. Development and validation of the solution process for plasma equilibrium in the experimental toroidal fusion devices is the main subject of this work. Solution of the nonlinear 2D stationary problem as posed by the Grad-Shafranov equation gives quantitative information about plasma equilibrium inside the vacuum chamber of hot fusion devices. This study suggests solving plasma equilibrium equation which is essential in toroidal nuclear fusion devices, using a mesh-free method in a condition that the plasma boundary is unknown. The Grad-Shafranov equation hasmore » been solved numerically by the point interpolation collocation mesh-free method. Important features of this approach include truly mesh free, simple mathematical relationships between points and acceptable precision in comparison with the parametric results. The calculation process has been done by using the regular and irregular nodal distribution and support domains with different points. The relative error between numerical and analytical solution is discussed for several test examples such as small size Damavand tokamak, ITER-like equilibrium, NSTX-like equilibrium, and typical Spheromak.« less

Combined AIE/EBE/GMRES approach to incompressible flows. [Adaptive Implicit-Explicit/Grouped Element-by-Element/Generalized Minimum Residuals

NASA Technical Reports Server (NTRS)

Liou, J.; Tezduyar, T. E.

1990-01-01

Adaptive implicit-explicit (AIE), grouped element-by-element (GEBE), and generalized minimum residuals (GMRES) solution techniques for incompressible flows are combined. In this approach, the GEBE and GMRES iteration methods are employed to solve the equation systems resulting from the implicitly treated elements, and therefore no direct solution effort is involved. The benchmarking results demonstrate that this approach can substantially reduce the CPU time and memory requirements in large-scale flow problems. Although the description of the concepts and the numerical demonstration are based on the incompressible flows, the approach presented here is applicable to larger class of problems in computational mechanics.

Coherent diffractive imaging using randomly coded masks

DOE PAGES

Seaberg, Matthew H.; d'Aspremont, Alexandre; Turner, Joshua J.

2015-12-07

We experimentally demonstrate an extension to coherent diffractive imaging that encodes additional information through the use of a series of randomly coded masks, removing the need for typical object-domain constraints while guaranteeing a unique solution to the phase retrieval problem. Phase retrieval is performed using a numerical convex relaxation routine known as “PhaseCut,” an iterative algorithm known for its stability and for its ability to find the global solution, which can be found efficiently and which is robust to noise. As a result, the experiment is performed using a laser diode at 532.2 nm, enabling rapid prototyping for future X-raymore » synchrotron and even free electron laser experiments.« less

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.

Coherent diffractive imaging using randomly coded masks

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

Seaberg, Matthew H., E-mail: seaberg@slac.stanford.edu; Linac Coherent Light Source, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025; D'Aspremont, Alexandre

2015-12-07

We experimentally demonstrate an extension to coherent diffractive imaging that encodes additional information through the use of a series of randomly coded masks, removing the need for typical object-domain constraints while guaranteeing a unique solution to the phase retrieval problem. Phase retrieval is performed using a numerical convex relaxation routine known as “PhaseCut,” an iterative algorithm known for its stability and for its ability to find the global solution, which can be found efficiently and which is robust to noise. The experiment is performed using a laser diode at 532.2 nm, enabling rapid prototyping for future X-ray synchrotron and even freemore » electron laser experiments.« less

Heat transfer evaluation in a plasma core reactor

NASA Technical Reports Server (NTRS)

Smith, D. E.; Smith, T. M.; Stoenescu, M. L.

1976-01-01

Numerical evaluations of heat transfer in a fissioning uranium plasma core reactor cavity, operating with seeded hydrogen propellant, was performed. A two-dimensional analysis is based on an assumed flow pattern and cavity wall heat exchange rate. Various iterative schemes were required by the nature of the radiative field and by the solid seed vaporization. Approximate formulations of the radiative heat flux are generally used, due to the complexity of the solution of a rigorously formulated problem. The present work analyzes the sensitivity of the results with respect to approximations of the radiative field, geometry, seed vaporization coefficients and flow pattern. The results present temperature, heat flux, density and optical depth distributions in the reactor cavity, acceptable simplifying assumptions, and iterative schemes. The present calculations, performed in cartesian and spherical coordinates, are applicable to any most general heat transfer problem.

Microwave beam broadening due to turbulent plasma density fluctuations within the limit of the Born approximation and beyond

NASA Astrophysics Data System (ADS)

Köhn, A.; Guidi, L.; Holzhauer, E.; Maj, O.; Poli, E.; Snicker, A.; Weber, H.

2018-07-01

Plasma turbulence, and edge density fluctuations in particular, can under certain conditions broaden the cross-section of injected microwave beams significantly. This can be a severe problem for applications relying on well-localized deposition of the microwave power, like the control of MHD instabilities. Here we investigate this broadening mechanism as a function of fluctuation level, background density and propagation length in a fusion-relevant scenario using two numerical codes, the full-wave code IPF-FDMC and the novel wave kinetic equation solver WKBeam. The latter treats the effects of fluctuations using a statistical approach, based on an iterative solution of the scattering problem (Born approximation). The full-wave simulations are used to benchmark this approach. The Born approximation is shown to be valid over a large parameter range, including ITER-relevant scenarios.

Efficient Solution of Three-Dimensional Problems of Acoustic and Electromagnetic Scattering by Open Surfaces

NASA Technical Reports Server (NTRS)

Turc, Catalin; Anand, Akash; Bruno, Oscar; Chaubell, Julian

2011-01-01

We present a computational methodology (a novel Nystrom approach based on use of a non-overlapping patch technique and Chebyshev discretizations) for efficient solution of problems of acoustic and electromagnetic scattering by open surfaces. Our integral equation formulations (1) Incorporate, as ansatz, the singular nature of open-surface integral-equation solutions, and (2) For the Electric Field Integral Equation (EFIE), use analytical regularizes that effectively reduce the number of iterations required by iterative linear-algebra solution based on Krylov-subspace iterative solvers.

Analytical study and numerical solution of the inverse source problem arising in thermoacoustic tomography

NASA Astrophysics Data System (ADS)

Holman, Benjamin R.

In recent years, revolutionary "hybrid" or "multi-physics" methods of medical imaging have emerged. By combining two or three different types of waves these methods overcome limitations of classical tomography techniques and deliver otherwise unavailable, potentially life-saving diagnostic information. Thermoacoustic (and photoacoustic) tomography is the most developed multi-physics imaging modality. Thermo- and photo- acoustic tomography require reconstructing initial acoustic pressure in a body from time series of pressure measured on a surface surrounding the body. For the classical case of free space wave propagation, various reconstruction techniques are well known. However, some novel measurement schemes place the object of interest between reflecting walls that form a de facto resonant cavity. In this case, known methods cannot be used. In chapter 2 we present a fast iterative reconstruction algorithm for measurements made at the walls of a rectangular reverberant cavity with a constant speed of sound. We prove the convergence of the iterations under a certain sufficient condition, and demonstrate the effectiveness and efficiency of the algorithm in numerical simulations. In chapter 3 we consider the more general problem of an arbitrarily shaped resonant cavity with a non constant speed of sound and present the gradual time reversal method for computing solutions to the inverse source problem. It consists in solving back in time on the interval [0, T] the initial/boundary value problem for the wave equation, with the Dirichlet boundary data multiplied by a smooth cutoff function. If T is sufficiently large one obtains a good approximation to the initial pressure; in the limit of large T such an approximation converges (under certain conditions) to the exact solution.

Evaluation of the Ross fast solution of Richards’ equation in unfavourable conditions for standard finite element methods

NASA Astrophysics Data System (ADS)

Crevoisier, David; Chanzy, André; Voltz, Marc

2009-06-01

Ross [Ross PJ. Modeling soil water and solute transport - fast, simplified numerical solutions. Agron J 2003;95:1352-61] developed a fast, simplified method for solving Richards' equation. This non-iterative 1D approach, using Brooks and Corey [Brooks RH, Corey AT. Hydraulic properties of porous media. Hydrol. papers, Colorado St. Univ., Fort Collins; 1964] hydraulic functions, allows a significant reduction in computing time while maintaining the accuracy of the results. The first aim of this work is to confirm these results in a more extensive set of problems, including those that would lead to serious numerical difficulties for the standard numerical method. The second aim is to validate a generalisation of the Ross method to other mathematical representations of hydraulic functions. The Ross method is compared with the standard finite element model, Hydrus-1D [Simunek J, Sejna M, Van Genuchten MTh. The HYDRUS-1D and HYDRUS-2D codes for estimating unsaturated soil hydraulic and solutes transport parameters. Agron Abstr 357; 1999]. Computing time, accuracy of results and robustness of numerical schemes are monitored in 1D simulations involving different types of homogeneous soils, grids and hydrological conditions. The Ross method associated with modified Van Genuchten hydraulic functions [Vogel T, Cislerova M. On the reliability of unsaturated hydraulic conductivity calculated from the moisture retention curve. Transport Porous Media 1988;3:1-15] proves in every tested scenario to be more robust numerically, and the compromise of computing time/accuracy is seen to be particularly improved on coarse grids. Ross method run from 1.25 to 14 times faster than Hydrus-1D.

Exact self-similarity solution of the Navier-Stokes equations for a porous channel with orthogonally moving walls

NASA Astrophysics Data System (ADS)

Dauenhauer, Eric C.; Majdalani, Joseph

2003-06-01

This article describes a self-similarity solution of the Navier-Stokes equations for a laminar, incompressible, and time-dependent flow that develops within a channel possessing permeable, moving walls. The case considered here pertains to a channel that exhibits either injection or suction across two opposing porous walls while undergoing uniform expansion or contraction. Instances of direct application include the modeling of pulsating diaphragms, sweat cooling or heating, isotope separation, filtration, paper manufacturing, irrigation, and the grain regression during solid propellant combustion. To start, the stream function and the vorticity equation are used in concert to yield a partial differential equation that lends itself to a similarity transformation. Following this similarity transformation, the original problem is reduced to solving a fourth-order differential equation in one similarity variable η that combines both space and time dimensions. Since two of the four auxiliary conditions are of the boundary value type, a numerical solution becomes dependent upon two initial guesses. In order to achieve convergence, the governing equation is first transformed into a function of three variables: The two guesses and η. At the outset, a suitable numerical algorithm is applied by solving the resulting set of twelve first-order ordinary differential equations with two unspecified start-up conditions. In seeking the two unknown initial guesses, the rapidly converging inverse Jacobian method is applied in an iterative fashion. Numerical results are later used to ascertain a deeper understanding of the flow character. The numerical scheme enables us to extend the solution range to physical settings not considered in previous studies. Moreover, the numerical approach broadens the scope to cover both suction and injection cases occurring with simultaneous wall motion.

Axisymmetric Vortices with Swirl

NASA Astrophysics Data System (ADS)

Elcrat, A.

2007-11-01

This talk is concerned with finding solutions of the Euler equations by solving elliptic boundary value problems for the Bragg-Hawthorne equation L u= -urr -(1/r)ur - = r^2f (u) + h(u). Theoretical results have been given for previously (Elcrat and Miller, Differential and Integral Equations 16(4) 2003, 949-968) for problems with swirl and general classes of profile functions f, h by iterating Lu(n+1)= rf(u)n)) + h(u(n)), and showing u(n) converges montonically to a solution. The solutions obtained depend on the initial guess, which can be thought of as prescribing level sets of the vortex. When a computational program was attempted these monotone iterations turned out to be numerically unstable, and a stable computation was acheived by fixing the moment of the cross section of a vortex in the merideanal plane. (This generalizes previous computational results in Elcrat, Fornberg and Miller, JFM 433 2001, (315-328) We obtain famillies of vortices related to vortex rings with swirl, Moffatt's generalization of Hill's vortex and tubes of vorticity with swirl wrapped around the symmetry axis. The vortices are embedded in either an irrotational flow or a flow with shear, and we deal with the transition form no swirl in the vortex to flow with only swirl, a Beltrami flow.

To Boldly Go Where No Man has Gone Before: Seeking Gaia's Astrometric Solution with AGIS

NASA Astrophysics Data System (ADS)

Lammers, U.; Lindegren, L.; O'Mullane, W.; Hobbs, D.

2009-09-01

Gaia is ESA's ambitious space astrometry mission with a foreseen launch date in late 2011. Its main objective is to perform a stellar census of the 1,000 million brightest objects in our galaxy (completeness to V=20 mag) from which an astrometric catalog of micro-arcsec (μas) level accuracy will be constructed. A key element in this endeavor is the Astrometric Global Iterative Solution (AGIS) - the mathematical and numerical framework for combining the ≈80 available observations per star obtained during Gaia's 5 yr lifetime into a single global astrometic solution. AGIS consists of four main algorithmic cores which improve the source astrometic parameters, satellite attitude, calibration, and global parameters in a block-iterative manner. We present and discuss this basic scheme, the algorithms themselves and the overarching system architecture. The latter is a data-driven distributed processing framework designed to achieve an overall system performance that is not I/O limited. AGIS is being developed as a pure Java system by a small number of geographically distributed European groups. We present some of the software engineering aspects of the project and show used methodologies and tools. Finally we will briefly discuss how AGIS is embedded into the overall Gaia data processing architecture.

Numerical modeling for the retrofit of the hydraulic cooling subsystems in operating power plant

NASA Astrophysics Data System (ADS)

AlSaqoor, S.; Alahmer, A.; Al Quran, F.; Andruszkiewicz, A.; Kubas, K.; Regucki, P.; Wędrychowicz, W.

2017-08-01

This paper presents the possibility of using the numerical methods to analyze the work of hydraulic systems on the example of a cooling system of a power boiler auxiliary devices. The variety of conditions at which hydraulic system that operated in specific engineering subsystems requires an individualized approach to the model solutions that have been developed for these systems modernizing. A mathematical model of a series-parallel propagation for the cooling water was derived and iterative methods were used to solve the system of nonlinear equations. The results of numerical calculations made it possible to analyze different variants of a modernization of the studied system and to indicate its critical elements. An economic analysis of different options allows an investor to choose an optimal variant of a reconstruction of the installation.

Sensitivity calculations for iteratively solved problems

NASA Technical Reports Server (NTRS)

Haftka, R. T.

1985-01-01

The calculation of sensitivity derivatives of solutions of iteratively solved systems of algebraic equations is investigated. A modified finite difference procedure is presented which improves the accuracy of the calculated derivatives. The procedure is demonstrated for a simple algebraic example as well as an element-by-element preconditioned conjugate gradient iterative solution technique applied to truss examples.

Experimental and numerical study of control of flow separation of a symmetric airfoil with trapped vortex cavity

NASA Astrophysics Data System (ADS)

Shahid, Abdullah Bin; Mashud, Mohammad

2017-06-01

This paper summarizes the experimental campaign and numerical analysis performed aimed to analyze the potential benefit available employing a trapping vortex cell system on a high thickness symmetric aero-foil without steady suction or injection mass flow. In this work, the behavior of a two dimensional model equipped with a span wise adjusted circular cavity has been researched. Pressure distribution on the model surface and inside and the complete flow field round the model have been measured. Experimental tests have been performed varying the wind tunnel speed and also the angle of attack. For numerical analysis the two dimensional model of the airfoil and the mesh is formed through ANSYS Meshing that is run in Fluent for numerical iterate solution. In the paper the performed test campaign, the airfoil design, the adopted experimental set-up, the numerical analysis, the data post process and the results description are reported, compared a discussed.

Numerical simulation of freshwater/seawater interaction in a dual-permeability karst system with conduits: the development of discrete-continuum VDFST-CFP model

NASA Astrophysics Data System (ADS)

Xu, Zexuan; Hu, Bill

2016-04-01

Dual-permeability karst aquifers of porous media and conduit networks with significant different hydrological characteristics are widely distributed in the world. Discrete-continuum numerical models, such as MODFLOW-CFP and CFPv2, have been verified as appropriate approaches to simulate groundwater flow and solute transport in numerical modeling of karst hydrogeology. On the other hand, seawater intrusion associated with fresh groundwater resources contamination has been observed and investigated in numbers of coastal aquifers, especially under conditions of sea level rise. Density-dependent numerical models including SEAWAT are able to quantitatively evaluate the seawater/freshwater interaction processes. A numerical model of variable-density flow and solute transport - conduit flow process (VDFST-CFP) is developed to provide a better description of seawater intrusion and submarine groundwater discharge in a coastal karst aquifer with conduits. The coupling discrete-continuum VDFST-CFP model applies Darcy-Weisbach equation to simulate non-laminar groundwater flow in the conduit system in which is conceptualized and discretized as pipes, while Darcy equation is still used in continuum porous media. Density-dependent groundwater flow and solute transport equations with appropriate density terms in both conduit and porous media systems are derived and numerically solved using standard finite difference method with an implicit iteration procedure. Synthetic horizontal and vertical benchmarks are created to validate the newly developed VDFST-CFP model by comparing with other numerical models such as variable density SEAWAT, couplings of constant density groundwater flow and solute transport MODFLOW/MT3DMS and discrete-continuum CFPv2/UMT3D models. VDFST-CFP model improves the simulation of density dependent seawater/freshwater mixing processes and exchanges between conduit and matrix. Continuum numerical models greatly overestimated the flow rate under turbulent flow condition but discrete-continuum models provide more accurate results. Parameters sensitivities analysis indicates that conduit diameter and friction factor, matrix hydraulic conductivity and porosity are important parameters that significantly affect variable-density flow and solute transport simulation. The pros and cons of model assumptions, conceptual simplifications and numerical techniques in VDFST-CFP are discussed. In general, the development of VDFST-CFP model is an innovation in numerical modeling methodology and could be applied to quantitatively evaluate the seawater/freshwater interaction in coastal karst aquifers. Keywords: Discrete-continuum numerical model; Variable density flow and transport; Coastal karst aquifer; Non-laminar flow

Using a derivative-free optimization method for multiple solutions of inverse transport problems

DOE PAGES

Armstrong, Jerawan C.; Favorite, Jeffrey A.

2016-01-14

Identifying unknown components of an object that emits radiation is an important problem for national and global security. Radiation signatures measured from an object of interest can be used to infer object parameter values that are not known. This problem is called an inverse transport problem. An inverse transport problem may have multiple solutions and the most widely used approach for its solution is an iterative optimization method. This paper proposes a stochastic derivative-free global optimization algorithm to find multiple solutions of inverse transport problems. The algorithm is an extension of a multilevel single linkage (MLSL) method where a meshmore » adaptive direct search (MADS) algorithm is incorporated into the local phase. Furthermore, numerical test cases using uncollided fluxes of discrete gamma-ray lines are presented to show the performance of this new algorithm.« less

Stochastic porous media modeling and high-resolution schemes for numerical simulation of subsurface immiscible fluid flow transport

NASA Astrophysics Data System (ADS)

Brantson, Eric Thompson; Ju, Binshan; Wu, Dan; Gyan, Patricia Semwaah

2018-04-01

This paper proposes stochastic petroleum porous media modeling for immiscible fluid flow simulation using Dykstra-Parson coefficient (V DP) and autocorrelation lengths to generate 2D stochastic permeability values which were also used to generate porosity fields through a linear interpolation technique based on Carman-Kozeny equation. The proposed method of permeability field generation in this study was compared to turning bands method (TBM) and uniform sampling randomization method (USRM). On the other hand, many studies have also reported that, upstream mobility weighting schemes, commonly used in conventional numerical reservoir simulators do not accurately capture immiscible displacement shocks and discontinuities through stochastically generated porous media. This can be attributed to high level of numerical smearing in first-order schemes, oftentimes misinterpreted as subsurface geological features. Therefore, this work employs high-resolution schemes of SUPERBEE flux limiter, weighted essentially non-oscillatory scheme (WENO), and monotone upstream-centered schemes for conservation laws (MUSCL) to accurately capture immiscible fluid flow transport in stochastic porous media. The high-order schemes results match well with Buckley Leverett (BL) analytical solution without any non-oscillatory solutions. The governing fluid flow equations were solved numerically using simultaneous solution (SS) technique, sequential solution (SEQ) technique and iterative implicit pressure and explicit saturation (IMPES) technique which produce acceptable numerical stability and convergence rate. A comparative and numerical examples study of flow transport through the proposed method, TBM and USRM permeability fields revealed detailed subsurface instabilities with their corresponding ultimate recovery factors. Also, the impact of autocorrelation lengths on immiscible fluid flow transport were analyzed and quantified. A finite number of lines used in the TBM resulted into visual artifact banding phenomenon unlike the proposed method and USRM. In all, the proposed permeability and porosity fields generation coupled with the numerical simulator developed will aid in developing efficient mobility control schemes to improve on poor volumetric sweep efficiency in porous media.

Separation of Undersampled Composite Signals Using the Dantzig Selector with Overcomplete Dictionaries

DTIC Science & Technology

2014-06-02

2011). [22] Li, Q., Micchelli, C., Shen, L., and Xu, Y. A proximity algorithm acelerated by Gauss - Seidel iterations for L1/TV denoising models. Inverse...system of equations and their relationship to the solution of Model (2) and present an algorithm with an iterative approach for finding these solutions...Using the fixed-point characterization above, the (k + 1)th iteration of the prox- imity operator algorithm to find the solution of the Dantzig

Aerodynamic optimization by simultaneously updating flow variables and design parameters

NASA Technical Reports Server (NTRS)

Rizk, M. H.

1990-01-01

The application of conventional optimization schemes to aerodynamic design problems leads to inner-outer iterative procedures that are very costly. An alternative approach is presented based on the idea of updating the flow variable iterative solutions and the design parameter iterative solutions simultaneously. Two schemes based on this idea are applied to problems of correcting wind tunnel wall interference and optimizing advanced propeller designs. The first of these schemes is applicable to a limited class of two-design-parameter problems with an equality constraint. It requires the computation of a single flow solution. The second scheme is suitable for application to general aerodynamic problems. It requires the computation of several flow solutions in parallel. In both schemes, the design parameters are updated as the iterative flow solutions evolve. Computations are performed to test the schemes' efficiency, accuracy, and sensitivity to variations in the computational parameters.

Parallel solution of the symmetric tridiagonal eigenproblem. Research report

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

Jessup, E.R.

1989-10-01

This thesis discusses methods for computing all eigenvalues and eigenvectors of a symmetric tridiagonal matrix on a distributed-memory Multiple Instruction, Multiple Data multiprocessor. Only those techniques having the potential for both high numerical accuracy and significant large-grained parallelism are investigated. These include the QL method or Cuppen's divide and conquer method based on rank-one updating to compute both eigenvalues and eigenvectors, bisection to determine eigenvalues and inverse iteration to compute eigenvectors. To begin, the methods are compared with respect to computation time, communication time, parallel speed up, and accuracy. Experiments on an IPSC hypercube multiprocessor reveal that Cuppen's method ismore » the most accurate approach, but bisection with inverse iteration is the fastest and most parallel. Because the accuracy of the latter combination is determined by the quality of the computed eigenvectors, the factors influencing the accuracy of inverse iteration are examined. This includes, in part, statistical analysis of the effect of a starting vector with random components. These results are used to develop an implementation of inverse iteration producing eigenvectors with lower residual error and better orthogonality than those generated by the EISPACK routine TINVIT. This thesis concludes with adaptions of methods for the symmetric tridiagonal eigenproblem to the related problem of computing the singular value decomposition (SVD) of a bidiagonal matrix.« less

Parallel solution of the symmetric tridiagonal eigenproblem

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

Jessup, E.R.

1989-01-01

This thesis discusses methods for computing all eigenvalues and eigenvectors of a symmetric tridiagonal matrix on a distributed memory MIMD multiprocessor. Only those techniques having the potential for both high numerical accuracy and significant large-grained parallelism are investigated. These include the QL method or Cuppen's divide and conquer method based on rank-one updating to compute both eigenvalues and eigenvectors, bisection to determine eigenvalues, and inverse iteration to compute eigenvectors. To begin, the methods are compared with respect to computation time, communication time, parallel speedup, and accuracy. Experiments on an iPSC hyper-cube multiprocessor reveal that Cuppen's method is the most accuratemore » approach, but bisection with inverse iteration is the fastest and most parallel. Because the accuracy of the latter combination is determined by the quality of the computed eigenvectors, the factors influencing the accuracy of inverse iteration are examined. This includes, in part, statistical analysis of the effects of a starting vector with random components. These results are used to develop an implementation of inverse iteration producing eigenvectors with lower residual error and better orthogonality than those generated by the EISPACK routine TINVIT. This thesis concludes with adaptations of methods for the symmetric tridiagonal eigenproblem to the related problem of computing the singular value decomposition (SVD) of a bidiagonal matrix.« less

Solution of Dirac equation for Eckart potential and trigonometric Manning Rosen potential using asymptotic iteration method

NASA Astrophysics Data System (ADS)

Resita Arum, Sari; A, Suparmi; C, Cari

2016-01-01

The Dirac equation for Eckart potential and trigonometric Manning Rosen potential with exact spin symmetry is obtained using an asymptotic iteration method. The combination of the two potentials is substituted into the Dirac equation, then the variables are separated into radial and angular parts. The Dirac equation is solved by using an asymptotic iteration method that can reduce the second order differential equation into a differential equation with substitution variables of hypergeometry type. The relativistic energy is calculated using Matlab 2011. This study is limited to the case of spin symmetry. With the asymptotic iteration method, the energy spectra of the relativistic equations and equations of orbital quantum number l can be obtained, where both are interrelated between quantum numbers. The energy spectrum is also numerically solved using the Matlab software, where the increase in the radial quantum number nr causes the energy to decrease. The radial part and the angular part of the wave function are defined as hypergeometry functions and visualized with Matlab 2011. The results show that the disturbance of a combination of the Eckart potential and trigonometric Manning Rosen potential can change the radial part and the angular part of the wave function. Project supported by the Higher Education Project (Grant No. 698/UN27.11/PN/2015).

Relativistic electron kinetic effects on laser diagnostics in burning plasmas

NASA Astrophysics Data System (ADS)

Mirnov, V. V.; Den Hartog, D. J.

2018-02-01

Toroidal interferometry/polarimetry (TIP), poloidal polarimetry (PoPola), and Thomson scattering systems (TS) are major optical diagnostics being designed and developed for ITER. Each of them relies upon a sophisticated quantitative understanding of the electron response to laser light propagating through a burning plasma. Review of the theoretical results for two different applications is presented: interferometry/polarimetry (I/P) and polarization of Thomson scattered light, unified by the importance of relativistic (quadratic in vTe/c) electron kinetic effects. For I/P applications, rigorous analytical results are obtained perturbatively by expansion in powers of the small parameter τ = Te/me c2, where Te is electron temperature and me is electron rest mass. Experimental validation of the analytical models has been made by analyzing data of more than 1200 pulses collected from high-Te JET discharges. Based on this validation the relativistic analytical expressions are included in the error analysis and design projects of the ITER TIP and PoPola systems. The polarization properties of incoherent Thomson scattered light are being examined as a method of Te measurement relevant to ITER operational regimes. The theory is based on Stokes vector transformation and Mueller matrices formalism. The general approach is subdivided into frequency-integrated and frequency-resolved cases. For each of them, the exact analytical relativistic solutions are presented in the form of Mueller matrix elements averaged over the relativistic Maxwellian distribution function. New results related to the detailed verification of the frequency-resolved solutions are reported. The precise analytic expressions provide output much more rapidly than relativistic kinetic numerical codes allowing for direct real-time feedback control of ITER device operation.

Conservative tightly-coupled simulations of stochastic multiscale systems

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

Taverniers, Søren; Pigarov, Alexander Y.; Tartakovsky, Daniel M., E-mail: dmt@ucsd.edu

2016-05-15

Multiphysics problems often involve components whose macroscopic dynamics is driven by microscopic random fluctuations. The fidelity of simulations of such systems depends on their ability to propagate these random fluctuations throughout a computational domain, including subdomains represented by deterministic solvers. When the constituent processes take place in nonoverlapping subdomains, system behavior can be modeled via a domain-decomposition approach that couples separate components at the interfaces between these subdomains. Its coupling algorithm has to maintain a stable and efficient numerical time integration even at high noise strength. We propose a conservative domain-decomposition algorithm in which tight coupling is achieved by employingmore » either Picard's or Newton's iterative method. Coupled diffusion equations, one of which has a Gaussian white-noise source term, provide a computational testbed for analysis of these two coupling strategies. Fully-converged (“implicit”) coupling with Newton's method typically outperforms its Picard counterpart, especially at high noise levels. This is because the number of Newton iterations scales linearly with the amplitude of the Gaussian noise, while the number of Picard iterations can scale superlinearly. At large time intervals between two subsequent inter-solver communications, the solution error for single-iteration (“explicit”) Picard's coupling can be several orders of magnitude higher than that for implicit coupling. Increasing the explicit coupling's communication frequency reduces this difference, but the resulting increase in computational cost can make it less efficient than implicit coupling at similar levels of solution error, depending on the communication frequency of the latter and the noise strength. This trend carries over into higher dimensions, although at high noise strength explicit coupling may be the only computationally viable option.« less

D4Z - a new renumbering for iterative solution of ground-water flow and solute- transport equations

USGS Publications Warehouse

Kipp, K.L.; Russell, T.F.; Otto, J.S.

1992-01-01

D4 zig-zag (D4Z) is a new renumbering scheme for producing a reduced matrix to be solved by an incomplete LU preconditioned, restarted conjugate-gradient iterative solver. By renumbering alternate diagonals in a zig-zag fashion, a very low sensitivity of convergence rate to renumbering direction is obtained. For two demonstration problems involving groundwater flow and solute transport, iteration counts are related to condition numbers and spectra of the reduced matrices.

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.

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.

A new procedure for calculating contact stresses in gear teeth

NASA Technical Reports Server (NTRS)

Somprakit, Paisan; Huston, Ronald L.

1991-01-01

A numerical procedure for evaluating and monitoring contact stresses in meshing gear teeth is discussed. The procedure is intended to extend the range of applicability and to improve the accuracy of gear contact stress analysis. The procedure is based upon fundamental solution from the theory of elasticity. It is an iterative numerical procedure. The method is believed to have distinct advantages over the classical Hertz method, the finite-element method, and over existing approaches with the boundary element method. Unlike many classical contact stress analyses, friction effects and sliding are included. Slipping and sticking in the contact region are studied. Several examples are discussed. The results are in agreement with classical results. Applications are presented for spur gears.

A numerical algorithm for optimal feedback gains in high dimensional linear quadratic regulator problems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Ito, K.

1991-01-01

A hybrid method for computing the feedback gains in linear quadratic regulator problem is proposed. The method, which combines use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite-dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantages of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed, and numerical evidence of the efficacy of these ideas is presented.

A Strassen-Newton algorithm for high-speed parallelizable matrix inversion

NASA Technical Reports Server (NTRS)

Bailey, David H.; Ferguson, Helaman R. P.

1988-01-01

Techniques are described for computing matrix inverses by algorithms that are highly suited to massively parallel computation. The techniques are based on an algorithm suggested by Strassen (1969). Variations of this scheme use matrix Newton iterations and other methods to improve the numerical stability while at the same time preserving a very high level of parallelism. One-processor Cray-2 implementations of these schemes range from one that is up to 55 percent faster than a conventional library routine to one that is slower than a library routine but achieves excellent numerical stability. The problem of computing the solution to a single set of linear equations is discussed, and it is shown that this problem can also be solved efficiently using these techniques.

Three-dimensional analysis of tokamaks and stellarators

PubMed Central

Garabedian, Paul R.

2008-01-01

The NSTAB equilibrium and stability code and the TRAN Monte Carlo transport code furnish a simple but effective numerical simulation of essential features of present tokamak and stellarator experiments. When the mesh size is comparable to the island width, an accurate radial difference scheme in conservation form captures magnetic islands successfully despite a nested surface hypothesis imposed by the mathematics. Three-dimensional asymmetries in bifurcated numerical solutions of the axially symmetric tokamak problem are relevant to the observation of unstable neoclassical tearing modes and edge localized modes in experiments. Islands in compact stellarators with quasiaxial symmetry are easier to control, so these configurations will become good candidates for magnetic fusion if difficulties with safety and stability are encountered in the International Thermonuclear Experimental Reactor (ITER) project. PMID:18768807

A numerical algorithm for optimal feedback gains in high dimensional LQR problems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Ito, K.

1986-01-01

A hybrid method for computing the feedback gains in linear quadratic regulator problems is proposed. The method, which combines the use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated so as to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantage of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed and numerical evidence of the efficacy of our ideas presented.

Extension of transonic flow computational concepts in the analysis of cavitated bearings

NASA Technical Reports Server (NTRS)

Vijayaraghavan, D.; Keith, T. G., Jr.; Brewe, D. E.

1990-01-01

An analogy between the mathematical modeling of transonic potential flow and the flow in a cavitating bearing is described. Based on the similarities, characteristics of the cavitated region and jump conditions across the film reformation and rupture fronts are developed using the method of weak solutions. The mathematical analogy is extended by utilizing a few computational concepts of transonic flow to numerically model the cavitating bearing. Methods of shock fitting and shock capturing are discussed. Various procedures used in transonic flow computations are adapted to bearing cavitation applications, for example, type differencing, grid transformation, an approximate factorization technique, and Newton's iteration method. These concepts have proved to be successful and have vastly improved the efficiency of numerical modeling of cavitated bearings.

The solution of three-variable duct-flow equations

NASA Technical Reports Server (NTRS)

Stuart, A. R.; Hetherington, R.

1974-01-01

This paper establishes a numerical method for the solution of three-variable problems and is applied here to rotational flows through ducts of various cross sections. An iterative scheme is developed, the main feature of which is the addition of a duplicate variable to the forward component of velocity. Two forward components of velocity result from integrating two sets of first order ordinary differential equations for the streamline curvatures, in intersecting directions across the duct. Two pseudo-continuity equations are introduced with source/sink terms, whose strengths are dependent on the difference between the forward components of velocity. When convergence is obtained, the two forward components of velocity are identical, the source/sink terms are zero, and the original equations are satisfied. A computer program solves the exact equations and boundary conditions numerically. The method is economical and compares successfully with experiments on bent ducts of circular and rectangular cross section where secondary flows are caused by gradients of total pressure upstream.

Plastic zone size and crack tip opening displacement of a Dugdale crack interacting with a coated circular inclusion

NASA Astrophysics Data System (ADS)

Hoh, H. J.; Xiao, Z. M.; Luo, J.

2010-09-01

An analytical investigation on the plastic zone size of a crack near a coated circular inclusion under three different loading conditions of uniaxial tension, uniform tension and pure shear was carried out. Both the crack and coated circular inclusion are embedded in an infinite matrix, with the crack oriented along the radial direction of the inclusion. In the solution procedure, the crack is simulated as a continuous distribution of edge dislocations. With the Dugdale model of small-scale yielding [J. Mech. Phys. Solids 8 (1960) p. 100], two thin strips of yielded plastic zones are introduced at both crack tips. Using the solution for a coated circular inclusion interacting with a single dislocation as the Green's function, the physical problem is formulated into a set of singular integral equations. Using the method of Erdogan and Gupta [Q. J. Appl. Math. 29 (1972) p. 525] and iterative numerical procedures, the singular integral equations are solved numerically for the plastic zone sizes and crack tip opening displacement.

A model-adaptivity method for the solution of Lennard-Jones based adhesive contact problems

NASA Astrophysics Data System (ADS)

Ben Dhia, Hachmi; Du, Shuimiao

2018-05-01

The surface micro-interaction model of Lennard-Jones (LJ) is used for adhesive contact problems (ACP). To address theoretical and numerical pitfalls of this model, a sequence of partitions of contact models is adaptively constructed to both extend and approximate the LJ model. It is formed by a combination of the LJ model with a sequence of shifted-Signorini (or, alternatively, -Linearized-LJ) models, indexed by a shift parameter field. For each model of this sequence, a weak formulation of the associated local ACP is developed. To track critical localized adhesive areas, a two-step strategy is developed: firstly, a macroscopic frictionless (as first approach) linear-elastic contact problem is solved once to detect contact separation zones. Secondly, at each shift-adaptive iteration, a micro-macro ACP is re-formulated and solved within the multiscale Arlequin framework, with significant reduction of computational costs. Comparison of our results with available analytical and numerical solutions shows the effectiveness of our global strategy.

Application of Newton's method to the postbuckling of rings under pressure loadings

NASA Technical Reports Server (NTRS)

Thurston, Gaylen A.

1989-01-01

The postbuckling response of circular rings (or long cylinders) is examined. The rings are subjected to four types of external pressure loadings; each type of pressure is defined by its magnitude and direction at points on the buckled ring. Newton's method is applied to the nonlinear differential equations of the exact inextensional theory for the ring problem. A zeroth approximation for the solution of the nonlinear equations, based on the mode shape corresponding to the first buckling pressure, is derived in closed form for each of the four types of pressure. The zeroth approximation is used to start the iteration cycle in Newton's method to compute numerical solutions of the nonlinear equations. The zeroth approximations for the postbuckling pressure-deflection curves are compared with the converged solutions from Newton's method and with similar results reported in the literature.

Challenges and status of ITER conductor production

NASA Astrophysics Data System (ADS)

Devred, A.; Backbier, I.; Bessette, D.; Bevillard, G.; Gardner, M.; Jong, C.; Lillaz, F.; Mitchell, N.; Romano, G.; Vostner, A.

2014-04-01

Taking the relay of the large Hadron collider (LHC) at CERN, ITER has become the largest project in applied superconductivity. In addition to its technical complexity, ITER is also a management challenge as it relies on an unprecedented collaboration of seven partners, representing more than half of the world population, who provide 90% of the components as in-kind contributions. The ITER magnet system is one of the most sophisticated superconducting magnet systems ever designed, with an enormous stored energy of 51 GJ. It involves six of the ITER partners. The coils are wound from cable-in-conduit conductors (CICCs) made up of superconducting and copper strands assembled into a multistage cable, inserted into a conduit of butt-welded austenitic steel tubes. The conductors for the toroidal field (TF) and central solenoid (CS) coils require about 600 t of Nb3Sn strands while the poloidal field (PF) and correction coil (CC) and busbar conductors need around 275 t of Nb-Ti strands. The required amount of Nb3Sn strands far exceeds pre-existing industrial capacity and has called for a significant worldwide production scale up. The TF conductors are the first ITER components to be mass produced and are more than 50% complete. During its life time, the CS coil will have to sustain several tens of thousands of electromagnetic (EM) cycles to high current and field conditions, way beyond anything a large Nb3Sn coil has ever experienced. Following a comprehensive R&D program, a technical solution has been found for the CS conductor, which ensures stable performance versus EM and thermal cycling. Productions of PF, CC and busbar conductors are also underway. After an introduction to the ITER project and magnet system, we describe the ITER conductor procurements and the quality assurance/quality control programs that have been implemented to ensure production uniformity across numerous suppliers. Then, we provide examples of technical challenges that have been encountered and we present the status of ITER conductor production worldwide.

The Robin Hood method - A novel numerical method for electrostatic problems based on a non-local charge transfer

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

Lazic, Predrag; Stefancic, Hrvoje; Abraham, Hrvoje

2006-03-20

We introduce a novel numerical method, named the Robin Hood method, of solving electrostatic problems. The approach of the method is closest to the boundary element methods, although significant conceptual differences exist with respect to this class of methods. The method achieves equipotentiality of conducting surfaces by iterative non-local charge transfer. For each of the conducting surfaces, non-local charge transfers are performed between surface elements, which differ the most from the targeted equipotentiality of the surface. The method is tested against analytical solutions and its wide range of application is demonstrated. The method has appealing technical characteristics. For the problemmore » with N surface elements, the computational complexity of the method essentially scales with N {sup {alpha}}, where {alpha} < 2, the required computer memory scales with N, while the error of the potential decreases exponentially with the number of iterations for many orders of magnitude of the error, without the presence of the Critical Slowing Down. The Robin Hood method could prove useful in other classical or even quantum problems. Some future development ideas for possible applications outside electrostatics are addressed.« less

Eigensolutions of nonviscously damped systems based on the fixed-point iteration

NASA Astrophysics Data System (ADS)

Lázaro, Mario

2018-03-01

In this paper, nonviscous, nonproportional, symmetric vibrating structures are considered. Nonviscously damped systems present dissipative forces depending on the time history of the response via kernel hereditary functions. Solutions of the free motion equation leads to a nonlinear eigenvalue problem involving mass, stiffness and damping matrices, this latter as dependent on frequency. Viscous damping can be considered as a particular case, involving damping forces as function of the instantaneous velocity of the degrees of freedom. In this work, a new numerical procedure to compute eigensolutions is proposed. The method is based on the construction of certain recursive functions which, under a iterative scheme, allow to reach eigenvalues and eigenvectors simultaneously and avoiding computation of eigensensitivities. Eigenvalues can be read then as fixed-points of those functions. A deep analysis of the convergence is carried out, focusing specially on relating the convergence conditions and error-decay rate to the damping model features, such as the nonproportionality and the viscoelasticity. The method is validated using two 6 degrees of freedom numerical examples involving both nonviscous and viscous damping and a continuous system with a local nonviscous damper. The convergence and the sequences behavior are in agreement with the results foreseen by the theory.

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.

Estimation for the Linear Model With Uncertain Covariance Matrices

NASA Astrophysics Data System (ADS)

Zachariah, Dave; Shariati, Nafiseh; Bengtsson, Mats; Jansson, Magnus; Chatterjee, Saikat

2014-03-01

We derive a maximum a posteriori estimator for the linear observation model, where the signal and noise covariance matrices are both uncertain. The uncertainties are treated probabilistically by modeling the covariance matrices with prior inverse-Wishart distributions. The nonconvex problem of jointly estimating the signal of interest and the covariance matrices is tackled by a computationally efficient fixed-point iteration as well as an approximate variational Bayes solution. The statistical performance of estimators is compared numerically to state-of-the-art estimators from the literature and shown to perform favorably.

Ocean tides from Seasat-A

NASA Technical Reports Server (NTRS)

Hendershott, M. C.; Munk, W. H.; Zetler, B. D.

1974-01-01

Two procedures for the evaluation of global tides from SEASAT-A altimetry data are elaborated: an empirical method leading to the response functions for a grid of about 500 points from which the tide can be predicted for any point in the oceans, and a dynamic method which consists of iteratively modifying the parameters in a numerical solution to Laplace tide equations. It is assumed that the shape of the received altimeter signal can be interpreted for sea state and that orbit calculations are available so that absolute sea levels can be obtained.

Projection methods for line radiative transfer in spherical media.

NASA Astrophysics Data System (ADS)

Anusha, L. S.; Nagendra, K. N.

An efficient numerical method called the Preconditioned Bi-Conjugate Gradient (Pre-BiCG) method is presented for the solution of radiative transfer equation in spherical geometry. A variant of this method called Stabilized Preconditioned Bi-Conjugate Gradient (Pre-BiCG-STAB) is also presented. These methods are based on projections on the subspaces of the n dimensional Euclidean space mathbb {R}n called Krylov subspaces. The methods are shown to be faster in terms of convergence rate compared to the contemporary iterative methods such as Jacobi, Gauss-Seidel and Successive Over Relaxation (SOR).

Probing Majorana modes in the tunneling spectra of a resonant level.

PubMed

Korytár, R; Schmitteckert, P

2013-11-27

Unambiguous identification of Majorana physics presents an outstanding problem whose solution could render topological quantum computing feasible. We develop a numerical approach to treat finite-size superconducting chains supporting Majorana modes, which is based on iterative application of a two-site Bogoliubov transformation. We demonstrate the applicability of the method by studying a resonant level attached to the superconductor subject to external perturbations. In the topological phase, we show that the spectrum of a single resonant level allows us to distinguish peaks coming from Majorana physics from the Kondo resonance.

On the existence of mosaic-skeleton approximations for discrete analogues of integral operators

NASA Astrophysics Data System (ADS)

Kashirin, A. A.; Taltykina, M. Yu.

2017-09-01

Exterior three-dimensional Dirichlet problems for the Laplace and Helmholtz equations are considered. By applying methods of potential theory, they are reduced to equivalent Fredholm boundary integral equations of the first kind, for which discrete analogues, i.e., systems of linear algebraic equations (SLAEs) are constructed. The existence of mosaic-skeleton approximations for the matrices of the indicated systems is proved. These approximations make it possible to reduce the computational complexity of an iterative solution of the SLAEs. Numerical experiments estimating the capabilities of the proposed approach are described.

Krylov subspace iterative methods for boundary element method based near-field acoustic holography.

PubMed

Valdivia, Nicolas; Williams, Earl G

2005-02-01

The reconstruction of the acoustic field for general surfaces is obtained from the solution of a matrix system that results from a boundary integral equation discretized using boundary element methods. The solution to the resultant matrix system is obtained using iterative regularization methods that counteract the effect of noise on the measurements. These methods will not require the calculation of the singular value decomposition, which can be expensive when the matrix system is considerably large. Krylov subspace methods are iterative methods that have the phenomena known as "semi-convergence," i.e., the optimal regularization solution is obtained after a few iterations. If the iteration is not stopped, the method converges to a solution that generally is totally corrupted by errors on the measurements. For these methods the number of iterations play the role of the regularization parameter. We will focus our attention to the study of the regularizing properties from the Krylov subspace methods like conjugate gradients, least squares QR and the recently proposed Hybrid method. A discussion and comparison of the available stopping rules will be included. A vibrating plate is considered as an example to validate our results.

Preconditioned Mixed Spectral Element Methods for Elasticity and Stokes Problems

NASA Technical Reports Server (NTRS)

Pavarino, Luca F.

1996-01-01

Preconditioned iterative methods for the indefinite systems obtained by discretizing the linear elasticity and Stokes problems with mixed spectral elements in three dimensions are introduced and analyzed. The resulting stiffness matrices have the structure of saddle point problems with a penalty term, which is associated with the Poisson ratio for elasticity problems or with stabilization techniques for Stokes problems. The main results of this paper show that the convergence rate of the resulting algorithms is independent of the penalty parameter, the number of spectral elements Nu and mildly dependent on the spectral degree eta via the inf-sup constant. The preconditioners proposed for the whole indefinite system are block-diagonal and block-triangular. Numerical experiments presented in the final section show that these algorithms are a practical and efficient strategy for the iterative solution of the indefinite problems arising from mixed spectral element discretizations of elliptic systems.

Some Remarks on GMRES for Transport Theory

NASA Technical Reports Server (NTRS)

Patton, Bruce W.; Holloway, James Paul

2003-01-01

We review some work on the application of GMRES to the solution of the discrete ordinates transport equation in one-dimension. We note that GMRES can be applied directly to the angular flux vector, or it can be applied to only a vector of flux moments as needed to compute the scattering operator of the transport equation. In the former case we illustrate both the delights and defects of ILU right-preconditioners for problems with anisotropic scatter and for problems with upscatter. When working with flux moments we note that GMRES can be used as an accelerator for any existing transport code whose solver is based on a stationary fixed-point iteration, including transport sweeps and DSA transport sweeps. We also provide some numerical illustrations of this idea. We finally show how space can be traded for speed by taking multiple transport sweeps per GMRES iteration. Key Words: transport equation, GMRES, Krylov subspace

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.

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.

Fast secant methods for the iterative solution of large nonsymmetric linear systems

NASA Technical Reports Server (NTRS)

Deuflhard, Peter; Freund, Roland; Walter, Artur

1990-01-01

A family of secant methods based on general rank-1 updates was revisited in view of the construction of iterative solvers for large non-Hermitian linear systems. As it turns out, both Broyden's good and bad update techniques play a special role, but should be associated with two different line search principles. For Broyden's bad update technique, a minimum residual principle is natural, thus making it theoretically comparable with a series of well known algorithms like GMRES. Broyden's good update technique, however, is shown to be naturally linked with a minimum next correction principle, which asymptotically mimics a minimum error principle. The two minimization principles differ significantly for sufficiently large system dimension. Numerical experiments on discretized partial differential equations of convection diffusion type in 2-D with integral layers give a first impression of the possible power of the derived good Broyden variant.

Computing the optimal path in stochastic dynamical systems

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

Bauver, Martha; Forgoston, Eric, E-mail: eric.forgoston@montclair.edu; Billings, Lora

2016-08-15

In stochastic systems, one is often interested in finding the optimal path that maximizes the probability of escape from a metastable state or of switching between metastable states. Even for simple systems, it may be impossible to find an analytic form of the optimal path, and in high-dimensional systems, this is almost always the case. In this article, we formulate a constructive methodology that is used to compute the optimal path numerically. The method utilizes finite-time Lyapunov exponents, statistical selection criteria, and a Newton-based iterative minimizing scheme. The method is applied to four examples. The first example is a two-dimensionalmore » system that describes a single population with internal noise. This model has an analytical solution for the optimal path. The numerical solution found using our computational method agrees well with the analytical result. The second example is a more complicated four-dimensional system where our numerical method must be used to find the optimal path. The third example, although a seemingly simple two-dimensional system, demonstrates the success of our method in finding the optimal path where other numerical methods are known to fail. In the fourth example, the optimal path lies in six-dimensional space and demonstrates the power of our method in computing paths in higher-dimensional spaces.« less

The use of multigrid techniques in the solution of the Elrod algorithm for a dynamically loaded journal bearing. M.S. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Woods, Claudia M.

1988-01-01

A numerical solution to a theoretical model of vapor cavitation in a dynamically loaded journal bearing is developed, utilizing a multigrid iterative technique. The code is compared with a presently existing direct solution in terms of computational time and accuracy. The model is based on the Elrod algorithm, a control volume approach to the Reynolds equation which mimics the Jakobssen-Floberg and Olsson cavitation theory. Besides accounting for a moving cavitation boundary and conservation of mass at the boundary, it also conserves mass within the cavitated region via liquid striations. The mixed nature of the equations (elliptic in the full film zone and nonelliptic in the cavitated zone) coupled with the dynamic aspects of the problem create interesting difficulties for the present solution approach. Emphasis is placed on the methods found to eliminate solution instabilities. Excellent results are obtained for both accuracy and reduction of computational time.

A STRICTLY CONTRACTIVE PEACEMAN–RACHFORD SPLITTING METHOD FOR CONVEX PROGRAMMING

PubMed Central

BINGSHENG, HE; LIU, HAN; WANG, ZHAORAN; YUAN, XIAOMING

2014-01-01

In this paper, we focus on the application of the Peaceman–Rachford splitting method (PRSM) to a convex minimization model with linear constraints and a separable objective function. Compared to the Douglas–Rachford splitting method (DRSM), another splitting method from which the alternating direction method of multipliers originates, PRSM requires more restrictive assumptions to ensure its convergence, while it is always faster whenever it is convergent. We first illustrate that the reason for this difference is that the iterative sequence generated by DRSM is strictly contractive, while that generated by PRSM is only contractive with respect to the solution set of the model. With only the convexity assumption on the objective function of the model under consideration, the convergence of PRSM is not guaranteed. But for this case, we show that the first t iterations of PRSM still enable us to find an approximate solution with an accuracy of O(1/t). A worst-case O(1/t) convergence rate of PRSM in the ergodic sense is thus established under mild assumptions. After that, we suggest attaching an underdetermined relaxation factor with PRSM to guarantee the strict contraction of its iterative sequence and thus propose a strictly contractive PRSM. A worst-case O(1/t) convergence rate of this strictly contractive PRSM in a nonergodic sense is established. We show the numerical efficiency of the strictly contractive PRSM by some applications in statistical learning and image processing. PMID:25620862

Physics and engineering studies on the MITICA accelerator: comparison among possible design solutions

NASA Astrophysics Data System (ADS)

Agostinetti, P.; Antoni, V.; Cavenago, M.; Chitarin, G.; Pilan, N.; Marcuzzi, D.; Serianni, G.; Veltri, P.

2011-09-01

Consorzio RFX in Padova is currently using a comprehensive set of numerical and analytical codes, for the physics and engineering design of the SPIDER (Source for Production of Ion of Deuterium Extracted from RF plasma) and MITICA (Megavolt ITER Injector Concept Advancement) experiments, planned to be built at Consorzio RFX. This paper presents a set of studies on different possible geometries for the MITICA accelerator, with the objective to compare different design concepts and choose the most suitable one (or ones) to be further developed and possibly adopted in the experiment. Different design solutions have been discussed and compared, taking into account their advantages and drawbacks by both the physics and engineering points of view.

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.

On the wing behaviour of the overtones of self-localized modes

NASA Astrophysics Data System (ADS)

Dusi, R.; Wagner, M.

1998-08-01

In this paper the solutions for self-localized modes in a nonlinear chain are investigated. We present a converging iteration procedure, which is based on analytical information of the wings and which takes into account higher overtones of the solitonic oscillations. The accuracy is controlled in a step by step manner by means of a Gaussian error analysis. Our numerical procedure allows for highly accurate solutions, in all anharmonicity regimes, and beyond the rotating-wave approximation (RWA). It is found that the overtone wings change their analytical behaviour at certain critical values of the energy of the self-localized mode: there is a turnover in the exponent of descent. The results are shown for a Fermi-Pasta-Ulam (FPU) chain with quartic anharmonicity.

Implicit Kalman filtering

NASA Technical Reports Server (NTRS)

Skliar, M.; Ramirez, W. F.

1997-01-01

For an implicitly defined discrete system, a new algorithm for Kalman filtering is developed and an efficient numerical implementation scheme is proposed. Unlike the traditional explicit approach, the implicit filter can be readily applied to ill-conditioned systems and allows for generalization to descriptor systems. The implementation of the implicit filter depends on the solution of the congruence matrix equation (A1)(Px)(AT1) = Py. We develop a general iterative method for the solution of this equation, and prove necessary and sufficient conditions for convergence. It is shown that when the system matrices of an implicit system are sparse, the implicit Kalman filter requires significantly less computer time and storage to implement as compared to the traditional explicit Kalman filter. Simulation results are presented to illustrate and substantiate the theoretical developments.

Efficient computation of the Grünwald-Letnikov fractional diffusion derivative using adaptive time step memory

NASA Astrophysics Data System (ADS)

MacDonald, Christopher L.; Bhattacharya, Nirupama; Sprouse, Brian P.; Silva, Gabriel A.

2015-09-01

Computing numerical solutions to fractional differential equations can be computationally intensive due to the effect of non-local derivatives in which all previous time points contribute to the current iteration. In general, numerical approaches that depend on truncating part of the system history while efficient, can suffer from high degrees of error and inaccuracy. Here we present an adaptive time step memory method for smooth functions applied to the Grünwald-Letnikov fractional diffusion derivative. This method is computationally efficient and results in smaller errors during numerical simulations. Sampled points along the system's history at progressively longer intervals are assumed to reflect the values of neighboring time points. By including progressively fewer points backward in time, a temporally 'weighted' history is computed that includes contributions from the entire past of the system, maintaining accuracy, but with fewer points actually calculated, greatly improving computational efficiency.

Numerical study of steady dissipative mixed convection optically-thick micropolar flow with thermal radiation effects

NASA Astrophysics Data System (ADS)

Gupta, Diksha; Kumar, Lokendra; Bég, O. Anwar; Singh, Bani

2017-10-01

The objective of this paper is to study theoretically and numerically the effect of thermal radiation on mixed convection boundary layer flow of a dissipative micropolar non-Newtonian fluid from a continuously moving vertical porous sheet. The governing partial differential equations are transformed into a set of non-linear differential equations by using similarity transformations. These equations are solved iteratively with the Bellman-Kalaba quasi-linearization algorithm. This method converges quadratically and the solution is valid for a large range of parameters. The effects of transpiration (suction or injection) parameter, buoyancy parameter, radiation parameter and Eckert number on velocity, microrotation and temperature functions have been studied. Under a special case comparison of the present numerical results is made with the results available in the literature and an excellent agreement is found. Additionally skin friction and rate of heat transfer have also been computed. The study has applications in polymer processing.

Interpreting the Coulomb-field approximation for generalized-Born electrostatics using boundary-integral equation theory.

PubMed

Bardhan, Jaydeep P

2008-10-14

The importance of molecular electrostatic interactions in aqueous solution has motivated extensive research into physical models and numerical methods for their estimation. The computational costs associated with simulations that include many explicit water molecules have driven the development of implicit-solvent models, with generalized-Born (GB) models among the most popular of these. In this paper, we analyze a boundary-integral equation interpretation for the Coulomb-field approximation (CFA), which plays a central role in most GB models. This interpretation offers new insights into the nature of the CFA, which traditionally has been assessed using only a single point charge in the solute. The boundary-integral interpretation of the CFA allows the use of multiple point charges, or even continuous charge distributions, leading naturally to methods that eliminate the interpolation inaccuracies associated with the Still equation. This approach, which we call boundary-integral-based electrostatic estimation by the CFA (BIBEE/CFA), is most accurate when the molecular charge distribution generates a smooth normal displacement field at the solute-solvent boundary, and CFA-based GB methods perform similarly. Conversely, both methods are least accurate for charge distributions that give rise to rapidly varying or highly localized normal displacement fields. Supporting this analysis are comparisons of the reaction-potential matrices calculated using GB methods and boundary-element-method (BEM) simulations. An approximation similar to BIBEE/CFA exhibits complementary behavior, with superior accuracy for charge distributions that generate rapidly varying normal fields and poorer accuracy for distributions that produce smooth fields. This approximation, BIBEE by preconditioning (BIBEE/P), essentially generates initial guesses for preconditioned Krylov-subspace iterative BEMs. Thus, iterative refinement of the BIBEE/P results recovers the BEM solution; excellent agreement is obtained in only a few iterations. The boundary-integral-equation framework may also provide a means to derive rigorous results explaining how the empirical correction terms in many modern GB models significantly improve accuracy despite their simple analytical forms.

Topology optimization of natural convection: Flow in a differentially heated cavity

NASA Astrophysics Data System (ADS)

Saglietti, Clio; Schlatter, Philipp; Berggren, Martin; Henningson, Dan

2017-11-01

The goal of the present work is to develop methods for optimization of the design of natural convection cooled heat sinks, using resolved simulation of both fluid flow and heat transfer. We rely on mathematical programming techniques combined with direct numerical simulations in order to iteratively update the topology of a solid structure towards optimality, i.e. until the design yielding the best performance is found, while satisfying a specific set of constraints. The investigated test case is a two-dimensional differentially heated cavity, in which the two vertical walls are held at different temperatures. The buoyancy force induces a swirling convective flow around a solid structure, whose topology is optimized to maximize the heat flux through the cavity. We rely on the spectral-element code Nek5000 to compute a high-order accurate solution of the natural convection flow arising from the conjugate heat transfer in the cavity. The laminar, steady-state solution of the problem is evaluated with a time-marching scheme that has an increased convergence rate; the actual iterative optimization is obtained using a steepest-decent algorithm, and the gradients are conveniently computed using the continuous adjoint equations for convective heat transfer.

An iterated local search algorithm for the team orienteering problem with variable profits

NASA Astrophysics Data System (ADS)

Gunawan, Aldy; Ng, Kien Ming; Kendall, Graham; Lai, Junhan

2018-07-01

The orienteering problem (OP) is a routing problem that has numerous applications in various domains such as logistics and tourism. The objective is to determine a subset of vertices to visit for a vehicle so that the total collected score is maximized and a given time budget is not exceeded. The extensive application of the OP has led to many different variants, including the team orienteering problem (TOP) and the team orienteering problem with time windows. The TOP extends the OP by considering multiple vehicles. In this article, the team orienteering problem with variable profits (TOPVP) is studied. The main characteristic of the TOPVP is that the amount of score collected from a visited vertex depends on the duration of stay on that vertex. A mathematical programming model for the TOPVP is first presented and an algorithm based on iterated local search (ILS) that is able to solve modified benchmark instances is then proposed. It is concluded that ILS produces solutions which are comparable to those obtained by the commercial solver CPLEX for smaller instances. For the larger instances, ILS obtains good-quality solutions that have significantly better objective value than those found by CPLEX under reasonable computational times.

Iterative absolute electroanalytical approach to characterization of bulk redox conducting systems.

PubMed

Lewera, Adam; Miecznikowski, Krzysztof; Chojak, Malgorzata; Makowski, Oktawian; Golimowski, Jerzy; Kulesza, Pawel J

2004-05-15

A novel electroanalytical approach is proposed here, and it is demonstrated with the direct and simultaneous determination of two unknowns: the concentration of redox sites and the apparent diffusion coefficient for charge propagation in a single crystal of dodecatungstophosphoric acid. This Keggin-type polyoxometalate serves as a model bulk redox conducting inorganic material for solid-state voltammetry. The system has been investigated using an ultramicrodisk working electrode in the absence of external liquid supporting electrolyte. The analytical method requires numerical solution of the combination of two equations in which the first one describes current (or charge) in a well-defined (either spherical or linear) diffusional regime and the second general equation describes chronoamperometric (or normal pulse voltammetric current) under mixed (linear-spherical) conditions. The iterative approach is based on successive approximations through calculation and minimizing the least-squares error function. The method is fairly universal, and in principle, it can be extended to the investigation of other bulk systems including sol-gel processed materials, redox melts, and solutions on condition that they are electroactive and well behaved, they contain redox centers at sufficiently high level, and a number of electrons for the redox reaction considered is known.

Successive Over-Relaxation Technique for High-Performance Blind Image Deconvolution

DTIC Science & Technology

2015-06-08

deconvolution, space surveillance, Gauss - Seidel iteration 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT SAR 18, NUMBER OF PAGES 5...sensible approximate solutions to the ill-posed nonlinear inverse problem. These solutions are addresses as fixed points of the iteration which consists in...alternating approximations (AA) for the object and for the PSF performed with a prescribed number of inner iterative descents from trivial (zero

Task 7: ADPAC User's Manual

NASA Technical Reports Server (NTRS)

Hall, E. J.; Topp, D. A.; Delaney, R. A.

1996-01-01

The overall objective of this study was to develop a 3-D numerical analysis for compressor casing treatment flowfields. The current version of the computer code resulting from this study is referred to as ADPAC (Advanced Ducted Propfan Analysis Codes-Version 7). This report is intended to serve as a computer program user's manual for the ADPAC code developed under Tasks 6 and 7 of the NASA Contract. The ADPAC program is based on a flexible multiple- block grid discretization scheme permitting coupled 2-D/3-D mesh block solutions with application to a wide variety of geometries. Aerodynamic calculations are based on a four-stage Runge-Kutta time-marching finite volume solution technique with added numerical dissipation. Steady flow predictions are accelerated by a multigrid procedure. An iterative implicit algorithm is available for rapid time-dependent flow calculations, and an advanced two equation turbulence model is incorporated to predict complex turbulent flows. The consolidated code generated during this study is capable of executing in either a serial or parallel computing mode from a single source code. Numerous examples are given in the form of test cases to demonstrate the utility of this approach for predicting the aerodynamics of modem turbomachinery configurations.

Implementation of Preconditioned Dual-Time Procedures in OVERFLOW

NASA Technical Reports Server (NTRS)

Pandya, Shishir A.; Venkateswaran, Sankaran; Pulliam, Thomas H.; Kwak, Dochan (Technical Monitor)

2003-01-01

Preconditioning methods have become the method of choice for the solution of flowfields involving the simultaneous presence of low Mach and transonic regions. It is well known that these methods are important for insuring accurate numerical discretization as well as convergence efficiency over various operating conditions such as low Mach number, low Reynolds number and high Strouhal numbers. For unsteady problems, the preconditioning is introduced within a dual-time framework wherein the physical time-derivatives are used to march the unsteady equations and the preconditioned time-derivatives are used for purposes of numerical discretization and iterative solution. In this paper, we describe the implementation of the preconditioned dual-time methodology in the OVERFLOW code. To demonstrate the performance of the method, we employ both simple and practical unsteady flowfields, including vortex propagation in a low Mach number flow, flowfield of an impulsively started plate (Stokes' first problem) arid a cylindrical jet in a low Mach number crossflow with ground effect. All the results demonstrate that the preconditioning algorithm is responsible for improvements to both numerical accuracy and convergence efficiency and, thereby, enables low Mach number unsteady computations to be performed at a fraction of the cost of traditional time-marching methods.

An innovative hybrid 3D analytic-numerical model for air breathing parallel channel counter-flow PEM fuel cells.

PubMed

Tavčar, Gregor; Katrašnik, Tomaž

2014-01-01

The parallel straight channel PEM fuel cell model presented in this paper extends the innovative hybrid 3D analytic-numerical (HAN) approach previously published by the authors with capabilities to address ternary diffusion systems and counter-flow configurations. The model's core principle is modelling species transport by obtaining a 2D analytic solution for species concentration distribution in the plane perpendicular to the cannel gas-flow and coupling consecutive 2D solutions by means of a 1D numerical pipe-flow model. Electrochemical and other nonlinear phenomena are coupled to the species transport by a routine that uses derivative approximation with prediction-iteration. The latter is also the core of the counter-flow computation algorithm. A HAN model of a laboratory test fuel cell is presented and evaluated against a professional 3D CFD simulation tool showing very good agreement between results of the presented model and those of the CFD simulation. Furthermore, high accuracy results are achieved at moderate computational times, which is owed to the semi-analytic nature and to the efficient computational coupling of electrochemical kinetics and species transport.

Fast generating Greenberger-Horne-Zeilinger state via iterative interaction pictures

NASA Astrophysics Data System (ADS)

Huang, Bi-Hua; Chen, Ye-Hong; Wu, Qi-Cheng; Song, Jie; Xia, Yan

2016-10-01

We delve a little deeper into the construction of shortcuts to adiabatic passage for three-level systems by iterative interaction picture (multiple Schrödinger dynamics). As an application example, we use the deduced iterative based shortcuts to rapidly generate the Greenberger-Horne-Zeilinger (GHZ) state in a three-atom system with the help of quantum Zeno dynamics. Numerical simulation shows the dynamics designed by the iterative picture method is physically feasible and the shortcut scheme performs much better than that using the conventional adiabatic passage techniques. Also, the influences of various decoherence processes are discussed by numerical simulation and the results prove that the scheme is fast and robust against decoherence and operational imperfection.

Hierarchical Solution of the Traveling Salesman Problem with Random Dyadic Tilings

NASA Astrophysics Data System (ADS)

Kalmár-Nagy, Tamás; Bak, Bendegúz Dezső

We propose a hierarchical heuristic approach for solving the Traveling Salesman Problem (TSP) in the unit square. The points are partitioned with a random dyadic tiling and clusters are formed by the points located in the same tile. Each cluster is represented by its geometrical barycenter and a “coarse” TSP solution is calculated for these barycenters. Midpoints are placed at the middle of each edge in the coarse solution. Near-optimal (or optimal) minimum tours are computed for each cluster. The tours are concatenated using the midpoints yielding a solution for the original TSP. The method is tested on random TSPs (independent, identically distributed points in the unit square) up to 10,000 points as well as on a popular benchmark problem (att532 — coordinates of 532 American cities). Our solutions are 8-13% longer than the optimal ones. We also present an optimization algorithm for the partitioning to improve our solutions. This algorithm further reduces the solution errors (by several percent using 1000 iteration steps). The numerical experiments demonstrate the viability of the approach.

R2D2-A Fortran Program for Two-Dimensional Chemically Reacting, Hyperthermal, Internal Flows, Volume II.

DTIC Science & Technology

1980-01-01

is identified in the flow chart simply as "Compute VECT’s ( predictor solution)" and "Compute V’s ( corrector solution)." A significant portion of the...TrintoTo Tm ANDera ionT SToION 28 ITIME :1 PRINCIPAL SUBROUTINES WALLPOINT (ITER,DT) ITER - iteration index for MacCormack Algorithm (ITER=1 for predictor ...WEILERSTEIN, R RAY, 6 MILLER F33615-7- C -3016UNLASSIFIED GASL-TR-254-VBL-2 AFFDL-TR-79-3162-VOL-2 NII III hImllllllllll EIEIIIIIIEIIEE EEIIIIIIIIIIII H

A Multiuser Detector Based on Artificial Bee Colony Algorithm for DS-UWB Systems

PubMed Central

Liu, Xiaohui

2013-01-01

Artificial Bee Colony (ABC) algorithm is an optimization algorithm based on the intelligent behavior of honey bee swarm. The ABC algorithm was developed to solve optimizing numerical problems and revealed premising results in processing time and solution quality. In ABC, a colony of artificial bees search for rich artificial food sources; the optimizing numerical problems are converted to the problem of finding the best parameter which minimizes an objective function. Then, the artificial bees randomly discover a population of initial solutions and then iteratively improve them by employing the behavior: moving towards better solutions by means of a neighbor search mechanism while abandoning poor solutions. In this paper, an efficient multiuser detector based on a suboptimal code mapping multiuser detector and artificial bee colony algorithm (SCM-ABC-MUD) is proposed and implemented in direct-sequence ultra-wideband (DS-UWB) systems under the additive white Gaussian noise (AWGN) channel. The simulation results demonstrate that the BER and the near-far effect resistance performances of this proposed algorithm are quite close to those of the optimum multiuser detector (OMD) while its computational complexity is much lower than that of OMD. Furthermore, the BER performance of SCM-ABC-MUD is not sensitive to the number of active users and can obtain a large system capacity. PMID:23983638

Extended Analytic Device Optimization Employing Asymptotic Expansion

NASA Technical Reports Server (NTRS)

Mackey, Jonathan; Sehirlioglu, Alp; Dynsys, Fred

2013-01-01

Analytic optimization of a thermoelectric junction often introduces several simplifying assumptionsincluding constant material properties, fixed known hot and cold shoe temperatures, and thermallyinsulated leg sides. In fact all of these simplifications will have an effect on device performance,ranging from negligible to significant depending on conditions. Numerical methods, such as FiniteElement Analysis or iterative techniques, are often used to perform more detailed analysis andaccount for these simplifications. While numerical methods may stand as a suitable solution scheme,they are weak in gaining physical understanding and only serve to optimize through iterativesearching techniques. Analytic and asymptotic expansion techniques can be used to solve thegoverning system of thermoelectric differential equations with fewer or less severe assumptionsthan the classic case. Analytic methods can provide meaningful closed form solutions and generatebetter physical understanding of the conditions for when simplifying assumptions may be valid.In obtaining the analytic solutions a set of dimensionless parameters, which characterize allthermoelectric couples, is formulated and provide the limiting cases for validating assumptions.Presentation includes optimization of both classic rectangular couples as well as practically andtheoretically interesting cylindrical couples using optimization parameters physically meaningful toa cylindrical couple. Solutions incorporate the physical behavior for i) thermal resistance of hot andcold shoes, ii) variable material properties with temperature, and iii) lateral heat transfer through legsides.

Evaluation of integration methods for hybrid simulation of complex structural systems through collapse

NASA Astrophysics Data System (ADS)

Del Carpio R., Maikol; Hashemi, M. Javad; Mosqueda, Gilberto

2017-10-01

This study examines the performance of integration methods for hybrid simulation of large and complex structural systems in the context of structural collapse due to seismic excitations. The target application is not necessarily for real-time testing, but rather for models that involve large-scale physical sub-structures and highly nonlinear numerical models. Four case studies are presented and discussed. In the first case study, the accuracy of integration schemes including two widely used methods, namely, modified version of the implicit Newmark with fixed-number of iteration (iterative) and the operator-splitting (non-iterative) is examined through pure numerical simulations. The second case study presents the results of 10 hybrid simulations repeated with the two aforementioned integration methods considering various time steps and fixed-number of iterations for the iterative integration method. The physical sub-structure in these tests consists of a single-degree-of-freedom (SDOF) cantilever column with replaceable steel coupons that provides repeatable highlynonlinear behavior including fracture-type strength and stiffness degradations. In case study three, the implicit Newmark with fixed-number of iterations is applied for hybrid simulations of a 1:2 scale steel moment frame that includes a relatively complex nonlinear numerical substructure. Lastly, a more complex numerical substructure is considered by constructing a nonlinear computational model of a moment frame coupled to a hybrid model of a 1:2 scale steel gravity frame. The last two case studies are conducted on the same porotype structure and the selection of time steps and fixed number of iterations are closely examined in pre-test simulations. The generated unbalance forces is used as an index to track the equilibrium error and predict the accuracy and stability of the simulations.

Iteration with Spreadsheets.

ERIC Educational Resources Information Center

Smith, Michael

1990-01-01

Presents several examples of the iteration method using computer spreadsheets. Examples included are simple iterative sequences and the solution of equations using the Newton-Raphson formula, linear interpolation, and interval bisection. (YP)

Differential geometry based solvation model I: Eulerian formulation

NASA Astrophysics Data System (ADS)

Chen, Zhan; Baker, Nathan A.; Wei, G. W.

2010-11-01

This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the solvation process. Geometric measure theory is employed to rigorously convert a Lagrangian formulation of the surface energy into an Eulerian formulation so as to bring all energy terms into an equal footing. By optimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second-order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to both experimental and theoretical results in the literature.

Differential geometry based solvation model I: Eulerian formulation

PubMed Central

Chen, Zhan; Baker, Nathan A.; Wei, G. W.

2010-01-01

This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the salvation process. Geometric measure theory is employed to rigorously convert a Lagrangian formulation of the surface energy into an Eulerian formulation so as to bring all energy terms into an equal footing. By minimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to both experimental and theoretical results in the literature. PMID:20938489

Numerical Investigation of Hot Gas Ingestion by STOVL Aircraft

NASA Technical Reports Server (NTRS)

Vanka, S. P.

1998-01-01

This report compiles the various research activities conducted under the auspices of the NASA Grant NAG3-1026, "Numerical Investigation of Hot Gas Ingestion by STOVL Aircraft" during the period of April 1989 to April 1994. The effort involved the development of multigrid based algorithms and computer programs for the calculation of the flow and temperature fields generated by Short Take-off and Vertical Landing (STOVL) aircraft, while hovering in ground proximity. Of particular importance has been the interaction of the exhaust jets with the head wind which gives rise to the hot gas ingestion process. The objective of new STOVL designs to reduce the temperature of the gases ingested into the engine. The present work describes a solution algorithm for the multi-dimensional elliptic partial-differential equations governing fluid flow and heat transfer in general curvilinear coordinates. The solution algorithm is based on the multigrid technique which obtains rapid convergence of the iterative numerical procedure for the discrete equations. Initial efforts were concerned with the solution of the Cartesian form of the equations. This algorithm was applied to a simulated STOVL configuration in rectangular coordinates. In the next phase of the work, a computer code for general curvilinear coordinates was constructed. This was applied to model STOVL geometries on curvilinear grids. The code was also validated in model problems. In all these efforts, the standard k-Epsilon model was used.

A Riccati solution for the ideal MHD plasma response with applications to real-time stability control

NASA Astrophysics Data System (ADS)

Glasser, Alexander; Kolemen, Egemen; Glasser, A. H.

2018-03-01

Active feedback control of ideal MHD stability in a tokamak requires rapid plasma stability analysis. Toward this end, we reformulate the δW stability method with a Hamilton-Jacobi theory, elucidating analytical and numerical features of the generic tokamak ideal MHD stability problem. The plasma response matrix is demonstrated to be the solution of an ideal MHD matrix Riccati differential equation. Since Riccati equations are prevalent in the control theory literature, such a shift in perspective brings to bear a range of numerical methods that are well-suited to the robust, fast solution of control problems. We discuss the usefulness of Riccati techniques in solving the stiff ordinary differential equations often encountered in ideal MHD stability analyses—for example, in tokamak edge and stellarator physics. We demonstrate the applicability of such methods to an existing 2D ideal MHD stability code—DCON [A. H. Glasser, Phys. Plasmas 23, 072505 (2016)]—enabling its parallel operation in near real-time, with wall-clock time ≪1 s . Such speed may help enable active feedback ideal MHD stability control, especially in tokamak plasmas whose ideal MHD equilibria evolve with inductive timescale τ≳ 1s—as in ITER.

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.

A new preconditioner update strategy for the solution of sequences of linear systems in structural mechanics: application to saddle point problems in elasticity

NASA Astrophysics Data System (ADS)

Mercier, Sylvain; Gratton, Serge; Tardieu, Nicolas; Vasseur, Xavier

2017-12-01

Many applications in structural mechanics require the numerical solution of sequences of linear systems typically issued from a finite element discretization of the governing equations on fine meshes. The method of Lagrange multipliers is often used to take into account mechanical constraints. The resulting matrices then exhibit a saddle point structure and the iterative solution of such preconditioned linear systems is considered as challenging. A popular strategy is then to combine preconditioning and deflation to yield an efficient method. We propose an alternative that is applicable to the general case and not only to matrices with a saddle point structure. In this approach, we consider to update an existing algebraic or application-based preconditioner, using specific available information exploiting the knowledge of an approximate invariant subspace or of matrix-vector products. The resulting preconditioner has the form of a limited memory quasi-Newton matrix and requires a small number of linearly independent vectors. Numerical experiments performed on three large-scale applications in elasticity highlight the relevance of the new approach. We show that the proposed method outperforms the deflation method when considering sequences of linear systems with varying matrices.

Comparison with CLPX II airborne data using DMRT model

USGS Publications Warehouse

Xu, X.; Liang, D.; Andreadis, K.M.; Tsang, L.; Josberger, E.G.

2009-01-01

In this paper, we considered a physical-based model which use numerical solution of Maxwell Equations in three-dimensional simulations and apply into Dense Media Radiative Theory (DMRT). The model is validated in two specific dataset from the second Cold Land Processes Experiment (CLPX II) at Alaska and Colorado. The data were all obtain by the Ku-band (13.95GHz) observations using airborne imaging polarimetric scatterometer (POLSCAT). Snow is a densely packed media. To take into account the collective scattering and incoherent scattering, analytical Quasi-Crystalline Approximation (QCA) and Numerical Maxwell Equation Method of 3-D simulation (NMM3D) are used to calculate the extinction coefficient and phase matrix. DMRT equations were solved by iterative solution up to 2nd order for the case of small optical thickness and full multiple scattering solution by decomposing the diffuse intensities into Fourier series was used when optical thickness exceed unity. It was shown that the model predictions agree with the field experiment not only co-polarization but also cross-polarization. For Alaska region, the input snow structure data was obtain by the in situ ground observations, while for Colorado region, we combined the VIC model to get the snow profile. ??2009 IEEE.

An efficient and general numerical method to compute steady uniform vortices

NASA Astrophysics Data System (ADS)

Luzzatto-Fegiz, Paolo; Williamson, Charles H. K.

2011-07-01

Steady uniform vortices are widely used to represent high Reynolds number flows, yet their efficient computation still presents some challenges. Existing Newton iteration methods become inefficient as the vortices develop fine-scale features; in addition, these methods cannot, in general, find solutions with specified Casimir invariants. On the other hand, available relaxation approaches are computationally inexpensive, but can fail to converge to a solution. In this paper, we overcome these limitations by introducing a new discretization, based on an inverse-velocity map, which radically increases the efficiency of Newton iteration methods. In addition, we introduce a procedure to prescribe Casimirs and remove the degeneracies in the steady vorticity equation, thus ensuring convergence for general vortex configurations. We illustrate our methodology by considering several unbounded flows involving one or two vortices. Our method enables the computation, for the first time, of steady vortices that do not exhibit any geometric symmetry. In addition, we discover that, as the limiting vortex state for each flow is approached, each family of solutions traces a clockwise spiral in a bifurcation plot consisting of a velocity-impulse diagram. By the recently introduced "IVI diagram" stability approach [Phys. Rev. Lett. 104 (2010) 044504], each turn of this spiral is associated with a loss of stability for the steady flows. Such spiral structure is suggested to be a universal feature of steady, uniform-vorticity flows.

Cubic spline anchored grid pattern algorithm for high-resolution detection of subsurface cavities by the IR-CAT method

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

Kassab, A.J.; Pollard, J.E.

An algorithm is presented for the high-resolution detection of irregular-shaped subsurface cavities within irregular-shaped bodies by the IR-CAT method. The theoretical basis of the algorithm is rooted in the solution of an inverse geometric steady-state heat conduction problem. A Cauchy boundary condition is prescribed at the exposed surface, and the inverse geometric heat conduction problem is formulated by specifying the thermal condition at the inner cavities walls, whose unknown geometries are to be detected. The location of the inner cavities is initially estimated, and the domain boundaries are discretized. Linear boundary elements are used in conjunction with cubic splines formore » high resolution of the cavity walls. An anchored grid pattern (AGP) is established to constrain the cubic spline knots that control the inner cavity geometry to evolve along the AGP at each iterative step. A residual is defined measuring the difference between imposed and computed boundary conditions. A Newton-Raphson method with a Broyden update is used to automate the detection of inner cavity walls. During the iterative procedure, the movement of the inner cavity walls is restricted to physically realistic intermediate solutions. Numerical simulation demonstrates the superior resolution of the cubic spline AGP algorithm over the linear spline-based AGP in the detection of an irregular-shaped cavity. Numerical simulation is also used to test the sensitivity of the linear and cubic spline AGP algorithms by simulating bias and random error in measured surface temperature. The proposed AGP algorithm is shown to satisfactorily detect cavities with these simulated data.« less

Application of matched asymptotic expansions to lunar and interplanetary trajectories. Volume 2: Derivations of second-order asymptotic boundary value solutions

NASA Technical Reports Server (NTRS)

Lancaster, J. E.

1973-01-01

Previously published asymptotic solutions for lunar and interplanetery trajectories have been modified and combined to formulate a general analytical solution to the problem of N-bodies. The earlier first-order solutions, derived by the method of matched asymptotic expansions, have been extended to second order for the purpose of obtaining increased accuracy. The complete derivation of the second-order solution, including the application of a regorous matching principle, is given. It is shown that the outer and inner expansions can be matched in a region of order mu to the alpha power, where 2/5 alpha 1/2, and mu (the moon/earth or planet/sun mass ratio) is much less than one. The second-order asymptotic solution has been used as a basis for formulating a number of analytical two-point boundary value solutions. These include earth-to-moon, one- and two-impulse moon-to-Earth, and interplanetary solutions. Each is presented as an explicit analytical solution which does not require iterative steps to satisfy the boundary conditions. The complete derivation of each solution is shown, as well as instructions for numerical evaluation. For Vol. 1, see N73-27738.

Comparing the basins of attraction for several methods in the circular Sitnikov problem with spheroid primaries

NASA Astrophysics Data System (ADS)

Zotos, Euaggelos E.

2018-06-01

The circular Sitnikov problem, where the two primary bodies are prolate or oblate spheroids, is numerically investigated. In particular, the basins of convergence on the complex plane are revealed by using a large collection of numerical methods of several order. We consider four cases, regarding the value of the oblateness coefficient which determines the nature of the roots (attractors) of the system. For all cases we use the iterative schemes for performing a thorough and systematic classification of the nodes on the complex plane. The distribution of the iterations as well as the probability and their correlations with the corresponding basins of convergence are also discussed. Our numerical computations indicate that most of the iterative schemes provide relatively similar convergence structures on the complex plane. However, there are some numerical methods for which the corresponding basins of attraction are extremely complicated with highly fractal basin boundaries. Moreover, it is proved that the efficiency strongly varies between the numerical methods.

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.

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.

Solution of elliptic PDEs by fast Poisson solvers using a local relaxation factor

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung

1986-01-01

A large class of two- and three-dimensional, nonseparable elliptic partial differential equations (PDEs) is presently solved by means of novel one-step (D'Yakanov-Gunn) and two-step (accelerated one-step) iterative procedures, using a local, discrete Fourier analysis. In addition to being easily implemented and applicable to a variety of boundary conditions, these procedures are found to be computationally efficient on the basis of the results of numerical comparison with other established methods, which lack the present one's: (1) insensitivity to grid cell size and aspect ratio, and (2) ease of convergence rate estimation by means of the coefficient of the PDE being solved. The two-step procedure is numerically demonstrated to outperform the one-step procedure in the case of PDEs with variable coefficients.

Multitrace/singletrace formulations and Domain Decomposition Methods for the solution of Helmholtz transmission problems for bounded composite scatterers

NASA Astrophysics Data System (ADS)

Jerez-Hanckes, Carlos; Pérez-Arancibia, Carlos; Turc, Catalin

2017-12-01

We present Nyström discretizations of multitrace/singletrace formulations and non-overlapping Domain Decomposition Methods (DDM) for the solution of Helmholtz transmission problems for bounded composite scatterers with piecewise constant material properties. We investigate the performance of DDM with both classical Robin and optimized transmission boundary conditions. The optimized transmission boundary conditions incorporate square root Fourier multiplier approximations of Dirichlet to Neumann operators. While the multitrace/singletrace formulations as well as the DDM that use classical Robin transmission conditions are not particularly well suited for Krylov subspace iterative solutions of high-contrast high-frequency Helmholtz transmission problems, we provide ample numerical evidence that DDM with optimized transmission conditions constitute efficient computational alternatives for these type of applications. In the case of large numbers of subdomains with different material properties, we show that the associated DDM linear system can be efficiently solved via hierarchical Schur complements elimination.

On the synchrotron radiation reaction in external magnetic field

NASA Astrophysics Data System (ADS)

Tursunov, Arman; Kološ, Martin

2017-12-01

We study the dynamics of point electric charges undergoing radiation reaction force due to synchrotron radiation in the presence of external uniform magnetic field. The radiation reaction force cannot be neglected in many physical situations and its presence modifies the equations of motion significantly. The exact form of the equation of motion known as the Lorentz-Dirac equation contains higher order Schott term which leads to the appearance of the runaway solutions. We demonstrate effective computational ways to avoid such unphysical solutions and perform numerical integration of the dynamical equations. We show that in the ultrarelativistic case the Schott term is small and does not have considerable effect to the trajectory of a particle. We compare results with the covariant Landau-Lifshitz equation which is the first iteration of the Lorentz-Dirac equation. Even though the Landau-Lifshitz equation is thought to be approximative solution, we show that in realistic scenarios both approaches lead to identical results.

A fully vectorized numerical solution of the incompressible Navier-Stokes equations. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Patel, N.

1983-01-01

A vectorizable algorithm is presented for the implicit finite difference solution of the incompressible Navier-Stokes equations in general curvilinear coordinates. The unsteady Reynolds averaged Navier-Stokes equations solved are in two dimension and non-conservative primitive variable form. A two-layer algebraic eddy viscosity turbulence model is used to incorporate the effects of turbulence. Two momentum equations and a Poisson pressure equation, which is obtained by taking the divergence of the momentum equations and satisfying the continuity equation, are solved simultaneously at each time step. An elliptic grid generation approach is used to generate a boundary conforming coordinate system about an airfoil. The governing equations are expressed in terms of the curvilinear coordinates and are solved on a uniform rectangular computational domain. A checkerboard SOR, which can effectively utilize the computer architectural concept of vector processing, is used for iterative solution of the governing equations.

Zero-sum two-player game theoretic formulation of affine nonlinear discrete-time systems using neural networks.

PubMed

Mehraeen, Shahab; Dierks, Travis; Jagannathan, S; Crow, Mariesa L

2013-12-01

In this paper, the nearly optimal solution for discrete-time (DT) affine nonlinear control systems in the presence of partially unknown internal system dynamics and disturbances is considered. The approach is based on successive approximate solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which appears in optimal control. Successive approximation approach for updating control and disturbance inputs for DT nonlinear affine systems are proposed. Moreover, sufficient conditions for the convergence of the approximate HJI solution to the saddle point are derived, and an iterative approach to approximate the HJI equation using a neural network (NN) is presented. Then, the requirement of full knowledge of the internal dynamics of the nonlinear DT system is relaxed by using a second NN online approximator. The result is a closed-loop optimal NN controller via offline learning. A numerical example is provided illustrating the effectiveness of the approach.

Gain weighted eigenspace assignment

NASA Technical Reports Server (NTRS)

Davidson, John B.; Andrisani, Dominick, II

1994-01-01

This report presents the development of the gain weighted eigenspace assignment methodology. This provides a designer with a systematic methodology for trading off eigenvector placement versus gain magnitudes, while still maintaining desired closed-loop eigenvalue locations. This is accomplished by forming a cost function composed of a scalar measure of error between desired and achievable eigenvectors and a scalar measure of gain magnitude, determining analytical expressions for the gradients, and solving for the optimal solution by numerical iteration. For this development the scalar measure of gain magnitude is chosen to be a weighted sum of the squares of all the individual elements of the feedback gain matrix. An example is presented to demonstrate the method. In this example, solutions yielding achievable eigenvectors close to the desired eigenvectors are obtained with significant reductions in gain magnitude compared to a solution obtained using a previously developed eigenspace (eigenstructure) assignment method.

Statistical mechanics of an ideal active fluid confined in a channel

NASA Astrophysics Data System (ADS)

Wagner, Caleb; Baskaran, Aparna; Hagan, Michael

The statistical mechanics of ideal active Brownian particles (ABPs) confined in a channel is studied by obtaining the exact solution of the steady-state Smoluchowski equation for the 1-particle distribution function. The solution is derived using results from the theory of two-way diffusion equations, combined with an iterative procedure that is justified by numerical results. Using this solution, we quantify the effects of confinement on the spatial and orientational order of the ensemble. Moreover, we rigorously show that both the bulk density and the fraction of particles on the channel walls obey simple scaling relations as a function of channel width. By considering a constant-flux steady state, an effective diffusivity for ABPs is derived which shows signatures of the persistent motion that characterizes ABP trajectories. Finally, we discuss how our techniques generalize to other active models, including systems whose activity is modeled in terms of an Ornstein-Uhlenbeck process.

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

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.

An Iterative Local Updating Ensemble Smoother for Estimation and Uncertainty Assessment of Hydrologic Model Parameters With Multimodal Distributions

NASA Astrophysics Data System (ADS)

Zhang, Jiangjiang; Lin, Guang; Li, Weixuan; Wu, Laosheng; Zeng, Lingzao

2018-03-01

Ensemble smoother (ES) has been widely used in inverse modeling of hydrologic systems. However, for problems where the distribution of model parameters is multimodal, using ES directly would be problematic. One popular solution is to use a clustering algorithm to identify each mode and update the clusters with ES separately. However, this strategy may not be very efficient when the dimension of parameter space is high or the number of modes is large. Alternatively, we propose in this paper a very simple and efficient algorithm, i.e., the iterative local updating ensemble smoother (ILUES), to explore multimodal distributions of model parameters in nonlinear hydrologic systems. The ILUES algorithm works by updating local ensembles of each sample with ES to explore possible multimodal distributions. To achieve satisfactory data matches in nonlinear problems, we adopt an iterative form of ES to assimilate the measurements multiple times. Numerical cases involving nonlinearity and multimodality are tested to illustrate the performance of the proposed method. It is shown that overall the ILUES algorithm can well quantify the parametric uncertainties of complex hydrologic models, no matter whether the multimodal distribution exists.

Multilevel Iterative Methods in Nonlinear Computational Plasma Physics

NASA Astrophysics Data System (ADS)

Knoll, D. A.; Finn, J. M.

1997-11-01

Many applications in computational plasma physics involve the implicit numerical solution of coupled systems of nonlinear partial differential equations or integro-differential equations. Such problems arise in MHD, systems of Vlasov-Fokker-Planck equations, edge plasma fluid equations. We have been developing matrix-free Newton-Krylov algorithms for such problems and have applied these algorithms to the edge plasma fluid equations [1,2] and to the Vlasov-Fokker-Planck equation [3]. Recently we have found that with increasing grid refinement, the number of Krylov iterations required per Newton iteration has grown unmanageable [4]. This has led us to the study of multigrid methods as a means of preconditioning matrix-free Newton-Krylov methods. In this poster we will give details of the general multigrid preconditioned Newton-Krylov algorithm, as well as algorithm performance details on problems of interest in the areas of magnetohydrodynamics and edge plasma physics. Work supported by US DoE 1. Knoll and McHugh, J. Comput. Phys., 116, pg. 281 (1995) 2. Knoll and McHugh, Comput. Phys. Comm., 88, pg. 141 (1995) 3. Mousseau and Knoll, J. Comput. Phys. (1997) (to appear) 4. Knoll and McHugh, SIAM J. Sci. Comput. 19, (1998) (to appear)

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.

Calculation of the angular radiance distribution for a coupled atmosphere and canopy

NASA Technical Reports Server (NTRS)

Liang, Shunlin; Strahler, Alan H.

1993-01-01

The radiative transfer equations for a coupled atmosphere and canopy are solved numerically by an improved Gauss-Seidel iteration algorithm. The radiation field is decomposed into three components: unscattered sunlight, single scattering, and multiple scattering radiance for which the corresponding equations and boundary conditions are set up and their analytical or iterational solutions are explicitly derived. The classic Gauss-Seidel algorithm has been widely applied in atmospheric research. This is its first application for calculating the multiple scattering radiance of a coupled atmosphere and canopy. This algorithm enables us to obtain the internal radiation field as well as radiances at boundaries. Any form of bidirectional reflectance distribution function (BRDF) as a boundary condition can be easily incorporated into the iteration procedure. The hotspot effect of the canopy is accommodated by means of the modification of the extinction coefficients of upward single scattering radiation and unscattered sunlight using the formulation of Nilson and Kuusk. To reduce the computation for the case of large optical thickness, an improved iteration formula is derived to speed convergence. The upwelling radiances have been evaluated for different atmospheric conditions, leaf area index (LAI), leaf angle distribution (LAD), leaf size and so on. The formulation presented in this paper is also well suited to analyze the relative magnitude of multiple scattering radiance and single scattering radiance in both the visible and near infrared regions.

Development of solute transport models in YMPYRÄ framework to simulate solute migration in military shooting and training areas

NASA Astrophysics Data System (ADS)

Warsta, L.; Karvonen, T.

2017-12-01

There are currently 25 shooting and training areas in Finland managed by The Finnish Defence Forces (FDF), where military activities can cause contamination of open waters and groundwater reservoirs. In the YMPYRÄ project, a computer software framework is being developed that combines existing open environmental data and proprietary information collected by FDF with computational models to investigate current and prevent future environmental problems. A data centric philosophy is followed in the development of the system, i.e. the models are updated and extended to handle available data from different areas. The results generated by the models are summarized as easily understandable flow and risk maps that can be opened in GIS programs and used in environmental assessments by experts. Substances investigated with the system include explosives and metals such as lead, and both surface and groundwater dominated areas can be simulated. The YMPYRÄ framework is composed of a three dimensional soil and groundwater flow model, several solute transport models and an uncertainty assessment system. Solute transport models in the framework include particle based, stream tube and finite volume based approaches. The models can be used to simulate solute dissolution from source area, transport in the unsaturated layers to groundwater and finally migration in groundwater to water extraction wells and springs. The models can be used to simulate advection, dispersion, equilibrium adsorption on soil particles, solubility and dissolution from solute phase and dendritic solute decay chains. Correct numerical solutions were confirmed by comparing results to analytical 1D and 2D solutions and by comparing the numerical solutions to each other. The particle based and stream tube type solute transport models were useful as they could complement the traditional finite volume based approach which in certain circumstances produced numerical dispersion due to piecewise solution of the governing equations in computational grids and included computationally intensive and in some cases unstable iterative solutions. The YMPYRÄ framework is being developed by WaterHope, Gain Oy, and SITO Oy consulting companies and funded by FDF.

On the solution of evolution equations based on multigrid and explicit iterative methods

NASA Astrophysics Data System (ADS)

Zhukov, V. T.; Novikova, N. D.; Feodoritova, O. B.

2015-08-01

Two schemes for solving initial-boundary value problems for three-dimensional parabolic equations are studied. One is implicit and is solved using the multigrid method, while the other is explicit iterative and is based on optimal properties of the Chebyshev polynomials. In the explicit iterative scheme, the number of iteration steps and the iteration parameters are chosen as based on the approximation and stability conditions, rather than on the optimization of iteration convergence to the solution of the implicit scheme. The features of the multigrid scheme include the implementation of the intergrid transfer operators for the case of discontinuous coefficients in the equation and the adaptation of the smoothing procedure to the spectrum of the difference operators. The results produced by these schemes as applied to model problems with anisotropic discontinuous coefficients are compared.

The solution of the Elrod algorithm for a dynamically loaded journal bearing using multigrid techniques

NASA Technical Reports Server (NTRS)

Woods, Claudia M.; Brewe, David E.

1988-01-01

A numerical solution to a theoretical model of vapor cavitation in a dynamically loaded journal bearing is developed utilizing a multigrid iteration technique. The method is compared with a noniterative approach in terms of computational time and accuracy. The computational model is based on the Elrod algorithm, a control volume approach to the Reynolds equation which mimics the Jakobsson-Floberg and Olsson cavitation theory. Besides accounting for a moving cavitation boundary and conservation of mass at the boundary, it also conserves mass within the cavitated region via a smeared mass or striated flow extending to both surfaces in the film gap. The mixed nature of the equations (parabolic in the full film zone and hyperbolic in the cavitated zone) coupled with the dynamic aspects of the problem create interesting difficulties for the present solution approach. Emphasis is placed on the methods found to eliminate solution instabilities. Excellent results are obtained for both accuracy and reduction of computational time.

The solution of the Elrod algorithm for a dynamically loaded journal bearing using multigrid techniques

NASA Technical Reports Server (NTRS)

Woods, C. M.; Brewe, D. E.

1989-01-01

A numerical solution to a theoretical model of vapor cavitation in a dynamically loaded journal bearing is developed utilizing a multigrid iteration technique. The method is compared with a noniterative approach in terms of computational time and accuracy. The computational model is based on the Elrod algorithm, a control volume approach to the Reynolds equation which mimics the Jakobsson-Floberg and Olsson cavitation theory. Besides accounting for a moving cavitation boundary and conservation of mass at the boundary, it also conserves mass within the cavitated region via a smeared mass or striated flow extending to both surfaces in the film gap. The mixed nature of the equations (parabolic in the full film zone and hyperbolic in the cavitated zone) coupled with the dynamic aspects of the problem create interesting difficulties for the present solution approach. Emphasis is placed on the methods found to eliminate solution instabilities. Excellent results are obtained for both accuracy and reduction of computational time.

Function-Space-Based Solution Scheme for the Size-Modified Poisson-Boltzmann Equation in Full-Potential DFT.

PubMed

Ringe, Stefan; Oberhofer, Harald; Hille, Christoph; Matera, Sebastian; Reuter, Karsten

2016-08-09

The size-modified Poisson-Boltzmann (MPB) equation is an efficient implicit solvation model which also captures electrolytic solvent effects. It combines an account of the dielectric solvent response with a mean-field description of solvated finite-sized ions. We present a general solution scheme for the MPB equation based on a fast function-space-oriented Newton method and a Green's function preconditioned iterative linear solver. In contrast to popular multigrid solvers, this approach allows us to fully exploit specialized integration grids and optimized integration schemes. We describe a corresponding numerically efficient implementation for the full-potential density-functional theory (DFT) code FHI-aims. We show that together with an additional Stern layer correction the DFT+MPB approach can describe the mean activity coefficient of a KCl aqueous solution over a wide range of concentrations. The high sensitivity of the calculated activity coefficient on the employed ionic parameters thereby suggests to use extensively tabulated experimental activity coefficients of salt solutions for a systematic parametrization protocol.

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.

Comparative study of beam losses and heat loads reduction methods in MITICA beam source

NASA Astrophysics Data System (ADS)

Sartori, E.; Agostinetti, P.; Dal Bello, S.; Marcuzzi, D.; Serianni, G.; Sonato, P.; Veltri, P.

2014-02-01

In negative ion electrostatic accelerators a considerable fraction of extracted ions is lost by collision processes causing efficiency loss and heat deposition over the components. Stripping is proportional to the local density of gas, which is steadily injected in the plasma source; its pumping from the extraction and acceleration stages is a key functionality for the prototype of the ITER Neutral Beam Injector, and it can be simulated with the 3D code AVOCADO. Different geometric solutions were tested aiming at the reduction of the gas density. The parameter space considered is limited by constraints given by optics, aiming, voltage holding, beam uniformity, and mechanical feasibility. The guidelines of the optimization process are presented together with the proposed solutions and the results of numerical simulations.

Genetic algorithms for the vehicle routing problem

NASA Astrophysics Data System (ADS)

Volna, Eva

2016-06-01

The Vehicle Routing Problem (VRP) is one of the most challenging combinatorial optimization tasks. This problem consists in designing the optimal set of routes for fleet of vehicles in order to serve a given set of customers. Evolutionary algorithms are general iterative algorithms for combinatorial optimization. These algorithms have been found to be very effective and robust in solving numerous problems from a wide range of application domains. This problem is known to be NP-hard; hence many heuristic procedures for its solution have been suggested. For such problems it is often desirable to obtain approximate solutions, so they can be found fast enough and are sufficiently accurate for the purpose. In this paper we have performed an experimental study that indicates the suitable use of genetic algorithms for the vehicle routing problem.

Continuation of probability density functions using a generalized Lyapunov approach

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

Baars, S., E-mail: s.baars@rug.nl; Viebahn, J.P., E-mail: viebahn@cwi.nl; Mulder, T.E., E-mail: t.e.mulder@uu.nl

Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational methodology to use parameter continuation in determining probability density functions of systems of stochastic partial differential equations near fixed points, under a small noise approximation. Key innovation is the efficient solution of a generalized Lyapunov equation using an iterative method involving low-rank approximations. We apply and illustrate the capabilities of the method using a problem in physical oceanography, i.e. the occurrence of multiple steady states of the Atlantic Ocean circulation.

A constitutive material model for nonlinear finite element structural analysis using an iterative matrix approach

NASA Technical Reports Server (NTRS)

Koenig, Herbert A.; Chan, Kwai S.; Cassenti, Brice N.; Weber, Richard

1988-01-01

A unified numerical method for the integration of stiff time dependent constitutive equations is presented. The solution process is directly applied to a constitutive model proposed by Bodner. The theory confronts time dependent inelastic behavior coupled with both isotropic hardening and directional hardening behaviors. Predicted stress-strain responses from this model are compared to experimental data from cyclic tests on uniaxial specimens. An algorithm is developed for the efficient integration of the Bodner flow equation. A comparison is made with the Euler integration method. An analysis of computational time is presented for the three algorithms.

Explicitly computing geodetic coordinates from Cartesian coordinates

NASA Astrophysics Data System (ADS)

Zeng, Huaien

2013-04-01

This paper presents a new form of quartic equation based on Lagrange's extremum law and a Groebner basis under the constraint that the geodetic height is the shortest distance between a given point and the reference ellipsoid. A very explicit and concise formulae of the quartic equation by Ferrari's line is found, which avoids the need of a good starting guess for iterative methods. A new explicit algorithm is then proposed to compute geodetic coordinates from Cartesian coordinates. The convergence region of the algorithm is investigated and the corresponding correct solution is given. Lastly, the algorithm is validated with numerical experiments.

Self-consistent collective coordinate for reaction path and inertial mass

NASA Astrophysics Data System (ADS)

Wen, Kai; Nakatsukasa, Takashi

2016-11-01

We propose a numerical method to determine the optimal collective reaction path for a nucleus-nucleus collision, based on the adiabatic self-consistent collective coordinate (ASCC) method. We use an iterative method, combining the imaginary-time evolution and the finite amplitude method, for the solution of the ASCC coupled equations. It is applied to the simplest case, α -α scattering. We determine the collective path, the potential, and the inertial mass. The results are compared with other methods, such as the constrained Hartree-Fock method, Inglis's cranking formula, and the adiabatic time-dependent Hartree-Fock (ATDHF) method.

Generation of complementary sampled phase-only holograms.

PubMed

Tsang, P W M; Chow, Y T; Poon, T-C

2016-10-03

If an image is uniformly down-sampled into a sparse form and converted into a hologram, the phase component alone will be adequate to reconstruct the image. However, the appearance of the reconstructed image is degraded with numerous empty holes. In this paper, we present a low complexity and non-iterative solution to this problem. Briefly, two phase-only holograms are generated for an image, each based on a different down-sampling lattice. Subsequently, the holograms are displayed alternately at high frame rate. The reconstructed images of the 2 holograms will appear to be a single, densely sampled image with enhance visual quality.

Energy: Economic activity and energy demand; link to energy flow. Example: France

NASA Astrophysics Data System (ADS)

1980-10-01

The data derived from the EXPLOR and EPOM, Energy Flow Optimization Model are described. The core of the EXPLOR model is a circular system of relations involving consumer's demand, producer's outputs, and market prices. The solution of this system of relations is obtained by successive iterations; the final output is a coherent system of economic accounts. The computer program for this transition is described. The work conducted by comparing different energy demand models is summarized. The procedure is illustrated by a numerical projection to 1980 and 1985 using the existing version of the EXPLOR France model.

Efficiency Analysis of the Parallel Implementation of the SIMPLE Algorithm on Multiprocessor Computers

NASA Astrophysics Data System (ADS)

Lashkin, S. V.; Kozelkov, A. S.; Yalozo, A. V.; Gerasimov, V. Yu.; Zelensky, D. K.

2017-12-01

This paper describes the details of the parallel implementation of the SIMPLE algorithm for numerical solution of the Navier-Stokes system of equations on arbitrary unstructured grids. The iteration schemes for the serial and parallel versions of the SIMPLE algorithm are implemented. In the description of the parallel implementation, special attention is paid to computational data exchange among processors under the condition of the grid model decomposition using fictitious cells. We discuss the specific features for the storage of distributed matrices and implementation of vector-matrix operations in parallel mode. It is shown that the proposed way of matrix storage reduces the number of interprocessor exchanges. A series of numerical experiments illustrates the effect of the multigrid SLAE solver tuning on the general efficiency of the algorithm; the tuning involves the types of the cycles used (V, W, and F), the number of iterations of a smoothing operator, and the number of cells for coarsening. Two ways (direct and indirect) of efficiency evaluation for parallelization of the numerical algorithm are demonstrated. The paper presents the results of solving some internal and external flow problems with the evaluation of parallelization efficiency by two algorithms. It is shown that the proposed parallel implementation enables efficient computations for the problems on a thousand processors. Based on the results obtained, some general recommendations are made for the optimal tuning of the multigrid solver, as well as for selecting the optimal number of cells per processor.

Derivative free Davidon-Fletcher-Powell (DFP) for solving symmetric systems of nonlinear equations

NASA Astrophysics Data System (ADS)

Mamat, M.; Dauda, M. K.; Mohamed, M. A. bin; Waziri, M. Y.; Mohamad, F. S.; Abdullah, H.

2018-03-01

Research from the work of engineers, economist, modelling, industry, computing, and scientist are mostly nonlinear equations in nature. Numerical solution to such systems is widely applied in those areas of mathematics. Over the years, there has been significant theoretical study to develop methods for solving such systems, despite these efforts, unfortunately the methods developed do have deficiency. In a contribution to solve systems of the form F(x) = 0, x ∈ Rn , a derivative free method via the classical Davidon-Fletcher-Powell (DFP) update is presented. This is achieved by simply approximating the inverse Hessian matrix with {Q}k+1-1 to θkI. The modified method satisfied the descent condition and possess local superlinear convergence properties. Interestingly, without computing any derivative, the proposed method never fail to converge throughout the numerical experiments. The output is based on number of iterations and CPU time, different initial starting points were used on a solve 40 benchmark test problems. With the aid of the squared norm merit function and derivative-free line search technique, the approach yield a method of solving symmetric systems of nonlinear equations that is capable of significantly reducing the CPU time and number of iteration, as compared to its counterparts. A comparison between the proposed method and classical DFP update were made and found that the proposed methodis the top performer and outperformed the existing method in almost all the cases. In terms of number of iterations, out of the 40 problems solved, the proposed method solved 38 successfully, (95%) while classical DFP solved 2 problems (i.e. 05%). In terms of CPU time, the proposed method solved 29 out of the 40 problems given, (i.e.72.5%) successfully whereas classical DFP solves 11 (27.5%). The method is valid in terms of derivation, reliable in terms of number of iterations and accurate in terms of CPU time. Thus, suitable and achived the objective.

An asymptotic-preserving Lagrangian algorithm for the time-dependent anisotropic heat transport equation

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

Chacon, Luis; del-Castillo-Negrete, Diego; Hauck, Cory D.

2014-09-01

We propose a Lagrangian numerical algorithm for a time-dependent, anisotropic temperature transport equation in magnetized plasmas in the large guide field regime. The approach is based on an analytical integral formal solution of the parallel (i.e., along the magnetic field) transport equation with sources, and it is able to accommodate both local and non-local parallel heat flux closures. The numerical implementation is based on an operator-split formulation, with two straightforward steps: a perpendicular transport step (including sources), and a Lagrangian (field-line integral) parallel transport step. Algorithmically, the first step is amenable to the use of modern iterative methods, while themore » second step has a fixed cost per degree of freedom (and is therefore scalable). Accuracy-wise, the approach is free from the numerical pollution introduced by the discrete parallel transport term when the perpendicular to parallel transport coefficient ratio X ⊥ /X ∥ becomes arbitrarily small, and is shown to capture the correct limiting solution when ε = X⊥L 2 ∥/X1L 2 ⊥ → 0 (with L∥∙ L⊥ , the parallel and perpendicular diffusion length scales, respectively). Therefore, the approach is asymptotic-preserving. We demonstrate the capabilities of the scheme with several numerical experiments with varying magnetic field complexity in two dimensions, including the case of transport across a magnetic island.« less

A SEMI-LAGRANGIAN TWO-LEVEL PRECONDITIONED NEWTON-KRYLOV SOLVER FOR CONSTRAINED DIFFEOMORPHIC IMAGE REGISTRATION.

PubMed

Mang, Andreas; Biros, George

2017-01-01

We propose an efficient numerical algorithm for the solution of diffeomorphic image registration problems. We use a variational formulation constrained by a partial differential equation (PDE), where the constraints are a scalar transport equation. We use a pseudospectral discretization in space and second-order accurate semi-Lagrangian time stepping scheme for the transport equations. We solve for a stationary velocity field using a preconditioned, globalized, matrix-free Newton-Krylov scheme. We propose and test a two-level Hessian preconditioner. We consider two strategies for inverting the preconditioner on the coarse grid: a nested preconditioned conjugate gradient method (exact solve) and a nested Chebyshev iterative method (inexact solve) with a fixed number of iterations. We test the performance of our solver in different synthetic and real-world two-dimensional application scenarios. We study grid convergence and computational efficiency of our new scheme. We compare the performance of our solver against our initial implementation that uses the same spatial discretization but a standard, explicit, second-order Runge-Kutta scheme for the numerical time integration of the transport equations and a single-level preconditioner. Our improved scheme delivers significant speedups over our original implementation. As a highlight, we observe a 20 × speedup for a two dimensional, real world multi-subject medical image registration problem.

Accelerating the weighted histogram analysis method by direct inversion in the iterative subspace.

PubMed

Zhang, Cheng; Lai, Chun-Liang; Pettitt, B Montgomery

The weighted histogram analysis method (WHAM) for free energy calculations is a valuable tool to produce free energy differences with the minimal errors. Given multiple simulations, WHAM obtains from the distribution overlaps the optimal statistical estimator of the density of states, from which the free energy differences can be computed. The WHAM equations are often solved by an iterative procedure. In this work, we use a well-known linear algebra algorithm which allows for more rapid convergence to the solution. We find that the computational complexity of the iterative solution to WHAM and the closely-related multiple Bennett acceptance ratio (MBAR) method can be improved by using the method of direct inversion in the iterative subspace. We give examples from a lattice model, a simple liquid and an aqueous protein solution.

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

Jo, J.C.; Shin, W.K.; Choi, C.Y.

Transient heat transfer problems with phase changes (Stefan problems) occur in many engineering situations, including potential core melting and solidification during pressurized-water-reactor severe accidents, ablation of thermal shields, melting and solidification of alloys, and many others. This article addresses the numerical analysis of nonlinear transient heat transfer with melting or solidification. An effective and simple procedure is presented for the simulation of the motion of the boundary and the transient temperature field during the phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual-reciprocity boundary-element method. The dual-reciprocity boundary-element approach providedmore » in this article is much simpler than the usual boundary-element method in applying a reciprocity principle and an available technique for dealing with the domain integral of the boundary element formulation simultaneously. In this article, attention is focused on two-dimensional melting (ablation)/solidification problems for simplicity. The accuracy and effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of some examples of one-phase ablation/solidification problems with their known semianalytical or numerical solutions where available.« less

Efficient solution of the simplified P N equations

DOE PAGES

Hamilton, Steven P.; Evans, Thomas M.

2014-12-23

We show new solver strategies for the multigroup SPN equations for nuclear reactor analysis. By forming the complete matrix over space, moments, and energy a robust set of solution strategies may be applied. Moreover, power iteration, shifted power iteration, Rayleigh quotient iteration, Arnoldi's method, and a generalized Davidson method, each using algebraic and physics-based multigrid preconditioners, have been compared on C5G7 MOX test problem as well as an operational PWR model. These results show that the most ecient approach is the generalized Davidson method, that is 30-40 times faster than traditional power iteration and 6-10 times faster than Arnoldi's method.

Locally expansive solutions for a class of iterative equations.

PubMed

Song, Wei; Chen, Sheng

2013-01-01

Iterative equations which can be expressed by the following form f (n) (x) = H(x, f(x), f (2)(x),…, f (n-1)(x)), where n ≥ 2, are investigated. Conditions for the existence of locally expansive C (1) solutions for such equations are given.

Nonlinear and parallel algorithms for finite element discretizations of the incompressible Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Arteaga, Santiago Egido

1998-12-01

The steady-state Navier-Stokes equations are of considerable interest because they are used to model numerous common physical phenomena. The applications encountered in practice often involve small viscosities and complicated domain geometries, and they result in challenging problems in spite of the vast attention that has been dedicated to them. In this thesis we examine methods for computing the numerical solution of the primitive variable formulation of the incompressible equations on distributed memory parallel computers. We use the Galerkin method to discretize the differential equations, although most results are stated so that they apply also to stabilized methods. We also reformulate some classical results in a single framework and discuss some issues frequently dismissed in the literature, such as the implementation of pressure space basis and non- homogeneous boundary values. We consider three nonlinear methods: Newton's method, Oseen's (or Picard) iteration, and sequences of Stokes problems. All these iterative nonlinear methods require solving a linear system at every step. Newton's method has quadratic convergence while that of the others is only linear; however, we obtain theoretical bounds showing that Oseen's iteration is more robust, and we confirm it experimentally. In addition, although Oseen's iteration usually requires more iterations than Newton's method, the linear systems it generates tend to be simpler and its overall costs (in CPU time) are lower. The Stokes problems result in linear systems which are easier to solve, but its convergence is much slower, so that it is competitive only for large viscosities. Inexact versions of these methods are studied, and we explain why the best timings are obtained using relatively modest error tolerances in solving the corresponding linear systems. We also present a new damping optimization strategy based on the quadratic nature of the Navier-Stokes equations, which improves the robustness of all the linearization strategies considered and whose computational cost is negligible. The algebraic properties of these systems depend on both the discretization and nonlinear method used. We study in detail the positive definiteness and skewsymmetry of the advection submatrices (essentially, convection-diffusion problems). We propose a discretization based on a new trilinear form for Newton's method. We solve the linear systems using three Krylov subspace methods, GMRES, QMR and TFQMR, and compare the advantages of each. Our emphasis is on parallel algorithms, and so we consider preconditioners suitable for parallel computers such as line variants of the Jacobi and Gauss- Seidel methods, alternating direction implicit methods, and Chebyshev and least squares polynomial preconditioners. These work well for moderate viscosities (moderate Reynolds number). For small viscosities we show that effective parallel solution of the advection subproblem is a critical factor to improve performance. Implementation details on a CM-5 are presented.

Parabolized Navier-Stokes Code for Computing Magneto-Hydrodynamic Flowfields

NASA Technical Reports Server (NTRS)

Mehta, Unmeel B. (Technical Monitor); Tannehill, J. C.

2003-01-01

This report consists of two published papers, 'Computation of Magnetohydrodynamic Flows Using an Iterative PNS Algorithm' and 'Numerical Simulation of Turbulent MHD Flows Using an Iterative PNS Algorithm'.

Sequential-Optimization-Based Framework for Robust Modeling and Design of Heterogeneous Catalytic Systems

DOE PAGES

Rangarajan, Srinivas; Maravelias, Christos T.; Mavrikakis, Manos

2017-11-09

Here, we present a general optimization-based framework for (i) ab initio and experimental data driven mechanistic modeling and (ii) optimal catalyst design of heterogeneous catalytic systems. Both cases are formulated as a nonlinear optimization problem that is subject to a mean-field microkinetic model and thermodynamic consistency requirements as constraints, for which we seek sparse solutions through a ridge (L 2 regularization) penalty. The solution procedure involves an iterative sequence of forward simulation of the differential algebraic equations pertaining to the microkinetic model using a numerical tool capable of handling stiff systems, sensitivity calculations using linear algebra, and gradient-based nonlinear optimization.more » A multistart approach is used to explore the solution space, and a hierarchical clustering procedure is implemented for statistically classifying potentially competing solutions. An example of methanol synthesis through hydrogenation of CO and CO 2 on a Cu-based catalyst is used to illustrate the framework. The framework is fast, is robust, and can be used to comprehensively explore the model solution and design space of any heterogeneous catalytic system.« less

Sequential-Optimization-Based Framework for Robust Modeling and Design of Heterogeneous Catalytic Systems

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

Rangarajan, Srinivas; Maravelias, Christos T.; Mavrikakis, Manos

Here, we present a general optimization-based framework for (i) ab initio and experimental data driven mechanistic modeling and (ii) optimal catalyst design of heterogeneous catalytic systems. Both cases are formulated as a nonlinear optimization problem that is subject to a mean-field microkinetic model and thermodynamic consistency requirements as constraints, for which we seek sparse solutions through a ridge (L 2 regularization) penalty. The solution procedure involves an iterative sequence of forward simulation of the differential algebraic equations pertaining to the microkinetic model using a numerical tool capable of handling stiff systems, sensitivity calculations using linear algebra, and gradient-based nonlinear optimization.more » A multistart approach is used to explore the solution space, and a hierarchical clustering procedure is implemented for statistically classifying potentially competing solutions. An example of methanol synthesis through hydrogenation of CO and CO 2 on a Cu-based catalyst is used to illustrate the framework. The framework is fast, is robust, and can be used to comprehensively explore the model solution and design space of any heterogeneous catalytic system.« less

Solution of the three-dimensional Helmholtz equation with nonlocal boundary conditions

NASA Technical Reports Server (NTRS)

Hodge, Steve L.; Zorumski, William E.; Watson, Willie R.

1995-01-01

The Helmholtz equation is solved within a three-dimensional rectangular duct with a nonlocal radiation boundary condition at the duct exit plane. This condition accurately models the acoustic admittance at an arbitrarily-located computational boundary plane. A linear system of equations is constructed with second-order central differences for the Helmholtz operator and second-order backward differences for both local admittance conditions and the gradient term in the nonlocal radiation boundary condition. The resulting matrix equation is large, sparse, and non-Hermitian. The size and structure of the matrix makes direct solution techniques impractical; as a result, a nonstationary iterative technique is used for its solution. The theory behind the nonstationary technique is reviewed, and numerical results are presented for radiation from both a point source and a planar acoustic source. The solutions with the nonlocal boundary conditions are invariant to the location of the computational boundary, and the same nonlocal conditions are valid for all solutions. The nonlocal conditions thus provide a means of minimizing the size of three-dimensional computational domains.

Novel aspects of plasma control in ITER

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

Humphreys, D.; Jackson, G.; Walker, M.

2015-02-15

ITER plasma control design solutions and performance requirements are strongly driven by its nuclear mission, aggressive commissioning constraints, and limited number of operational discharges. In addition, high plasma energy content, heat fluxes, neutron fluxes, and very long pulse operation place novel demands on control performance in many areas ranging from plasma boundary and divertor regulation to plasma kinetics and stability control. Both commissioning and experimental operations schedules provide limited time for tuning of control algorithms relative to operating devices. Although many aspects of the control solutions required by ITER have been well-demonstrated in present devices and even designed satisfactorily formore » ITER application, many elements unique to ITER including various crucial integration issues are presently under development. We describe selected novel aspects of plasma control in ITER, identifying unique parts of the control problem and highlighting some key areas of research remaining. Novel control areas described include control physics understanding (e.g., current profile regulation, tearing mode (TM) suppression), control mathematics (e.g., algorithmic and simulation approaches to high confidence robust performance), and integration solutions (e.g., methods for management of highly subscribed control resources). We identify unique aspects of the ITER TM suppression scheme, which will pulse gyrotrons to drive current within a magnetic island, and turn the drive off following suppression in order to minimize use of auxiliary power and maximize fusion gain. The potential role of active current profile control and approaches to design in ITER are discussed. Issues and approaches to fault handling algorithms are described, along with novel aspects of actuator sharing in ITER.« less

Novel aspects of plasma control in ITER

DOE PAGES

Humphreys, David; Ambrosino, G.; de Vries, Peter; ...

2015-02-12

ITER plasma control design solutions and performance requirements are strongly driven by its nuclear mission, aggressive commissioning constraints, and limited number of operational discharges. In addition, high plasma energy content, heat fluxes, neutron fluxes, and very long pulse operation place novel demands on control performance in many areas ranging from plasma boundary and divertor regulation to plasma kinetics and stability control. Both commissioning and experimental operations schedules provide limited time for tuning of control algorithms relative to operating devices. Although many aspects of the control solutions required by ITER have been well-demonstrated in present devices and even designed satisfactorily formore » ITER application, many elements unique to ITER including various crucial integration issues are presently under development. We describe selected novel aspects of plasma control in ITER, identifying unique parts of the control problem and highlighting some key areas of research remaining. Novel control areas described include control physics understanding (e.g. current profile regulation, tearing mode suppression (TM)), control mathematics (e.g. algorithmic and simulation approaches to high confidence robust performance), and integration solutions (e.g. methods for management of highly-subscribed control resources). We identify unique aspects of the ITER TM suppression scheme, which will pulse gyrotrons to drive current within a magnetic island, and turn the drive off following suppression in order to minimize use of auxiliary power and maximize fusion gain. The potential role of active current profile control and approaches to design in ITER are discussed. Finally, issues and approaches to fault handling algorithms are described, along with novel aspects of actuator sharing in ITER.« less

WATSFAR: numerical simulation of soil WATer and Solute fluxes using a FAst and Robust method

NASA Astrophysics Data System (ADS)

Crevoisier, David; Voltz, Marc

2013-04-01

To simulate the evolution of hydro- and agro-systems, numerous spatialised models are based on a multi-local approach and improvement of simulation accuracy by data-assimilation techniques are now used in many application field. The latest acquisition techniques provide a large amount of experimental data, which increase the efficiency of parameters estimation and inverse modelling approaches. In turn simulations are often run on large temporal and spatial domains which requires a large number of model runs. Eventually, despite the regular increase in computing capacities, the development of fast and robust methods describing the evolution of saturated-unsaturated soil water and solute fluxes is still a challenge. Ross (2003, Agron J; 95:1352-1361) proposed a method, solving 1D Richards' and convection-diffusion equation, that fulfil these characteristics. The method is based on a non iterative approach which reduces the numerical divergence risks and allows the use of coarser spatial and temporal discretisations, while assuring a satisfying accuracy of the results. Crevoisier et al. (2009, Adv Wat Res; 32:936-947) proposed some technical improvements and validated this method on a wider range of agro- pedo- climatic situations. In this poster, we present the simulation code WATSFAR which generalises the Ross method to other mathematical representations of soil water retention curve (i.e. standard and modified van Genuchten model) and includes a dual permeability context (preferential fluxes) for both water and solute transfers. The situations tested are those known to be the less favourable when using standard numerical methods: fine textured and extremely dry soils, intense rainfall and solute fluxes, soils near saturation, ... The results of WATSFAR have been compared with the standard finite element model Hydrus. The analysis of these comparisons highlights two main advantages for WATSFAR, i) robustness: even on fine textured soil or high water and solute fluxes - where Hydrus simulations may fail to converge - no numerical problem appears, and ii) accuracy of simulations even for loose spatial domain discretisations, which can only be obtained by Hydrus with fine discretisations.

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.

Analysis of energy states in modulation doped multiquantum well heterostructures

NASA Technical Reports Server (NTRS)

Ji, G.; Henderson, T.; Peng, C. K.; Huang, D.; Morkoc, H.

1990-01-01

A precise and effective numerical procedure to model the band diagram of modulation doped multiquantum well heterostructures is presented. This method is based on a self-consistent iterative solution of the Schroedinger equation and the Poisson equation. It can be used rather easily in any arbitrary modulation-doped structure. In addition to confined energy subbands, the unconfined states can be calculated as well. Examples on realistic device structures are given to demonstrate capabilities of this procedure. The numerical results are in good agreement with experiments. With the aid of this method the transitions involving both the confined and unconfined conduction subbands in a modulation doped AlGaAs/GaAs superlattice, and in a strained layer InGaAs/GaAs superlattice are identified. These results represent the first observation of unconfined transitions in modulation doped multiquantum well structures.

Study on longitudinal force simulation of heavy-haul train

NASA Astrophysics Data System (ADS)

Chang, Chongyi; Guo, Gang; Wang, Junbiao; Ma, Yingming

2017-04-01

The longitudinal dynamics model of heavy-haul trains and air brake model used in the longitudinal train dynamics (LTDs) are established. The dry friction damping hysteretic characteristic of steel friction draft gears is simulated by the equation which describes the suspension forces in truck leaf springs. The model of draft gears introduces dynamic loading force, viscous friction of steel friction and the damping force. Consequently, the numerical model of the draft gears is brought forward. The equation of LTDs is strongly non-linear. In order to solve the response of the strongly non-linear system, the high-precision and equilibrium iteration method based on the Newmark-β method is presented and numerical analysis is made. Longitudinal dynamic forces of the 20,000 tonnes heavy-haul train are tested, and models and solution method provided are verified by the test results.

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

Altsybeyev, V.V., E-mail: v.altsybeev@spbu.ru; Ponomarev, V.A.

The particle tracking method with a so-called gun iteration for modeling the space charge is discussed in the following paper. We suggest to apply the emission model based on the Gauss's law for the calculation of the space charge limited current density distribution using considered method. Based on the presented emission model we have developed a numerical algorithm for this calculations. This approach allows us to perform accurate and low time consumpting numerical simulations for different vacuum sources with the curved emitting surfaces and also in the presence of additional physical effects such as bipolar flows and backscattered electrons. Themore » results of the simulations of the cylindrical diode and diode with elliptical emitter with the use of axysimmetric coordinates are presented. The high efficiency and accuracy of the suggested approach are confirmed by the obtained results and comparisons with the analytical solutions.« less

Correlation between discrete probability and reaction front propagation rate in heterogeneous mixtures

NASA Astrophysics Data System (ADS)

Naine, Tarun Bharath; Gundawar, Manoj Kumar

2017-09-01

We demonstrate a very powerful correlation between the discrete probability of distances of neighboring cells and thermal wave propagation rate, for a system of cells spread on a one-dimensional chain. A gamma distribution is employed to model the distances of neighboring cells. In the absence of an analytical solution and the differences in ignition times of adjacent reaction cells following non-Markovian statistics, invariably the solution for thermal wave propagation rate for a one-dimensional system with randomly distributed cells is obtained by numerical simulations. However, such simulations which are based on Monte-Carlo methods require several iterations of calculations for different realizations of distribution of adjacent cells. For several one-dimensional systems, differing in the value of shaping parameter of the gamma distribution, we show that the average reaction front propagation rates obtained by a discrete probability between two limits, shows excellent agreement with those obtained numerically. With the upper limit at 1.3, the lower limit depends on the non-dimensional ignition temperature. Additionally, this approach also facilitates the prediction of burning limits of heterogeneous thermal mixtures. The proposed method completely eliminates the need for laborious, time intensive numerical calculations where the thermal wave propagation rates can now be calculated based only on macroscopic entity of discrete probability.

Analytical Solution for Optimum Design of Furrow Irrigation Systems

NASA Astrophysics Data System (ADS)

Kiwan, M. E.

1996-05-01

An analytical solution for the optimum design of furrow irrigation systems is derived. The non-linear calculus optimization method is used to formulate a general form for designing the optimum system elements under circumstances of maximizing the water application efficiency of the system during irrigation. Different system bases and constraints are considered in the solution. A full irrigation water depth is considered to be achieved at the tail of the furrow line. The solution is based on neglecting the recession and depletion times after off-irrigation. This assumption is valid in the case of open-end (free gradient) furrow systems rather than closed-end (closed dike) systems. Illustrative examples for different systems are presented and the results are compared with the output obtained using an iterative numerical solution method. The final derived solution is expressed as a function of the furrow length ratio (the furrow length to the water travelling distance). The function of water travelling developed by Reddy et al. is considered for reaching the optimum solution. As practical results from the study, the optimum furrow elements for free gradient systems can be estimated to achieve the maximum application efficiency, i.e. furrow length, water inflow rate and cutoff irrigation time.

A numerical solution for the diffusion equation in hydrogeologic systems

USGS Publications Warehouse

Ishii, A.L.; Healy, R.W.; Striegl, Robert G.

1989-01-01

The documentation of a computer code for the numerical solution of the linear diffusion equation in one or two dimensions in Cartesian or cylindrical coordinates is presented. Applications of the program include molecular diffusion, heat conduction, and fluid flow in confined systems. The flow media may be anisotropic and heterogeneous. The model is formulated by replacing the continuous linear diffusion equation by discrete finite-difference approximations at each node in a block-centered grid. The resulting matrix equation is solved by the method of preconditioned conjugate gradients. The conjugate gradient method does not require the estimation of iteration parameters and is guaranteed convergent in the absence of rounding error. The matrixes are preconditioned to decrease the steps to convergence. The model allows the specification of any number of boundary conditions for any number of stress periods, and the output of a summary table for selected nodes showing flux and the concentration of the flux quantity for each time step. The model is written in a modular format for ease of modification. The model was verified by comparison of numerical and analytical solutions for cases of molecular diffusion, two-dimensional heat transfer, and axisymmetric radial saturated fluid flow. Application of the model to a hypothetical two-dimensional field situation of gas diffusion in the unsaturated zone is demonstrated. The input and output files are included as a check on program installation. The definition of variables, input requirements, flow chart, and program listing are included in the attachments. (USGS)

Preconditioned MoM Solutions for Complex Planar Arrays

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

Fasenfest, B J; Jackson, D; Champagne, N

2004-01-23

The numerical analysis of large arrays is a complex problem. There are several techniques currently under development in this area. One such technique is the FAIM (Faster Adaptive Integral Method). This method uses a modification of the standard AIM approach which takes into account the reusability properties of matrices that arise from identical array elements. If the array consists of planar conducting bodies, the array elements are meshed using standard subdomain basis functions, such as the RWG basis. These bases are then projected onto a regular grid of interpolating polynomials. This grid can then be used in a 2D ormore » 3D FFT to accelerate the matrix-vector product used in an iterative solver. The method has been proven to greatly reduce solve time by speeding the matrix-vector product computation. The FAIM approach also reduces fill time and memory requirements, since only the near element interactions need to be calculated exactly. The present work extends FAIM by modifying it to allow for layered material Green's Functions and dielectrics. In addition, a preconditioner is implemented to greatly reduce the number of iterations required for a solution. The general scheme of the FAIM method is reported in; this contribution is limited to presenting new results.« less

A broadband fast multipole accelerated boundary element method for the three dimensional Helmholtz equation.

PubMed

Gumerov, Nail A; Duraiswami, Ramani

2009-01-01

The development of a fast multipole method (FMM) accelerated iterative solution of the boundary element method (BEM) for the Helmholtz equations in three dimensions is described. The FMM for the Helmholtz equation is significantly different for problems with low and high kD (where k is the wavenumber and D the domain size), and for large problems the method must be switched between levels of the hierarchy. The BEM requires several approximate computations (numerical quadrature, approximations of the boundary shapes using elements), and these errors must be balanced against approximations introduced by the FMM and the convergence criterion for iterative solution. These different errors must all be chosen in a way that, on the one hand, excess work is not done and, on the other, that the error achieved by the overall computation is acceptable. Details of translation operators for low and high kD, choice of representations, and BEM quadrature schemes, all consistent with these approximations, are described. A novel preconditioner using a low accuracy FMM accelerated solver as a right preconditioner is also described. Results of the developed solvers for large boundary value problems with 0.0001 less, similarkD less, similar500 are presented and shown to perform close to theoretical expectations.

Extended Lagrangian Excited State Molecular Dynamics

DOE PAGES

Bjorgaard, Josiah August; Sheppard, Daniel Glen; Tretiak, Sergei; ...

2018-01-09

In this work, an extended Lagrangian framework for excited state molecular dynamics (XL-ESMD) using time-dependent self-consistent field theory is proposed. The formulation is a generalization of the extended Lagrangian formulations for ground state Born–Oppenheimer molecular dynamics [Phys. Rev. Lett. 2008 100, 123004]. The theory is implemented, demonstrated, and evaluated using a time-dependent semiempirical model, though it should be generally applicable to ab initio theory. The simulations show enhanced energy stability and a significantly reduced computational cost associated with the iterative solutions of both the ground state and the electronically excited states. Relaxed convergence criteria can therefore be used both formore » the self-consistent ground state optimization and for the iterative subspace diagonalization of the random phase approximation matrix used to calculate the excited state transitions. In conclusion, the XL-ESMD approach is expected to enable numerically efficient excited state molecular dynamics for such methods as time-dependent Hartree–Fock (TD-HF), Configuration Interactions Singles (CIS), and time-dependent density functional theory (TD-DFT).« less

Full waveform inversion of combined towed streamer and limited OBS seismic data: a theoretical study

NASA Astrophysics Data System (ADS)

Yang, Huachen; Zhang, Jianzhong

2018-06-01

In marine seismic oil exploration, full waveform inversion (FWI) of towed-streamer data is used to reconstruct velocity models. However, the FWI of towed-streamer data easily converges to a local minimum solution due to the lack of low-frequency content. In this paper, we propose a new FWI technique using towed-streamer data, its integrated data sets and limited OBS data. Both integrated towed-streamer seismic data and OBS data have low-frequency components. Therefore, at early iterations in the new FWI technique, the OBS data combined with the integrated towed-streamer data sets reconstruct an appropriate background model. And the towed-streamer seismic data play a major role in later iterations to improve the resolution of the model. The new FWI technique is tested on numerical examples. The results show that when starting models are not accurate enough, the models inverted using the new FWI technique are superior to those inverted using conventional FWI.

Development of MCAERO wing design panel method with interactive graphics module

NASA Technical Reports Server (NTRS)

Hawk, J. D.; Bristow, D. R.

1984-01-01

A reliable and efficient iterative method has been developed for designing wing section contours corresponding to a prescribed subcritical pressure distribution. The design process is initialized by using MCAERO (MCAIR 3-D Subsonic Potential Flow Analysis Code) to analyze a baseline configuration. A second program DMCAERO is then used to calculate a matrix containing the partial derivative of potential at each control point with respect to each unknown geometry parameter by applying a first-order expansion to the baseline equations in MCAERO. This matrix is calculated only once but is used in each iteration cycle to calculate the geometry perturbation and to analyze the perturbed geometry. The potential on the new geometry is calculated by linear extrapolation from the baseline solution. This extrapolated potential is converted to velocity by numerical differentiation, and velocity is converted to pressure by using Bernoulli's equation. There is an interactive graphics option which allows the user to graphically display the results of the design process and to interactively change either the geometry or the prescribed pressure distribution.

Extended Lagrangian Excited State Molecular Dynamics

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

Bjorgaard, Josiah August; Sheppard, Daniel Glen; Tretiak, Sergei

In this work, an extended Lagrangian framework for excited state molecular dynamics (XL-ESMD) using time-dependent self-consistent field theory is proposed. The formulation is a generalization of the extended Lagrangian formulations for ground state Born–Oppenheimer molecular dynamics [Phys. Rev. Lett. 2008 100, 123004]. The theory is implemented, demonstrated, and evaluated using a time-dependent semiempirical model, though it should be generally applicable to ab initio theory. The simulations show enhanced energy stability and a significantly reduced computational cost associated with the iterative solutions of both the ground state and the electronically excited states. Relaxed convergence criteria can therefore be used both formore » the self-consistent ground state optimization and for the iterative subspace diagonalization of the random phase approximation matrix used to calculate the excited state transitions. In conclusion, the XL-ESMD approach is expected to enable numerically efficient excited state molecular dynamics for such methods as time-dependent Hartree–Fock (TD-HF), Configuration Interactions Singles (CIS), and time-dependent density functional theory (TD-DFT).« less

Extended Lagrangian Excited State Molecular Dynamics.

PubMed

Bjorgaard, J A; Sheppard, D; Tretiak, S; Niklasson, A M N

2018-02-13

An extended Lagrangian framework for excited state molecular dynamics (XL-ESMD) using time-dependent self-consistent field theory is proposed. The formulation is a generalization of the extended Lagrangian formulations for ground state Born-Oppenheimer molecular dynamics [Phys. Rev. Lett. 2008 100, 123004]. The theory is implemented, demonstrated, and evaluated using a time-dependent semiempirical model, though it should be generally applicable to ab initio theory. The simulations show enhanced energy stability and a significantly reduced computational cost associated with the iterative solutions of both the ground state and the electronically excited states. Relaxed convergence criteria can therefore be used both for the self-consistent ground state optimization and for the iterative subspace diagonalization of the random phase approximation matrix used to calculate the excited state transitions. The XL-ESMD approach is expected to enable numerically efficient excited state molecular dynamics for such methods as time-dependent Hartree-Fock (TD-HF), Configuration Interactions Singles (CIS), and time-dependent density functional theory (TD-DFT).

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.

Exploring inductive linearization for pharmacokinetic-pharmacodynamic systems of nonlinear ordinary differential equations.

PubMed

Hasegawa, Chihiro; Duffull, Stephen B

2018-02-01

Pharmacokinetic-pharmacodynamic systems are often expressed with nonlinear ordinary differential equations (ODEs). While there are numerous methods to solve such ODEs these methods generally rely on time-stepping solutions (e.g. Runge-Kutta) which need to be matched to the characteristics of the problem at hand. The primary aim of this study was to explore the performance of an inductive approximation which iteratively converts nonlinear ODEs to linear time-varying systems which can then be solved algebraically or numerically. The inductive approximation is applied to three examples, a simple nonlinear pharmacokinetic model with Michaelis-Menten elimination (E1), an integrated glucose-insulin model and an HIV viral load model with recursive feedback systems (E2 and E3, respectively). The secondary aim of this study was to explore the potential advantages of analytically solving linearized ODEs with two examples, again E3 with stiff differential equations and a turnover model of luteinizing hormone with a surge function (E4). The inductive linearization coupled with a matrix exponential solution provided accurate predictions for all examples with comparable solution time to the matched time-stepping solutions for nonlinear ODEs. The time-stepping solutions however did not perform well for E4, particularly when the surge was approximated by a square wave. In circumstances when either a linear ODE is particularly desirable or the uncertainty in matching the integrator to the ODE system is of potential risk, then the inductive approximation method coupled with an analytical integration method would be an appropriate alternative.

An eigenvalue approach for the automatic scaling of unknowns in model-based reconstructions: Application to real-time phase-contrast flow MRI.

PubMed

Tan, Zhengguo; Hohage, Thorsten; Kalentev, Oleksandr; Joseph, Arun A; Wang, Xiaoqing; Voit, Dirk; Merboldt, K Dietmar; Frahm, Jens

2017-12-01

The purpose of this work is to develop an automatic method for the scaling of unknowns in model-based nonlinear inverse reconstructions and to evaluate its application to real-time phase-contrast (RT-PC) flow magnetic resonance imaging (MRI). Model-based MRI reconstructions of parametric maps which describe a physical or physiological function require the solution of a nonlinear inverse problem, because the list of unknowns in the extended MRI signal equation comprises multiple functional parameters and all coil sensitivity profiles. Iterative solutions therefore rely on an appropriate scaling of unknowns to numerically balance partial derivatives and regularization terms. The scaling of unknowns emerges as a self-adjoint and positive-definite matrix which is expressible by its maximal eigenvalue and solved by power iterations. The proposed method is applied to RT-PC flow MRI based on highly undersampled acquisitions. Experimental validations include numerical phantoms providing ground truth and a wide range of human studies in the ascending aorta, carotid arteries, deep veins during muscular exercise and cerebrospinal fluid during deep respiration. For RT-PC flow MRI, model-based reconstructions with automatic scaling not only offer velocity maps with high spatiotemporal acuity and much reduced phase noise, but also ensure fast convergence as well as accurate and precise velocities for all conditions tested, i.e. for different velocity ranges, vessel sizes and the simultaneous presence of signals with velocity aliasing. In summary, the proposed automatic scaling of unknowns in model-based MRI reconstructions yields quantitatively reliable velocities for RT-PC flow MRI in various experimental scenarios. Copyright © 2017 John Wiley & Sons, Ltd.

On a new iterative method for solving linear systems and comparison results

NASA Astrophysics Data System (ADS)

Jing, Yan-Fei; Huang, Ting-Zhu

2008-10-01

In Ujevic [A new iterative method for solving linear systems, Appl. Math. Comput. 179 (2006) 725-730], the author obtained a new iterative method for solving linear systems, which can be considered as a modification of the Gauss-Seidel method. In this paper, we show that this is a special case from a point of view of projection techniques. And a different approach is established, which is both theoretically and numerically proven to be better than (at least the same as) Ujevic's. As the presented numerical examples show, in most cases, the convergence rate is more than one and a half that of Ujevic.

Calculation of plasma dielectric response in inhomogeneous magnetic field near electron cyclotron resonance

NASA Astrophysics Data System (ADS)

Evstatiev, Evstati; Svidzinski, Vladimir; Spencer, Andy; Galkin, Sergei

2014-10-01

Full wave 3-D modeling of RF fields in hot magnetized nonuniform plasma requires calculation of nonlocal conductivity kernel describing the dielectric response of such plasma to the RF field. In many cases, the conductivity kernel is a localized function near the test point which significantly simplifies numerical solution of the full wave 3-D problem. Preliminary results of feasibility analysis of numerical calculation of the conductivity kernel in a 3-D hot nonuniform magnetized plasma in the electron cyclotron frequency range will be reported. This case is relevant to modeling of ECRH in ITER. The kernel is calculated by integrating the linearized Vlasov equation along the unperturbed particle's orbits. Particle's orbits in the nonuniform equilibrium magnetic field are calculated numerically by one of the Runge-Kutta methods. RF electric field is interpolated on a specified grid on which the conductivity kernel is discretized. The resulting integrals in the particle's initial velocity and time are then calculated numerically. Different optimization approaches of the integration are tested in this feasibility analysis. Work is supported by the U.S. DOE SBIR program.

Numerical modeling and optimization of the Iguassu gas centrifuge

NASA Astrophysics Data System (ADS)

Bogovalov, S. V.; Borman, V. D.; Borisevich, V. D.; Tronin, V. N.; Tronin, I. V.

2017-07-01

The full procedure of the numerical calculation of the optimized parameters of the Iguassu gas centrifuge (GC) is under discussion. The procedure consists of a few steps. On the first step the problem of a hydrodynamical flow of the gas in the rotating rotor of the GC is solved numerically. On the second step the problem of diffusion of the binary mixture of isotopes is solved. The separation power of the gas centrifuge is calculated after that. On the last step the time consuming procedure of optimization of the GC is performed providing us the maximum of the separation power. The optimization is based on the BOBYQA method exploring the results of numerical simulations of the hydrodynamics and diffusion of the mixture of isotopes. Fast convergence of calculations is achieved due to exploring of a direct solver at the solution of the hydrodynamical and diffusion parts of the problem. Optimized separative power and optimal internal parameters of the Iguassu GC with 1 m rotor were calculated using the developed approach. Optimization procedure converges in 45 iterations taking 811 minutes.

Optimization methods and silicon solar cell numerical models

NASA Technical Reports Server (NTRS)

Girardini, K.; Jacobsen, S. E.

1986-01-01

An optimization algorithm for use with numerical silicon solar cell models was developed. By coupling an optimization algorithm with a solar cell model, it is possible to simultaneously vary design variables such as impurity concentrations, front junction depth, back junction depth, and cell thickness to maximize the predicted cell efficiency. An optimization algorithm was developed and interfaced with the Solar Cell Analysis Program in 1 Dimension (SCAP1D). SCAP1D uses finite difference methods to solve the differential equations which, along with several relations from the physics of semiconductors, describe mathematically the performance of a solar cell. A major obstacle is that the numerical methods used in SCAP1D require a significant amount of computer time, and during an optimization the model is called iteratively until the design variables converge to the values associated with the maximum efficiency. This problem was alleviated by designing an optimization code specifically for use with numerically intensive simulations, to reduce the number of times the efficiency has to be calculated to achieve convergence to the optimal solution.

Spectrum transformation for divergent iterations

NASA Technical Reports Server (NTRS)

Gupta, Murli M.

1991-01-01

Certain spectrum transformation techniques are described that can be used to transform a diverging iteration into a converging one. Two techniques are considered called spectrum scaling and spectrum enveloping and how to obtain the optimum values of the transformation parameters is discussed. Numerical examples are given to show how this technique can be used to transform diverging iterations into converging ones; this technique can also be used to accelerate the convergence of otherwise convergent iterations.

A numerical study of steady crystal growth in a vertical Bridgman device

NASA Astrophysics Data System (ADS)

Jalics, Miklos Kalman

Electronics based on semiconductors creates an enormous demand for high quality semiconductor single crystals. The vertical Bridgman device is commonly used for growing single crystals for a variety of materials such as GaAs, InP and HgCdTe. A mathematical model is presented for steady crystal growth under conditions where crystal growth is determined strictly by heat transfer. The ends of the ampoule are chosen far away from the insulation zone to allow for steady growth. A numerical solution is sought for this mathematical model. The equations are transformed into a rectangular geometry and appropriate finite difference techniques are applied on the transformed equations. Newton's method solves the nonlinear problem. To improve efficiency GMRES with preconditioning is used to compute the Newton iterates. The numerical results are used to compare with two current asymptotic theories that assume small Biot numbers. Results indicate that one of the asymptotic theories is accurate for even moderate Biot numbers.

Global strength assessment in oblique waves of a large gas carrier ship, based on a non-linear iterative method

NASA Astrophysics Data System (ADS)

Domnisoru, L.; Modiga, A.; Gasparotti, C.

2016-08-01

At the ship's design, the first step of the hull structural assessment is based on the longitudinal strength analysis, with head wave equivalent loads by the ships' classification societies’ rules. This paper presents an enhancement of the longitudinal strength analysis, considering the general case of the oblique quasi-static equivalent waves, based on the own non-linear iterative procedure and in-house program. The numerical approach is developed for the mono-hull ships, without restrictions on 3D-hull offset lines non-linearities, and involves three interlinked iterative cycles on floating, pitch and roll trim equilibrium conditions. Besides the ship-wave equilibrium parameters, the ship's girder wave induced loads are obtained. As numerical study case we have considered a large LPG liquefied petroleum gas carrier. The numerical results of the large LPG are compared with the statistical design values from several ships' classification societies’ rules. This study makes possible to obtain the oblique wave conditions that are inducing the maximum loads into the large LPG ship's girder. The numerical results of this study are pointing out that the non-linear iterative approach is necessary for the computation of the extreme loads induced by the oblique waves, ensuring better accuracy of the large LPG ship's longitudinal strength assessment.

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.

Dynamical coupling between magnetic equilibrium and transport in tokamak scenario modelling, with application to current ramps

NASA Astrophysics Data System (ADS)

Fable, E.; Angioni, C.; Ivanov, A. A.; Lackner, K.; Maj, O.; Medvedev, S. Yu; Pautasso, G.; Pereverzev, G. V.; Treutterer, W.; the ASDEX Upgrade Team

2013-07-01

The modelling of tokamak scenarios requires the simultaneous solution of both the time evolution of the plasma kinetic profiles and of the magnetic equilibrium. Their dynamical coupling involves additional complications, which are not present when the two physical problems are solved separately. Difficulties arise in maintaining consistency in the time evolution among quantities which appear in both the transport and the Grad-Shafranov equations, specifically the poloidal and toroidal magnetic fluxes as a function of each other and of the geometry. The required consistency can be obtained by means of iteration cycles, which are performed outside the equilibrium code and which can have different convergence properties depending on the chosen numerical scheme. When these external iterations are performed, the stability of the coupled system becomes a concern. In contrast, if these iterations are not performed, the coupled system is numerically stable, but can become physically inconsistent. By employing a novel scheme (Fable E et al 2012 Nucl. Fusion submitted), which ensures stability and physical consistency among the same quantities that appear in both the transport and magnetic equilibrium equations, a newly developed version of the ASTRA transport code (Pereverzev G V et al 1991 IPP Report 5/42), which is coupled to the SPIDER equilibrium code (Ivanov A A et al 2005 32nd EPS Conf. on Plasma Physics (Tarragona, 27 June-1 July) vol 29C (ECA) P-5.063), in both prescribed- and free-boundary modes is presented here for the first time. The ASTRA-SPIDER coupled system is then applied to the specific study of the modelling of controlled current ramp-up in ASDEX Upgrade discharges.

Convergence Results on Iteration Algorithms to Linear Systems

PubMed Central

Wang, Zhuande; Yang, Chuansheng; Yuan, Yubo

2014-01-01

In order to solve the large scale linear systems, backward and Jacobi iteration algorithms are employed. The convergence is the most important issue. In this paper, a unified backward iterative matrix is proposed. It shows that some well-known iterative algorithms can be deduced with it. The most important result is that the convergence results have been proved. Firstly, the spectral radius of the Jacobi iterative matrix is positive and the one of backward iterative matrix is strongly positive (lager than a positive constant). Secondly, the mentioned two iterations have the same convergence results (convergence or divergence simultaneously). Finally, some numerical experiments show that the proposed algorithms are correct and have the merit of backward methods. PMID:24991640

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.

First-Order Hyperbolic System Method for Time-Dependent Advection-Diffusion Problems

NASA Technical Reports Server (NTRS)

Mazaheri, Alireza; Nishikawa, Hiroaki

2014-01-01

A time-dependent extension of the first-order hyperbolic system method for advection-diffusion problems is introduced. Diffusive/viscous terms are written and discretized as a hyperbolic system, which recovers the original equation in the steady state. The resulting scheme offers advantages over traditional schemes: a dramatic simplification in the discretization, high-order accuracy in the solution gradients, and orders-of-magnitude convergence acceleration. The hyperbolic advection-diffusion system is discretized by the second-order upwind residual-distribution scheme in a unified manner, and the system of implicit-residual-equations is solved by Newton's method over every physical time step. The numerical results are presented for linear and nonlinear advection-diffusion problems, demonstrating solutions and gradients produced to the same order of accuracy, with rapid convergence over each physical time step, typically less than five Newton iterations.

Solution of Cubic Equations by Iteration Methods on a Pocket Calculator

ERIC Educational Resources Information Center

Bamdad, Farzad

2004-01-01

A method to provide students a vision of how they can write iteration programs on an inexpensive programmable pocket calculator, without requiring a PC or a graphing calculator is developed. Two iteration methods are used, successive-approximations and bisection methods.

Time-dependent spectral renormalization method

NASA Astrophysics Data System (ADS)

Cole, Justin T.; Musslimani, Ziad H.

2017-11-01

The spectral renormalization method was introduced by Ablowitz and Musslimani (2005) as an effective way to numerically compute (time-independent) bound states for certain nonlinear boundary value problems. In this paper, we extend those ideas to the time domain and introduce a time-dependent spectral renormalization method as a numerical means to simulate linear and nonlinear evolution equations. The essence of the method is to convert the underlying evolution equation from its partial or ordinary differential form (using Duhamel's principle) into an integral equation. The solution sought is then viewed as a fixed point in both space and time. The resulting integral equation is then numerically solved using a simple renormalized fixed-point iteration method. Convergence is achieved by introducing a time-dependent renormalization factor which is numerically computed from the physical properties of the governing evolution equation. The proposed method has the ability to incorporate physics into the simulations in the form of conservation laws or dissipation rates. This novel scheme is implemented on benchmark evolution equations: the classical nonlinear Schrödinger (NLS), integrable PT symmetric nonlocal NLS and the viscous Burgers' equations, each of which being a prototypical example of a conservative and dissipative dynamical system. Numerical implementation and algorithm performance are also discussed.

Approximate Solution of Time-Fractional Advection-Dispersion Equation via Fractional Variational Iteration Method

PubMed Central

İbiş, Birol

2014-01-01

This paper aims to obtain the approximate solution of time-fractional advection-dispersion equation (FADE) involving Jumarie's modification of Riemann-Liouville derivative by the fractional variational iteration method (FVIM). FVIM provides an analytical approximate solution in the form of a convergent series. Some examples are given and the results indicate that the FVIM is of high accuracy, more efficient, and more convenient for solving time FADEs. PMID:24578662

An efficient algorithm for the generalized Foldy-Lax formulation

NASA Astrophysics Data System (ADS)

Huang, Kai; Li, Peijun; Zhao, Hongkai

2013-02-01

Consider the scattering of a time-harmonic plane wave incident on a two-scale heterogeneous medium, which consists of scatterers that are much smaller than the wavelength and extended scatterers that are comparable to the wavelength. In this work we treat those small scatterers as isotropic point scatterers and use a generalized Foldy-Lax formulation to model wave propagation and capture multiple scattering among point scatterers and extended scatterers. Our formulation is given as a coupled system, which combines the original Foldy-Lax formulation for the point scatterers and the regular boundary integral equation for the extended obstacle scatterers. The existence and uniqueness of the solution for the formulation is established in terms of physical parameters such as the scattering coefficient and the separation distances. Computationally, an efficient physically motivated Gauss-Seidel iterative method is proposed to solve the coupled system, where only a linear system of algebraic equations for point scatterers or a boundary integral equation for a single extended obstacle scatterer is required to solve at each step of iteration. The convergence of the iterative method is also characterized in terms of physical parameters. Numerical tests for the far-field patterns of scattered fields arising from uniformly or randomly distributed point scatterers and single or multiple extended obstacle scatterers are presented.

US NDC Modernization Iteration E2 Prototyping Report: User Interface Framework

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

Lewis, Jennifer E.; Palmer, Melanie A.; Vickers, James Wallace

2014-12-01

During the second iteration of the US NDC Modernization Elaboration phase (E2), the SNL US NDC Modernization project team completed follow-on Rich Client Platform (RCP) exploratory prototyping related to the User Interface Framework (UIF). The team also developed a survey of browser-based User Interface solutions and completed exploratory prototyping for selected solutions. This report presents the results of the browser-based UI survey, summarizes the E2 browser-based UI and RCP prototyping work, and outlines a path forward for the third iteration of the Elaboration phase (E3).

A Mathematica program for the approximate analytical solution to a nonlinear undamped Duffing equation by a new approximate approach

NASA Astrophysics Data System (ADS)

Wu, Dongmei; Wang, Zhongcheng

2006-03-01

According to Mickens [R.E. Mickens, Comments on a Generalized Galerkin's method for non-linear oscillators, J. Sound Vib. 118 (1987) 563], the general HB (harmonic balance) method is an approximation to the convergent Fourier series representation of the periodic solution of a nonlinear oscillator and not an approximation to an expansion in terms of a small parameter. Consequently, for a nonlinear undamped Duffing equation with a driving force Bcos(ωx), to find a periodic solution when the fundamental frequency is identical to ω, the corresponding Fourier series can be written as y˜(x)=∑n=1m acos[(2n-1)ωx]. How to calculate the coefficients of the Fourier series efficiently with a computer program is still an open problem. For HB method, by substituting approximation y˜(x) into force equation, expanding the resulting expression into a trigonometric series, then letting the coefficients of the resulting lowest-order harmonic be zero, one can obtain approximate coefficients of approximation y˜(x) [R.E. Mickens, Comments on a Generalized Galerkin's method for non-linear oscillators, J. Sound Vib. 118 (1987) 563]. But for nonlinear differential equations such as Duffing equation, it is very difficult to construct higher-order analytical approximations, because the HB method requires solving a set of algebraic equations for a large number of unknowns with very complex nonlinearities. To overcome the difficulty, forty years ago, Urabe derived a computational method for Duffing equation based on Galerkin procedure [M. Urabe, A. Reiter, Numerical computation of nonlinear forced oscillations by Galerkin's procedure, J. Math. Anal. Appl. 14 (1966) 107-140]. Dooren obtained an approximate solution of the Duffing oscillator with a special set of parameters by using Urabe's method [R. van Dooren, Stabilization of Cowell's classic finite difference method for numerical integration, J. Comput. Phys. 16 (1974) 186-192]. In this paper, in the frame of the general HB method, we present a new iteration algorithm to calculate the coefficients of the Fourier series. By using this new method, the iteration procedure starts with a(x)cos(ωx)+b(x)sin(ωx), and the accuracy may be improved gradually by determining new coefficients a,a,… will be produced automatically in an one-by-one manner. In all the stage of calculation, we need only to solve a cubic equation. Using this new algorithm, we develop a Mathematica program, which demonstrates following main advantages over the previous HB method: (1) it avoids solving a set of associate nonlinear equations; (2) it is easier to be implemented into a computer program, and produces a highly accurate solution with analytical expression efficiently. It is interesting to find that, generally, for a given set of parameters, a nonlinear Duffing equation can have three independent oscillation modes. For some sets of the parameters, it can have two modes with complex displacement and one with real displacement. But in some cases, it can have three modes, all of them having real displacement. Therefore, we can divide the parameters into two classes, according to the solution property: there is only one mode with real displacement and there are three modes with real displacement. This program should be useful to study the dynamically periodic behavior of a Duffing oscillator and can provide an approximate analytical solution with high-accuracy for testing the error behavior of newly developed numerical methods with a wide range of parameters. Program summaryTitle of program:AnalyDuffing.nb Catalogue identifier:ADWR_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWR_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions:none Computer for which the program is designed and others on which it has been tested:the program has been designed for a microcomputer and been tested on the microcomputer. Computers:IBM PC Installations:the address(es) of your computer(s) Operating systems under which the program has been tested:Windows XP Programming language used:Software Mathematica 4.2, 5.0 and 5.1 No. of lines in distributed program, including test data, etc.:23 663 No. of bytes in distributed program, including test data, etc.:152 321 Distribution format:tar.gz Memory required to execute with typical data:51 712 Bytes No. of bits in a word: No. of processors used:1 Has the code been vectorized?:no Peripherals used:no Program Library subprograms used:no Nature of physical problem:To find an approximate solution with analytical expressions for the undamped nonlinear Duffing equation with periodic driving force when the fundamental frequency is identical to the driving force. Method of solution:In the frame of the general HB method, by using a new iteration algorithm to calculate the coefficients of the Fourier series, we can obtain an approximate analytical solution with high-accuracy efficiently. Restrictions on the complexity of the problem:For problems, which have a large driving frequency, the convergence may be a little slow, because more iterative times are needed. Typical running time:several seconds Unusual features of the program:For an undamped Duffing equation, it can provide all the solutions or the oscillation modes with real displacement for any interesting parameters, for the required accuracy, efficiently. The program can be used to study the dynamically periodic behavior of a nonlinear oscillator, and can provide a high-accurate approximate analytical solution for developing high-accurate numerical method.

Iterative Methods for Solving Nonlinear Parabolic Problem in Pension Saving Management

NASA Astrophysics Data System (ADS)

Koleva, M. N.

2011-11-01

In this work we consider a nonlinear parabolic equation, obtained from Riccati like transformation of the Hamilton-Jacobi-Bellman equation, arising in pension saving management. We discuss two numerical iterative methods for solving the model problem—fully implicit Picard method and mixed Picard-Newton method, which preserves the parabolic characteristics of the differential problem. Numerical experiments for comparison the accuracy and effectiveness of the algorithms are discussed. Finally, observations are given.

Theoretical stability in coefficient inverse problems for general hyperbolic equations with numerical reconstruction

NASA Astrophysics Data System (ADS)

Yu, Jie; Liu, Yikan; Yamamoto, Masahiro

2018-04-01

In this article, we investigate the determination of the spatial component in the time-dependent second order coefficient of a hyperbolic equation from both theoretical and numerical aspects. By the Carleman estimates for general hyperbolic operators and an auxiliary Carleman estimate, we establish local Hölder stability with either partial boundary or interior measurements under certain geometrical conditions. For numerical reconstruction, we minimize a Tikhonov functional which penalizes the gradient of the unknown function. Based on the resulting variational equation, we design an iteration method which is updated by solving a Poisson equation at each step. One-dimensional prototype examples illustrate the numerical performance of the proposed iteration.

Application of NASA General-Purpose Solver to Large-Scale Computations in Aeroacoustics

NASA Technical Reports Server (NTRS)

Watson, Willie R.; Storaasli, Olaf O.

2004-01-01

Of several iterative and direct equation solvers evaluated previously for computations in aeroacoustics, the most promising was the NASA-developed General-Purpose Solver (winner of NASA's 1999 software of the year award). This paper presents detailed, single-processor statistics of the performance of this solver, which has been tailored and optimized for large-scale aeroacoustic computations. The statistics, compiled using an SGI ORIGIN 2000 computer with 12 Gb available memory (RAM) and eight available processors, are the central processing unit time, RAM requirements, and solution error. The equation solver is capable of solving 10 thousand complex unknowns in as little as 0.01 sec using 0.02 Gb RAM, and 8.4 million complex unknowns in slightly less than 3 hours using all 12 Gb. This latter solution is the largest aeroacoustics problem solved to date with this technique. The study was unable to detect any noticeable error in the solution, since noise levels predicted from these solution vectors are in excellent agreement with the noise levels computed from the exact solution. The equation solver provides a means for obtaining numerical solutions to aeroacoustics problems in three dimensions.

Verification of Software: The Textbook and Real Problems

NASA Technical Reports Server (NTRS)

Carlson, Jan-Renee

2006-01-01

The process of verification, or determining the order of accuracy of computational codes, can be problematic when working with large, legacy computational methods that have been used extensively in industry or government. Verification does not ensure that the computer program is producing a physically correct solution, it ensures merely that the observed order of accuracy of solutions are the same as the theoretical order of accuracy. The Method of Manufactured Solutions (MMS) is one of several ways for determining the order of accuracy. MMS is used to verify a series of computer codes progressing in sophistication from "textbook" to "real life" applications. The degree of numerical precision in the computations considerably influenced the range of mesh density to achieve the theoretical order of accuracy even for 1-D problems. The choice of manufactured solutions and mesh form shifted the observed order in specific areas but not in general. Solution residual (iterative) convergence was not always achieved for 2-D Euler manufactured solutions. L(sub 2,norm) convergence differed variable to variable therefore an observed order of accuracy could not be determined conclusively in all cases, the cause of which is currently under investigation.

Modifying PASVART to solve singular nonlinear 2-point boundary problems

NASA Technical Reports Server (NTRS)

Fulton, James P.

1988-01-01

To study the buckling and post-buckling behavior of shells and various other structures, one must solve a nonlinear 2-point boundary problem. Since closed-form analytic solutions for such problems are virtually nonexistent, numerical approximations are inevitable. This makes the availability of accurate and reliable software indispensable. In a series of papers Lentini and Pereyra, expanding on the work of Keller, developed PASVART: an adaptive finite difference solver for nonlinear 2-point boundary problems. While the program does produce extremely accurate solutions with great efficiency, it is hindered by a major limitation. PASVART will only locate isolated solutions of the problem. In buckling problems, the solution set is not unique. It will contain singular or bifurcation points, where different branches of the solution set may intersect. Thus, PASVART is useless precisely when the problem becomes interesting. To resolve this deficiency we propose a modification of PASVART that will enable the user to perform a more complete bifurcation analysis. PASVART would be combined with the Thurston bifurcation solution: as adaptation of Newton's method that was motivated by the work of Koiter 3 are reinterpreted in terms of an iterative computational method by Thurston.

Numerical Technology for Large-Scale Computational Electromagnetics

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

Sharpe, R; Champagne, N; White, D

The key bottleneck of implicit computational electromagnetics tools for large complex geometries is the solution of the resulting linear system of equations. The goal of this effort was to research and develop critical numerical technology that alleviates this bottleneck for large-scale computational electromagnetics (CEM). The mathematical operators and numerical formulations used in this arena of CEM yield linear equations that are complex valued, unstructured, and indefinite. Also, simultaneously applying multiple mathematical modeling formulations to different portions of a complex problem (hybrid formulations) results in a mixed structure linear system, further increasing the computational difficulty. Typically, these hybrid linear systems aremore » solved using a direct solution method, which was acceptable for Cray-class machines but does not scale adequately for ASCI-class machines. Additionally, LLNL's previously existing linear solvers were not well suited for the linear systems that are created by hybrid implicit CEM codes. Hence, a new approach was required to make effective use of ASCI-class computing platforms and to enable the next generation design capabilities. Multiple approaches were investigated, including the latest sparse-direct methods developed by our ASCI collaborators. In addition, approaches that combine domain decomposition (or matrix partitioning) with general-purpose iterative methods and special purpose pre-conditioners were investigated. Special-purpose pre-conditioners that take advantage of the structure of the matrix were adapted and developed based on intimate knowledge of the matrix properties. Finally, new operator formulations were developed that radically improve the conditioning of the resulting linear systems thus greatly reducing solution time. The goal was to enable the solution of CEM problems that are 10 to 100 times larger than our previous capability.« less

On the joint inversion of geophysical data for models of the coupled core-mantle system

NASA Technical Reports Server (NTRS)

Voorhies, Coerte V.

1991-01-01

Joint inversion of magnetic, earth rotation, geoid, and seismic data for a unified model of the coupled core-mantle system is proposed and shown to be possible. A sample objective function is offered and simplified by targeting results from independent inversions and summary travel time residuals instead of original observations. These data are parameterized in terms of a very simple, closed model of the topographically coupled core-mantle system. Minimization of the simplified objective function leads to a nonlinear inverse problem; an iterative method for solution is presented. Parameterization and method are emphasized; numerical results are not presented.

Solution of partial differential equations on vector and parallel computers

NASA Technical Reports Server (NTRS)

Ortega, J. M.; Voigt, R. G.

1985-01-01

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed.