Distributed Adaptive Finite-Time Approach for Formation-Containment Control of Networked Nonlinear Systems Under Directed Topology.

PubMed

Wang, Yujuan; Song, Yongduan; Ren, Wei

2017-07-06

This paper presents a distributed adaptive finite-time control solution to the formation-containment problem for multiple networked systems with uncertain nonlinear dynamics and directed communication constraints. By integrating the special topology feature of the new constructed symmetrical matrix, the technical difficulty in finite-time formation-containment control arising from the asymmetrical Laplacian matrix under single-way directed communication is circumvented. Based upon fractional power feedback of the local error, an adaptive distributed control scheme is established to drive the leaders into the prespecified formation configuration in finite time. Meanwhile, a distributed adaptive control scheme, independent of the unavailable inputs of the leaders, is designed to keep the followers within a bounded distance from the moving leaders and then to make the followers enter the convex hull shaped by the formation of the leaders in finite time. The effectiveness of the proposed control scheme is confirmed by the simulation.

Implementation of Implicit Adaptive Mesh Refinement in an Unstructured Finite-Volume Flow Solver

NASA Technical Reports Server (NTRS)

Schwing, Alan M.; Nompelis, Ioannis; Candler, Graham V.

2013-01-01

This paper explores the implementation of adaptive mesh refinement in an unstructured, finite-volume solver. Unsteady and steady problems are considered. The effect on the recovery of high-order numerics is explored and the results are favorable. Important to this work is the ability to provide a path for efficient, implicit time advancement. A method using a simple refinement sensor based on undivided differences is discussed and applied to a practical problem: a shock-shock interaction on a hypersonic, inviscid double-wedge. Cases are compared to uniform grids without the use of adapted meshes in order to assess error and computational expense. Discussion of difficulties, advances, and future work prepare this method for additional research. The potential for this method in more complicated flows is described.

Disturbance observer based active and adaptive synchronization of energy resource chaotic system.

PubMed

Wei, Wei; Wang, Meng; Li, Donghai; Zuo, Min; Wang, Xiaoyi

2016-11-01

In this paper, synchronization of a three-dimensional energy resource chaotic system is considered. For the sake of achieving the synchronization between the drive and response systems, two different nonlinear control approaches, i.e. active control with known parameters and adaptive control with unknown parameters, have been designed. In order to guarantee the transient performance, finite-time boundedness (FTB) and finite-time stability (FTS) are introduced in the design of active control and adaptive control, respectively. Simultaneously, in view of the existence of disturbances, a new disturbance observer is proposed to estimate the disturbance. The conditions of the asymptotic stability for the closed-loop system are obtained. Numerical simulations are provided to illustrate the proposed approaches. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Using Multithreading for the Automatic Load Balancing of 2D Adaptive Finite Element Meshes

NASA Technical Reports Server (NTRS)

Heber, Gerd; Biswas, Rupak; Thulasiraman, Parimala; Gao, Guang R.; Bailey, David H. (Technical Monitor)

1998-01-01

In this paper, we present a multi-threaded approach for the automatic load balancing of adaptive finite element (FE) meshes. The platform of our choice is the EARTH multi-threaded system which offers sufficient capabilities to tackle this problem. We implement the question phase of FE applications on triangular meshes, and exploit the EARTH token mechanism to automatically balance the resulting irregular and highly nonuniform workload. We discuss the results of our experiments on EARTH-SP2, an implementation of EARTH on the IBM SP2, with different load balancing strategies that are built into the runtime system.

A Solution Adaptive Structured/Unstructured Overset Grid Flow Solver with Applications to Helicopter Rotor Flows

NASA Technical Reports Server (NTRS)

Duque, Earl P. N.; Biswas, Rupak; Strawn, Roger C.

1995-01-01

This paper summarizes a method that solves both the three dimensional thin-layer Navier-Stokes equations and the Euler equations using overset structured and solution adaptive unstructured grids with applications to helicopter rotor flowfields. The overset structured grids use an implicit finite-difference method to solve the thin-layer Navier-Stokes/Euler equations while the unstructured grid uses an explicit finite-volume method to solve the Euler equations. Solutions on a helicopter rotor in hover show the ability to accurately convect the rotor wake. However, isotropic subdivision of the tetrahedral mesh rapidly increases the overall problem size.

Adaptive disturbance compensation finite control set optimal control for PMSM systems based on sliding mode extended state observer

NASA Astrophysics Data System (ADS)

Wu, Yun-jie; Li, Guo-fei

2018-01-01

Based on sliding mode extended state observer (SMESO) technique, an adaptive disturbance compensation finite control set optimal control (FCS-OC) strategy is proposed for permanent magnet synchronous motor (PMSM) system driven by voltage source inverter (VSI). So as to improve robustness of finite control set optimal control strategy, a SMESO is proposed to estimate the output-effect disturbance. The estimated value is fed back to finite control set optimal controller for implementing disturbance compensation. It is indicated through theoretical analysis that the designed SMESO could converge in finite time. The simulation results illustrate that the proposed adaptive disturbance compensation FCS-OC possesses better dynamical response behavior in the presence of disturbance.

Finite Element Analysis of Folded Airbag in Frontal Impact of Adapted Vehicles for Disabled Drivers

NASA Astrophysics Data System (ADS)

Masiá, J.; Eixerés, B.; Dols, J. F.; Esquerdo, T. V.

2009-11-01

The car control adaptations are used in vehicles in order to facilitate the driving to persons with physical handicaps. This does not have to suppose a decrease of the passive safety that is required to the vehicles. In order to analyze this relation there will be characterized the different control adaptations that are in use together with the different devices of passive safety that can be mounted in the vehicles in diverse cases of impact in order to generate models of simulation. The methodology used to generate this simulation consists of the first phase in which there develops the three-dimensional model of the driving place. For it, there has been used a commercial software of three-dimensional design. Once realized this one divides, the model is imported to the finite elements software in which meshing is generated. Finally, dynamic simulation software is used to assign the most important characteristics like material properties, contact interfaces, gas expansion models, airbag fold types, etc.

Adaptive sliding mode control for finite-time stability of quad-rotor UAVs with parametric uncertainties.

PubMed

Mofid, Omid; Mobayen, Saleh

2018-01-01

Adaptive control methods are developed for stability and tracking control of flight systems in the presence of parametric uncertainties. This paper offers a design technique of adaptive sliding mode control (ASMC) for finite-time stabilization of unmanned aerial vehicle (UAV) systems with parametric uncertainties. Applying the Lyapunov stability concept and finite-time convergence idea, the recommended control method guarantees that the states of the quad-rotor UAV are converged to the origin with a finite-time convergence rate. Furthermore, an adaptive-tuning scheme is advised to guesstimate the unknown parameters of the quad-rotor UAV at any moment. Finally, simulation results are presented to exhibit the helpfulness of the offered technique compared to the previous methods. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

An Analysis of a Finite Element Method for Convection-Diffusion Problems. Part II. A Posteriori Error Estimates and Adaptivity.

DTIC Science & Technology

1983-03-01

AN ANALYSIS OF A FINITE ELEMENT METHOD FOR CONVECTION- DIFFUSION PROBLEMS PART II: A POSTERIORI ERROR ESTIMATES AND ADAPTIVITY by W. G. Szymczak Y 6a...PERIOD COVERED AN ANALYSIS OF A FINITE ELEMENT METHOD FOR final life of the contract CONVECTION- DIFFUSION PROBLEM S. Part II: A POSTERIORI ERROR ...Element Method for Convection- Diffusion Problems. Part II: A Posteriori Error Estimates and Adaptivity W. G. Szvmczak and I. Babu~ka# Laboratory for

Finite-time hybrid projective synchronization of the drive-response complex networks with distributed-delay via adaptive intermittent control

NASA Astrophysics Data System (ADS)

Cheng, Lin; Yang, Yongqing; Li, Li; Sui, Xin

2018-06-01

This paper studies the finite-time hybrid projective synchronization of the drive-response complex networks. In the model, general transmission delays and distributed delays are also considered. By designing the adaptive intermittent controllers, the response network can achieve hybrid projective synchronization with the drive system in finite time. Based on finite-time stability theory and several differential inequalities, some simple finite-time hybrid projective synchronization criteria are derived. Two numerical examples are given to illustrate the effectiveness of the proposed method.

Multiple-copy state discrimination: Thinking globally, acting locally

NASA Astrophysics Data System (ADS)

Higgins, B. L.; Doherty, A. C.; Bartlett, S. D.; Pryde, G. J.; Wiseman, H. M.

2011-05-01

We theoretically investigate schemes to discriminate between two nonorthogonal quantum states given multiple copies. We consider a number of state discrimination schemes as applied to nonorthogonal, mixed states of a qubit. In particular, we examine the difference that local and global optimization of local measurements makes to the probability of obtaining an erroneous result, in the regime of finite numbers of copies N, and in the asymptotic limit as N→∞. Five schemes are considered: optimal collective measurements over all copies, locally optimal local measurements in a fixed single-qubit measurement basis, globally optimal fixed local measurements, locally optimal adaptive local measurements, and globally optimal adaptive local measurements. Here an adaptive measurement is one in which the measurement basis can depend on prior measurement results. For each of these measurement schemes we determine the probability of error (for finite N) and the scaling of this error in the asymptotic limit. In the asymptotic limit, it is known analytically (and we verify numerically) that adaptive schemes have no advantage over the optimal fixed local scheme. Here we show moreover that, in this limit, the most naive scheme (locally optimal fixed local measurements) is as good as any noncollective scheme except for states with less than 2% mixture. For finite N, however, the most sophisticated local scheme (globally optimal adaptive local measurements) is better than any other noncollective scheme for any degree of mixture.

Multiple-copy state discrimination: Thinking globally, acting locally

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

Higgins, B. L.; Pryde, G. J.; Wiseman, H. M.

2011-05-15

We theoretically investigate schemes to discriminate between two nonorthogonal quantum states given multiple copies. We consider a number of state discrimination schemes as applied to nonorthogonal, mixed states of a qubit. In particular, we examine the difference that local and global optimization of local measurements makes to the probability of obtaining an erroneous result, in the regime of finite numbers of copies N, and in the asymptotic limit as N{yields}{infinity}. Five schemes are considered: optimal collective measurements over all copies, locally optimal local measurements in a fixed single-qubit measurement basis, globally optimal fixed local measurements, locally optimal adaptive local measurements,more » and globally optimal adaptive local measurements. Here an adaptive measurement is one in which the measurement basis can depend on prior measurement results. For each of these measurement schemes we determine the probability of error (for finite N) and the scaling of this error in the asymptotic limit. In the asymptotic limit, it is known analytically (and we verify numerically) that adaptive schemes have no advantage over the optimal fixed local scheme. Here we show moreover that, in this limit, the most naive scheme (locally optimal fixed local measurements) is as good as any noncollective scheme except for states with less than 2% mixture. For finite N, however, the most sophisticated local scheme (globally optimal adaptive local measurements) is better than any other noncollective scheme for any degree of mixture.« less

An adaptive mesh-moving and refinement procedure for one-dimensional conservation laws

NASA Technical Reports Server (NTRS)

Biswas, Rupak; Flaherty, Joseph E.; Arney, David C.

1993-01-01

We examine the performance of an adaptive mesh-moving and /or local mesh refinement procedure for the finite difference solution of one-dimensional hyperbolic systems of conservation laws. Adaptive motion of a base mesh is designed to isolate spatially distinct phenomena, and recursive local refinement of the time step and cells of the stationary or moving base mesh is performed in regions where a refinement indicator exceeds a prescribed tolerance. These adaptive procedures are incorporated into a computer code that includes a MacCormack finite difference scheme wih Davis' artificial viscosity model and a discretization error estimate based on Richardson's extrapolation. Experiments are conducted on three problems in order to qualify the advantages of adaptive techniques relative to uniform mesh computations and the relative benefits of mesh moving and refinement. Key results indicate that local mesh refinement, with and without mesh moving, can provide reliable solutions at much lower computational cost than possible on uniform meshes; that mesh motion can be used to improve the results of uniform mesh solutions for a modest computational effort; that the cost of managing the tree data structure associated with refinement is small; and that a combination of mesh motion and refinement reliably produces solutions for the least cost per unit accuracy.

On the dynamics of some grid adaption schemes

NASA Technical Reports Server (NTRS)

Sweby, Peter K.; Yee, Helen C.

1994-01-01

The dynamics of a one-parameter family of mesh equidistribution schemes coupled with finite difference discretisations of linear and nonlinear convection-diffusion model equations is studied numerically. It is shown that, when time marched to steady state, the grid adaption not only influences the stability and convergence rate of the overall scheme, but can also introduce spurious dynamics to the numerical solution procedure.

Numerical difficulties and computational procedures for thermo-hydro-mechanical coupled problems of saturated porous media

NASA Astrophysics Data System (ADS)

Simoni, L.; Secchi, S.; Schrefler, B. A.

2008-12-01

This paper analyses the numerical difficulties commonly encountered in solving fully coupled numerical models and proposes a numerical strategy apt to overcome them. The proposed procedure is based on space refinement and time adaptivity. The latter, which in mainly studied here, is based on the use of a finite element approach in the space domain and a Discontinuous Galerkin approximation within each time span. Error measures are defined for the jump of the solution at each time station. These constitute the parameters allowing for the time adaptivity. Some care is however, needed for a useful definition of the jump measures. Numerical tests are presented firstly to demonstrate the advantages and shortcomings of the method over the more traditional use of finite differences in time, then to assess the efficiency of the proposed procedure for adapting the time step. The proposed method reveals its efficiency and simplicity to adapt the time step in the solution of coupled field problems.

A finite-difference method for the variable coefficient Poisson equation on hierarchical Cartesian meshes

NASA Astrophysics Data System (ADS)

Raeli, Alice; Bergmann, Michel; Iollo, Angelo

2018-02-01

We consider problems governed by a linear elliptic equation with varying coefficients across internal interfaces. The solution and its normal derivative can undergo significant variations through these internal boundaries. We present a compact finite-difference scheme on a tree-based adaptive grid that can be efficiently solved using a natively parallel data structure. The main idea is to optimize the truncation error of the discretization scheme as a function of the local grid configuration to achieve second-order accuracy. Numerical illustrations are presented in two and three-dimensional configurations.

A new finite element and finite difference hybrid method for computing electrostatics of ionic solvated biomolecule

NASA Astrophysics Data System (ADS)

Ying, Jinyong; Xie, Dexuan

2015-10-01

The Poisson-Boltzmann equation (PBE) is one widely-used implicit solvent continuum model for calculating electrostatics of ionic solvated biomolecule. In this paper, a new finite element and finite difference hybrid method is presented to solve PBE efficiently based on a special seven-overlapped box partition with one central box containing the solute region and surrounded by six neighboring boxes. In particular, an efficient finite element solver is applied to the central box while a fast preconditioned conjugate gradient method using a multigrid V-cycle preconditioning is constructed for solving a system of finite difference equations defined on a uniform mesh of each neighboring box. Moreover, the PBE domain, the box partition, and an interface fitted tetrahedral mesh of the central box can be generated adaptively for a given PQR file of a biomolecule. This new hybrid PBE solver is programmed in C, Fortran, and Python as a software tool for predicting electrostatics of a biomolecule in a symmetric 1:1 ionic solvent. Numerical results on two test models with analytical solutions and 12 proteins validate this new software tool, and demonstrate its high performance in terms of CPU time and memory usage.

Adaptive finite element method for turbulent flow near a propeller

NASA Astrophysics Data System (ADS)

Pelletier, Dominique; Ilinca, Florin; Hetu, Jean-Francois

1994-11-01

This paper presents an adaptive finite element method based on remeshing to solve incompressible turbulent free shear flow near a propeller. Solutions are obtained in primitive variables using a highly accurate finite element approximation on unstructured grids. Turbulence is modeled by a mixing length formulation. Two general purpose error estimators, which take into account swirl and the variation of the eddy viscosity, are presented and applied to the turbulent wake of a propeller. Predictions compare well with experimental measurements. The proposed adaptive scheme is robust, reliable and cost effective.

A diffuse-interface method for two-phase flows with soluble surfactants

PubMed Central

Teigen, Knut Erik; Song, Peng; Lowengrub, John; Voigt, Axel

2010-01-01

A method is presented to solve two-phase problems involving soluble surfactants. The incompressible Navier–Stokes equations are solved along with equations for the bulk and interfacial surfactant concentrations. A non-linear equation of state is used to relate the surface tension to the interfacial surfactant concentration. The method is based on the use of a diffuse interface, which allows a simple implementation using standard finite difference or finite element techniques. Here, finite difference methods on a block-structured adaptive grid are used, and the resulting equations are solved using a non-linear multigrid method. Results are presented for a drop in shear flow in both 2D and 3D, and the effect of solubility is discussed. PMID:21218125

Earthquake Rupture Dynamics using Adaptive Mesh Refinement and High-Order Accurate Numerical Methods

NASA Astrophysics Data System (ADS)

Kozdon, J. E.; Wilcox, L.

2013-12-01

Our goal is to develop scalable and adaptive (spatial and temporal) numerical methods for coupled, multiphysics problems using high-order accurate numerical methods. To do so, we are developing an opensource, parallel library known as bfam (available at http://bfam.in). The first application to be developed on top of bfam is an earthquake rupture dynamics solver using high-order discontinuous Galerkin methods and summation-by-parts finite difference methods. In earthquake rupture dynamics, wave propagation in the Earth's crust is coupled to frictional sliding on fault interfaces. This coupling is two-way, required the simultaneous simulation of both processes. The use of laboratory-measured friction parameters requires near-fault resolution that is 4-5 orders of magnitude higher than that needed to resolve the frequencies of interest in the volume. This, along with earlier simulations using a low-order, finite volume based adaptive mesh refinement framework, suggest that adaptive mesh refinement is ideally suited for this problem. The use of high-order methods is motivated by the high level of resolution required off the fault in earlier the low-order finite volume simulations; we believe this need for resolution is a result of the excessive numerical dissipation of low-order methods. In bfam spatial adaptivity is handled using the p4est library and temporal adaptivity will be accomplished through local time stepping. In this presentation we will present the guiding principles behind the library as well as verification of code against the Southern California Earthquake Center dynamic rupture code validation test problems.

A fully consistent and conservative vertically adaptive coordinate system for SLIM 3D v0.4 with an application to the thermocline oscillations of Lake Tanganyika

NASA Astrophysics Data System (ADS)

Delandmeter, Philippe; Lambrechts, Jonathan; Legat, Vincent; Vallaeys, Valentin; Naithani, Jaya; Thiery, Wim; Remacle, Jean-François; Deleersnijder, Eric

2018-03-01

The discontinuous Galerkin (DG) finite element method is well suited for the modelling, with a relatively small number of elements, of three-dimensional flows exhibiting strong velocity or density gradients. Its performance can be highly enhanced by having recourse to r-adaptivity. Here, a vertical adaptive mesh method is developed for DG finite elements. This method, originally designed for finite difference schemes, is based on the vertical diffusion of the mesh nodes, with the diffusivity controlled by the density jumps at the mesh element interfaces. The mesh vertical movement is determined by means of a conservative arbitrary Lagrangian-Eulerian (ALE) formulation. Though conservativity is naturally achieved, tracer consistency is obtained by a suitable construction of the mesh vertical velocity field, which is defined in such a way that it is fully compatible with the tracer and continuity equations at a discrete level. The vertically adaptive mesh approach is implemented in the three-dimensional version of the geophysical and environmental flow Second-generation Louvain-la-Neuve Ice-ocean Model (SLIM 3D; www.climate.be/slim). Idealised benchmarks, aimed at simulating the oscillations of a sharp thermocline, are dealt with. Then, the relevance of the vertical adaptivity technique is assessed by simulating thermocline oscillations of Lake Tanganyika. The results are compared to measured vertical profiles of temperature, showing similar stratification and outcropping events.

Biology-Culture Co-evolution in Finite Populations.

PubMed

de Boer, Bart; Thompson, Bill

2018-01-19

Language is the result of two concurrent evolutionary processes: biological and cultural inheritance. An influential evolutionary hypothesis known as the moving target problem implies inherent limitations on the interactions between our two inheritance streams that result from a difference in pace: the speed of cultural evolution is thought to rule out cognitive adaptation to culturally evolving aspects of language. We examine this hypothesis formally by casting it as as a problem of adaptation in time-varying environments. We present a mathematical model of biology-culture co-evolution in finite populations: a generalisation of the Moran process, treating co-evolution as coupled non-independent Markov processes, providing a general formulation of the moving target hypothesis in precise probabilistic terms. Rapidly varying culture decreases the probability of biological adaptation. However, we show that this effect declines with population size and with stronger links between biology and culture: in realistically sized finite populations, stochastic effects can carry cognitive specialisations to fixation in the face of variable culture, especially if the effects of those specialisations are amplified through cultural evolution. These results support the view that language arises from interactions between our two major inheritance streams, rather than from one primary evolutionary process that dominates another.

Finite element analysis and genetic algorithm optimization design for the actuator placement on a large adaptive structure

NASA Astrophysics Data System (ADS)

Sheng, Lizeng

The dissertation focuses on one of the major research needs in the area of adaptive/intelligent/smart structures, the development and application of finite element analysis and genetic algorithms for optimal design of large-scale adaptive structures. We first review some basic concepts in finite element method and genetic algorithms, along with the research on smart structures. Then we propose a solution methodology for solving a critical problem in the design of a next generation of large-scale adaptive structures---optimal placements of a large number of actuators to control thermal deformations. After briefly reviewing the three most frequently used general approaches to derive a finite element formulation, the dissertation presents techniques associated with general shell finite element analysis using flat triangular laminated composite elements. The element used here has three nodes and eighteen degrees of freedom and is obtained by combining a triangular membrane element and a triangular plate bending element. The element includes the coupling effect between membrane deformation and bending deformation. The membrane element is derived from the linear strain triangular element using Cook's transformation. The discrete Kirchhoff triangular (DKT) element is used as the plate bending element. For completeness, a complete derivation of the DKT is presented. Geometrically nonlinear finite element formulation is derived for the analysis of adaptive structures under the combined thermal and electrical loads. Next, we solve the optimization problems of placing a large number of piezoelectric actuators to control thermal distortions in a large mirror in the presence of four different thermal loads. We then extend this to a multi-objective optimization problem of determining only one set of piezoelectric actuator locations that can be used to control the deformation in the same mirror under the action of any one of the four thermal loads. A series of genetic algorithms, GA Version 1, 2 and 3, were developed to find the optimal locations of piezoelectric actuators from the order of 1021 ˜ 1056 candidate placements. Introducing a variable population approach, we improve the flexibility of selection operation in genetic algorithms. Incorporating mutation and hill climbing into micro-genetic algorithms, we are able to develop a more efficient genetic algorithm. Through extensive numerical experiments, we find that the design search space for the optimal placements of a large number of actuators is highly multi-modal and that the most distinct nature of genetic algorithms is their robustness. They give results that are random but with only a slight variability. The genetic algorithms can be used to get adequate solution using a limited number of evaluations. To get the highest quality solution, multiple runs including different random seed generators are necessary. The investigation time can be significantly reduced using a very coarse grain parallel computing. Overall, the methodology of using finite element analysis and genetic algorithm optimization provides a robust solution approach for the challenging problem of optimal placements of a large number of actuators in the design of next generation of adaptive structures.

Quality assessment and control of finite element solutions

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Babuska, Ivo

1987-01-01

Status and some recent developments in the techniques for assessing the reliability of finite element solutions are summarized. Discussion focuses on a number of aspects including: the major types of errors in the finite element solutions; techniques used for a posteriori error estimation and the reliability of these estimators; the feedback and adaptive strategies for improving the finite element solutions; and postprocessing approaches used for improving the accuracy of stresses and other important engineering data. Also, future directions for research needed to make error estimation and adaptive movement practical are identified.

Large Eddy simulation of compressible flows with a low-numerical dissipation patch-based adaptive mesh refinement method

NASA Astrophysics Data System (ADS)

Pantano, Carlos

2005-11-01

We describe a hybrid finite difference method for large-eddy simulation (LES) of compressible flows with a low-numerical dissipation scheme and structured adaptive mesh refinement (SAMR). Numerical experiments and validation calculations are presented including a turbulent jet and the strongly shock-driven mixing of a Richtmyer-Meshkov instability. The approach is a conservative flux-based SAMR formulation and as such, it utilizes refinement to computational advantage. The numerical method for the resolved scale terms encompasses the cases of scheme alternation and internal mesh interfaces resulting from SAMR. An explicit centered scheme that is consistent with a skew-symmetric finite difference formulation is used in turbulent flow regions while a weighted essentially non-oscillatory (WENO) scheme is employed to capture shocks. The subgrid stresses and transports are calculated by means of the streched-vortex model, Misra & Pullin (1997)

Finite-time master-slave synchronization and parameter identification for uncertain Lurie systems.

PubMed

Wang, Tianbo; Zhao, Shouwei; Zhou, Wuneng; Yu, Weiqin

2014-07-01

This paper investigates the finite-time master-slave synchronization and parameter identification problem for uncertain Lurie systems based on the finite-time stability theory and the adaptive control method. The finite-time master-slave synchronization means that the state of a slave system follows with that of a master system in finite time, which is more reasonable than the asymptotical synchronization in applications. The uncertainties include the unknown parameters and noise disturbances. An adaptive controller and update laws which ensures the synchronization and parameter identification to be realized in finite time are constructed. Finally, two numerical examples are given to show the effectiveness of the proposed method. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Finite Element Analysis of Adaptive-Stiffening and Shape-Control SMA Hybrid Composites

NASA Technical Reports Server (NTRS)

Gao, Xiujie; Burton, Deborah; Turner, Travis L.; Brinson, Catherine

2005-01-01

Shape memory alloy hybrid composites with adaptive-stiffening or morphing functions are simulated using finite element analysis. The composite structure is a laminated fiber-polymer composite beam with embedded SMA ribbons at various positions with respect to the neutral axis of the beam. Adaptive stiffening or morphing is activated via selective resistance heating of the SMA ribbons or uniform thermal loads on the beam. The thermomechanical behavior of these composites was simulated in ABAQUS using user-defined SMA elements. The examples demonstrate the usefulness of the methods for the design and simulation of SMA hybrid composites. Keywords: shape memory alloys, Nitinol, ABAQUS, finite element analysis, post-buckling control, shape control, deflection control, adaptive stiffening, morphing, constitutive modeling, user element

New way for determining electron energy levels in quantum dots arrays using finite difference method

NASA Astrophysics Data System (ADS)

Dujardin, F.; Assaid, E.; Feddi, E.

2018-06-01

Electronic states are investigated in quantum dots arrays, depending on the type of cubic Bravais lattice (primitive, body centered or face centered) according to which the dots are arranged, the size of the dots and the interdot distance. It is shown that the ground state energy level can undergo significant variations when these parameters are modified. The results were obtained by means of finite difference method which has proved to be easily adaptable, efficient and precise. The symmetry properties of the lattice have been used to reduce the size of the Hamiltonian matrix.

Adaptive Finite Element Methods for Continuum Damage Modeling

NASA Technical Reports Server (NTRS)

Min, J. B.; Tworzydlo, W. W.; Xiques, K. E.

1995-01-01

The paper presents an application of adaptive finite element methods to the modeling of low-cycle continuum damage and life prediction of high-temperature components. The major objective is to provide automated and accurate modeling of damaged zones through adaptive mesh refinement and adaptive time-stepping methods. The damage modeling methodology is implemented in an usual way by embedding damage evolution in the transient nonlinear solution of elasto-viscoplastic deformation problems. This nonlinear boundary-value problem is discretized by adaptive finite element methods. The automated h-adaptive mesh refinements are driven by error indicators, based on selected principal variables in the problem (stresses, non-elastic strains, damage, etc.). In the time domain, adaptive time-stepping is used, combined with a predictor-corrector time marching algorithm. The time selection is controlled by required time accuracy. In order to take into account strong temperature dependency of material parameters, the nonlinear structural solution a coupled with thermal analyses (one-way coupling). Several test examples illustrate the importance and benefits of adaptive mesh refinements in accurate prediction of damage levels and failure time.

Adaptive mesh refinement for time-domain electromagnetics using vector finite elements :a feasibility study.

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

Turner, C. David; Kotulski, Joseph Daniel; Pasik, Michael Francis

This report investigates the feasibility of applying Adaptive Mesh Refinement (AMR) techniques to a vector finite element formulation for the wave equation in three dimensions. Possible error estimators are considered first. Next, approaches for refining tetrahedral elements are reviewed. AMR capabilities within the Nevada framework are then evaluated. We summarize our conclusions on the feasibility of AMR for time-domain vector finite elements and identify a path forward.

Corruption of accuracy and efficiency of Markov chain Monte Carlo simulation by inaccurate numerical implementation of conceptual hydrologic models

NASA Astrophysics Data System (ADS)

Schoups, G.; Vrugt, J. A.; Fenicia, F.; van de Giesen, N. C.

2010-10-01

Conceptual rainfall-runoff models have traditionally been applied without paying much attention to numerical errors induced by temporal integration of water balance dynamics. Reliance on first-order, explicit, fixed-step integration methods leads to computationally cheap simulation models that are easy to implement. Computational speed is especially desirable for estimating parameter and predictive uncertainty using Markov chain Monte Carlo (MCMC) methods. Confirming earlier work of Kavetski et al. (2003), we show here that the computational speed of first-order, explicit, fixed-step integration methods comes at a cost: for a case study with a spatially lumped conceptual rainfall-runoff model, it introduces artificial bimodality in the marginal posterior parameter distributions, which is not present in numerically accurate implementations of the same model. The resulting effects on MCMC simulation include (1) inconsistent estimates of posterior parameter and predictive distributions, (2) poor performance and slow convergence of the MCMC algorithm, and (3) unreliable convergence diagnosis using the Gelman-Rubin statistic. We studied several alternative numerical implementations to remedy these problems, including various adaptive-step finite difference schemes and an operator splitting method. Our results show that adaptive-step, second-order methods, based on either explicit finite differencing or operator splitting with analytical integration, provide the best alternative for accurate and efficient MCMC simulation. Fixed-step or adaptive-step implicit methods may also be used for increased accuracy, but they cannot match the efficiency of adaptive-step explicit finite differencing or operator splitting. Of the latter two, explicit finite differencing is more generally applicable and is preferred if the individual hydrologic flux laws cannot be integrated analytically, as the splitting method then loses its advantage.

An analysis of finite-difference and finite-volume formulations of conservation laws

NASA Technical Reports Server (NTRS)

Vinokur, Marcel

1986-01-01

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations--potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomeclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

An analysis of finite-difference and finite-volume formulations of conservation laws

NASA Technical Reports Server (NTRS)

Vinokur, Marcel

1989-01-01

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations: potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomenclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

Arbitrary-level hanging nodes for adaptive hphp-FEM approximations in 3D

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

Pavel Kus; Pavel Solin; David Andrs

2014-11-01

In this paper we discuss constrained approximation with arbitrary-level hanging nodes in adaptive higher-order finite element methods (hphp-FEM) for three-dimensional problems. This technique enables using highly irregular meshes, and it greatly simplifies the design of adaptive algorithms as it prevents refinements from propagating recursively through the finite element mesh. The technique makes it possible to design efficient adaptive algorithms for purely hexahedral meshes. We present a detailed mathematical description of the method and illustrate it with numerical examples.

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

Strauss, H.R.

This paper describes the code FEMHD, an adaptive finite element MHD code, which is applied in a number of different manners to model MHD behavior and edge plasma phenomena on a diverted tokamak. The code uses an unstructured triangular mesh in 2D and wedge shaped mesh elements in 3D. The code has been adapted to look at neutral and charged particle dynamics in the plasma scrape off region, and into a full MHD-particle code.

An interpolation-free ALE scheme for unsteady inviscid flows computations with large boundary displacements over three-dimensional adaptive grids

NASA Astrophysics Data System (ADS)

Re, B.; Dobrzynski, C.; Guardone, A.

2017-07-01

A novel strategy to solve the finite volume discretization of the unsteady Euler equations within the Arbitrary Lagrangian-Eulerian framework over tetrahedral adaptive grids is proposed. The volume changes due to local mesh adaptation are treated as continuous deformations of the finite volumes and they are taken into account by adding fictitious numerical fluxes to the governing equation. This peculiar interpretation enables to avoid any explicit interpolation of the solution between different grids and to compute grid velocities so that the Geometric Conservation Law is automatically fulfilled also for connectivity changes. The solution on the new grid is obtained through standard ALE techniques, thus preserving the underlying scheme properties, such as conservativeness, stability and monotonicity. The adaptation procedure includes node insertion, node deletion, edge swapping and points relocation and it is exploited both to enhance grid quality after the boundary movement and to modify the grid spacing to increase solution accuracy. The presented approach is assessed by three-dimensional simulations of steady and unsteady flow fields. The capability of dealing with large boundary displacements is demonstrated by computing the flow around the translating infinite- and finite-span NACA 0012 wing moving through the domain at the flight speed. The proposed adaptive scheme is applied also to the simulation of a pitching infinite-span wing, where the bi-dimensional character of the flow is well reproduced despite the three-dimensional unstructured grid. Finally, the scheme is exploited in a piston-induced shock-tube problem to take into account simultaneously the large deformation of the domain and the shock wave. In all tests, mesh adaptation plays a crucial role.

A Simple Algebraic Grid Adaptation Scheme with Applications to Two- and Three-dimensional Flow Problems

NASA Technical Reports Server (NTRS)

Hsu, Andrew T.; Lytle, John K.

1989-01-01

An algebraic adaptive grid scheme based on the concept of arc equidistribution is presented. The scheme locally adjusts the grid density based on gradients of selected flow variables from either finite difference or finite volume calculations. A user-prescribed grid stretching can be specified such that control of the grid spacing can be maintained in areas of known flowfield behavior. For example, the grid can be clustered near a wall for boundary layer resolution and made coarse near the outer boundary of an external flow. A grid smoothing technique is incorporated into the adaptive grid routine, which is found to be more robust and efficient than the weight function filtering technique employed by other researchers. Since the present algebraic scheme requires no iteration or solution of differential equations, the computer time needed for grid adaptation is trivial, making the scheme useful for three-dimensional flow problems. Applications to two- and three-dimensional flow problems show that a considerable improvement in flowfield resolution can be achieved by using the proposed adaptive grid scheme. Although the scheme was developed with steady flow in mind, it is a good candidate for unsteady flow computations because of its efficiency.

A multilevel correction adaptive finite element method for Kohn-Sham equation

NASA Astrophysics Data System (ADS)

Hu, Guanghui; Xie, Hehu; Xu, Fei

2018-02-01

In this paper, an adaptive finite element method is proposed for solving Kohn-Sham equation with the multilevel correction technique. In the method, the Kohn-Sham equation is solved on a fixed and appropriately coarse mesh with the finite element method in which the finite element space is kept improving by solving the derived boundary value problems on a series of adaptively and successively refined meshes. A main feature of the method is that solving large scale Kohn-Sham system is avoided effectively, and solving the derived boundary value problems can be handled efficiently by classical methods such as the multigrid method. Hence, the significant acceleration can be obtained on solving Kohn-Sham equation with the proposed multilevel correction technique. The performance of the method is examined by a variety of numerical experiments.

Adaptive Wavelet Modeling of Geophysical Data

NASA Astrophysics Data System (ADS)

Plattner, A.; Maurer, H.; Dahmen, W.; Vorloeper, J.

2009-12-01

Despite the ever-increasing power of modern computers, realistic modeling of complex three-dimensional Earth models is still a challenging task and requires substantial computing resources. The overwhelming majority of current geophysical modeling approaches includes either finite difference or non-adaptive finite element algorithms, and variants thereof. These numerical methods usually require the subsurface to be discretized with a fine mesh to accurately capture the behavior of the physical fields. However, this may result in excessive memory consumption and computing times. A common feature of most of these algorithms is that the modeled data discretizations are independent of the model complexity, which may be wasteful when there are only minor to moderate spatial variations in the subsurface parameters. Recent developments in the theory of adaptive numerical solvers have the potential to overcome this problem. Here, we consider an adaptive wavelet based approach that is applicable to a large scope of problems, also including nonlinear problems. To the best of our knowledge such algorithms have not yet been applied in geophysics. Adaptive wavelet algorithms offer several attractive features: (i) for a given subsurface model, they allow the forward modeling domain to be discretized with a quasi minimal number of degrees of freedom, (ii) sparsity of the associated system matrices is guaranteed, which makes the algorithm memory efficient, and (iii) the modeling accuracy scales linearly with computing time. We have implemented the adaptive wavelet algorithm for solving three-dimensional geoelectric problems. To test its performance, numerical experiments were conducted with a series of conductivity models exhibiting varying degrees of structural complexity. Results were compared with a non-adaptive finite element algorithm, which incorporates an unstructured mesh to best fit subsurface boundaries. Such algorithms represent the current state-of-the-art in geoelectrical modeling. An analysis of the numerical accuracy as a function of the number of degrees of freedom revealed that the adaptive wavelet algorithm outperforms the finite element solver for simple and moderately complex models, whereas the results become comparable for models with spatially highly variable electrical conductivities. The linear dependency of the modeling error and the computing time proved to be model-independent. This feature will allow very efficient computations using large-scale models as soon as our experimental code is optimized in terms of its implementation.

Convergence of an hp-Adaptive Finite Element Strategy in Two and Three Space-Dimensions

NASA Astrophysics Data System (ADS)

Bürg, Markus; Dörfler, Willy

2010-09-01

We show convergence of an automatic hp-adaptive refinement strategy for the finite element method on the elliptic boundary value problem. The strategy is a generalization of a refinement strategy proposed for one-dimensional situations to problems in two and three space-dimensions.

Adaptive Shape Functions and Internal Mesh Adaptation for Modelling Progressive Failure in Adhesively Bonded Joints

NASA Technical Reports Server (NTRS)

Stapleton, Scott; Gries, Thomas; Waas, Anthony M.; Pineda, Evan J.

2014-01-01

Enhanced finite elements are elements with an embedded analytical solution that can capture detailed local fields, enabling more efficient, mesh independent finite element analysis. The shape functions are determined based on the analytical model rather than prescribed. This method was applied to adhesively bonded joints to model joint behavior with one element through the thickness. This study demonstrates two methods of maintaining the fidelity of such elements during adhesive non-linearity and cracking without increasing the mesh needed for an accurate solution. The first method uses adaptive shape functions, where the shape functions are recalculated at each load step based on the softening of the adhesive. The second method is internal mesh adaption, where cracking of the adhesive within an element is captured by further discretizing the element internally to represent the partially cracked geometry. By keeping mesh adaptations within an element, a finer mesh can be used during the analysis without affecting the global finite element model mesh. Examples are shown which highlight when each method is most effective in reducing the number of elements needed to capture adhesive nonlinearity and cracking. These methods are validated against analogous finite element models utilizing cohesive zone elements.

Three-dimensional geoelectric modelling with optimal work/accuracy rate using an adaptive wavelet algorithm

NASA Astrophysics Data System (ADS)

Plattner, A.; Maurer, H. R.; Vorloeper, J.; Dahmen, W.

2010-08-01

Despite the ever-increasing power of modern computers, realistic modelling of complex 3-D earth models is still a challenging task and requires substantial computing resources. The overwhelming majority of current geophysical modelling approaches includes either finite difference or non-adaptive finite element algorithms and variants thereof. These numerical methods usually require the subsurface to be discretized with a fine mesh to accurately capture the behaviour of the physical fields. However, this may result in excessive memory consumption and computing times. A common feature of most of these algorithms is that the modelled data discretizations are independent of the model complexity, which may be wasteful when there are only minor to moderate spatial variations in the subsurface parameters. Recent developments in the theory of adaptive numerical solvers have the potential to overcome this problem. Here, we consider an adaptive wavelet-based approach that is applicable to a large range of problems, also including nonlinear problems. In comparison with earlier applications of adaptive solvers to geophysical problems we employ here a new adaptive scheme whose core ingredients arose from a rigorous analysis of the overall asymptotically optimal computational complexity, including in particular, an optimal work/accuracy rate. Our adaptive wavelet algorithm offers several attractive features: (i) for a given subsurface model, it allows the forward modelling domain to be discretized with a quasi minimal number of degrees of freedom, (ii) sparsity of the associated system matrices is guaranteed, which makes the algorithm memory efficient and (iii) the modelling accuracy scales linearly with computing time. We have implemented the adaptive wavelet algorithm for solving 3-D geoelectric problems. To test its performance, numerical experiments were conducted with a series of conductivity models exhibiting varying degrees of structural complexity. Results were compared with a non-adaptive finite element algorithm, which incorporates an unstructured mesh to best-fitting subsurface boundaries. Such algorithms represent the current state-of-the-art in geoelectric modelling. An analysis of the numerical accuracy as a function of the number of degrees of freedom revealed that the adaptive wavelet algorithm outperforms the finite element solver for simple and moderately complex models, whereas the results become comparable for models with high spatial variability of electrical conductivities. The linear dependence of the modelling error and the computing time proved to be model-independent. This feature will allow very efficient computations using large-scale models as soon as our experimental code is optimized in terms of its implementation.

MODFLOW-2000, The U.S. Geological Survey Modular Ground-Water Model -- GMG Linear Equation Solver Package Documentation

USGS Publications Warehouse

Wilson, John D.; Naff, Richard L.

2004-01-01

A geometric multigrid solver (GMG), based in the preconditioned conjugate gradient algorithm, has been developed for solving systems of equations resulting from applying the cell-centered finite difference algorithm to flow in porous media. This solver has been adapted to the U.S. Geological Survey ground-water flow model MODFLOW-2000. The documentation herein is a description of the solver and the adaptation to MODFLOW-2000.

Finite element methodology for integrated flow-thermal-structural analysis

NASA Technical Reports Server (NTRS)

Thornton, Earl A.; Ramakrishnan, R.; Vemaganti, G. R.

1988-01-01

Papers entitled, An Adaptive Finite Element Procedure for Compressible Flows and Strong Viscous-Inviscid Interactions, and An Adaptive Remeshing Method for Finite Element Thermal Analysis, were presented at the June 27 to 29, 1988, meeting of the AIAA Thermophysics, Plasma Dynamics and Lasers Conference, San Antonio, Texas. The papers describe research work supported under NASA/Langley Research Grant NsG-1321, and are submitted in fulfillment of the progress report requirement on the grant for the period ending February 29, 1988.

A novel adaptive sun tracker for spacecraft solar panel based on hybrid unsymmetric composite laminates

NASA Astrophysics Data System (ADS)

Wu, Zhangming; Li, Hao

2017-11-01

This paper proposes a novel adaptive sun tracker which is constructed by hybrid unsymmetric composite laminates. The adaptive sun tracker could be applied on spacecraft solar panels to increase their energy efficiency through decreasing the inclined angle between the sunlight and the solar panel normal. The sun tracker possesses a large rotation freedom and its rotation angle depends on the laminate temperature, which is affected by the light condition in the orbit. Both analytical model and finite element model (FEM) are developed for the sun tracker to predict its rotation angle in different light conditions. In this work, the light condition of the geosynchronous orbit on winter solstice is considered in the numerical prediction of the temperatures of the hybrid laminates. The final inclined angle between the sunlight and the solar panel normal during a solar day is computed using the finite element model. Parametric study of the adaptive sun tracker is conducted to improve its capacity and effectiveness of sun tracking. The improved adaptive sun tracker is lightweight and has a state-of-the-art design. In addition, the adaptive sun tracker does not consume any power of the solar panel, since it has no electrical driving devices. The proposed adaptive sun tracker provides a potential alternative to replace the traditional sophisticated electrical driving mechanisms for spacecraft solar panels.

Adaptive mixed finite element methods for Darcy flow in fractured porous media

NASA Astrophysics Data System (ADS)

Chen, Huangxin; Salama, Amgad; Sun, Shuyu

2016-10-01

In this paper, we propose adaptive mixed finite element methods for simulating the single-phase Darcy flow in two-dimensional fractured porous media. The reduced model that we use for the simulation is a discrete fracture model coupling Darcy flows in the matrix and the fractures, and the fractures are modeled by one-dimensional entities. The Raviart-Thomas mixed finite element methods are utilized for the solution of the coupled Darcy flows in the matrix and the fractures. In order to improve the efficiency of the simulation, we use adaptive mixed finite element methods based on novel residual-based a posteriori error estimators. In addition, we develop an efficient upscaling algorithm to compute the effective permeability of the fractured porous media. Several interesting examples of Darcy flow in the fractured porous media are presented to demonstrate the robustness of the algorithm.

Wavelet-based adaptation methodology combined with finite difference WENO to solve ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Do, Seongju; Li, Haojun; Kang, Myungjoo

2017-06-01

In this paper, we present an accurate and efficient wavelet-based adaptive weighted essentially non-oscillatory (WENO) scheme for hydrodynamics and ideal magnetohydrodynamics (MHD) equations arising from the hyperbolic conservation systems. The proposed method works with the finite difference weighted essentially non-oscillatory (FD-WENO) method in space and the third order total variation diminishing (TVD) Runge-Kutta (RK) method in time. The philosophy of this work is to use the lifted interpolating wavelets as not only detector for singularities but also interpolator. Especially, flexible interpolations can be performed by an inverse wavelet transformation. When the divergence cleaning method introducing auxiliary scalar field ψ is applied to the base numerical schemes for imposing divergence-free condition to the magnetic field in a MHD equation, the approximations to derivatives of ψ require the neighboring points. Moreover, the fifth order WENO interpolation requires large stencil to reconstruct high order polynomial. In such cases, an efficient interpolation method is necessary. The adaptive spatial differentiation method is considered as well as the adaptation of grid resolutions. In order to avoid the heavy computation of FD-WENO, in the smooth regions fixed stencil approximation without computing the non-linear WENO weights is used, and the characteristic decomposition method is replaced by a component-wise approach. Numerical results demonstrate that with the adaptive method we are able to resolve the solutions that agree well with the solution of the corresponding fine grid.

A full potential flow analysis with realistic wake influence for helicopter rotor airload prediction

NASA Technical Reports Server (NTRS)

Egolf, T. Alan; Sparks, S. Patrick

1987-01-01

A 3-D, quasi-steady, full potential flow solver was adapted to include realistic wake influence for the aerodynamic analysis of helicopter rotors. The method is based on a finite difference solution of the full potential equation, using an inner and outer domain procedure for the blade flowfield to accommodate wake effects. The nonlinear flow is computed in the inner domain region using a finite difference solution method. The wake is modeled by a vortex lattice using prescribed geometry techniques to allow for the inclusion of realistic rotor wakes. The key feature of the analysis is that vortices contained within the finite difference mesh (inner domain) were treated with a vortex embedding technique while the influence of the remaining portion of the wake (in the outer domain) is impressed as a boundary condition on the outer surface of the finite difference mesh. The solution procedure couples the wake influence with the inner domain solution in a consistent and efficient solution process. The method has been applied to both hover and forward flight conditions. Correlation with subsonic and transonic hover airload data is shown which demonstrates the merits of the approach.

Adaptive macro finite elements for the numerical solution of monodomain equations in cardiac electrophysiology.

PubMed

Heidenreich, Elvio A; Ferrero, José M; Doblaré, Manuel; Rodríguez, José F

2010-07-01

Many problems in biology and engineering are governed by anisotropic reaction-diffusion equations with a very rapidly varying reaction term. This usually implies the use of very fine meshes and small time steps in order to accurately capture the propagating wave while avoiding the appearance of spurious oscillations in the wave front. This work develops a family of macro finite elements amenable for solving anisotropic reaction-diffusion equations with stiff reactive terms. The developed elements are incorporated on a semi-implicit algorithm based on operator splitting that includes adaptive time stepping for handling the stiff reactive term. A linear system is solved on each time step to update the transmembrane potential, whereas the remaining ordinary differential equations are solved uncoupled. The method allows solving the linear system on a coarser mesh thanks to the static condensation of the internal degrees of freedom (DOF) of the macroelements while maintaining the accuracy of the finer mesh. The method and algorithm have been implemented in parallel. The accuracy of the method has been tested on two- and three-dimensional examples demonstrating excellent behavior when compared to standard linear elements. The better performance and scalability of different macro finite elements against standard finite elements have been demonstrated in the simulation of a human heart and a heterogeneous two-dimensional problem with reentrant activity. Results have shown a reduction of up to four times in computational cost for the macro finite elements with respect to equivalent (same number of DOF) standard linear finite elements as well as good scalability properties.

Finite-horizon control-constrained nonlinear optimal control using single network adaptive critics.

PubMed

Heydari, Ali; Balakrishnan, Sivasubramanya N

2013-01-01

To synthesize fixed-final-time control-constrained optimal controllers for discrete-time nonlinear control-affine systems, a single neural network (NN)-based controller called the Finite-horizon Single Network Adaptive Critic is developed in this paper. Inputs to the NN are the current system states and the time-to-go, and the network outputs are the costates that are used to compute optimal feedback control. Control constraints are handled through a nonquadratic cost function. Convergence proofs of: 1) the reinforcement learning-based training method to the optimal solution; 2) the training error; and 3) the network weights are provided. The resulting controller is shown to solve the associated time-varying Hamilton-Jacobi-Bellman equation and provide the fixed-final-time optimal solution. Performance of the new synthesis technique is demonstrated through different examples including an attitude control problem wherein a rigid spacecraft performs a finite-time attitude maneuver subject to control bounds. The new formulation has great potential for implementation since it consists of only one NN with single set of weights and it provides comprehensive feedback solutions online, though it is trained offline.

The Application of COMSOL Multiphysics Package on the Modelling of Complex 3-D Lithospheric Electrical Resistivity Structures - A Case Study from the Proterozoic Orogenic belt within the North China Craton

NASA Astrophysics Data System (ADS)

Guo, L.; Yin, Y.; Deng, M.; Guo, L.; Yan, J.

2017-12-01

At present, most magnetotelluric (MT) forward modelling and inversion codes are based on finite difference method. But its structured mesh gridding cannot be well adapted for the conditions with arbitrary topography or complex tectonic structures. By contrast, the finite element method is more accurate in calculating complex and irregular 3-D region and has lower requirement of function smoothness. However, the complexity of mesh gridding and limitation of computer capacity has been affecting its application. COMSOL Multiphysics is a cross-platform finite element analysis, solver and multiphysics full-coupling simulation software. It achieves highly accurate numerical simulations with high computational performance and outstanding multi-field bi-directional coupling analysis capability. In addition, its AC/DC and RF module can be used to easily calculate the electromagnetic responses of complex geological structures. Using the adaptive unstructured grid, the calculation is much faster. In order to improve the discretization technique of computing area, we use the combination of Matlab and COMSOL Multiphysics to establish a general procedure for calculating the MT responses for arbitrary resistivity models. The calculated responses include the surface electric and magnetic field components, impedance components, magnetic transfer functions and phase tensors. Then, the reliability of this procedure is certificated by 1-D, 2-D and 3-D and anisotropic forward modeling tests. Finally, we establish the 3-D lithospheric resistivity model for the Proterozoic Wutai-Hengshan Mts. within the North China Craton by fitting the real MT data collected there. The reliability of the model is also verified by induced vectors and phase tensors. Our model shows more details and better resolution, compared with the previously published 3-D model based on the finite difference method. In conclusion, COMSOL Multiphysics package is suitable for modeling the 3-D lithospheric resistivity structures under complex tectonic deformation backgrounds, which could be a good complement to the existing finite-difference inversion algorithms.

Emergence of distributed coordination in the Kolkata Paise Restaurant problem with finite information

NASA Astrophysics Data System (ADS)

Ghosh, Diptesh; Chakrabarti, Anindya S.

2017-10-01

In this paper, we study a large-scale distributed coordination problem and propose efficient adaptive strategies to solve the problem. The basic problem is to allocate finite number of resources to individual agents in the absence of a central planner such that there is as little congestion as possible and the fraction of unutilized resources is reduced as far as possible. In the absence of a central planner and global information, agents can employ adaptive strategies that uses only a finite knowledge about the competitors. In this paper, we show that a combination of finite information sets and reinforcement learning can increase the utilization fraction of resources substantially.

NASTRAN computer system level 12.1

NASA Technical Reports Server (NTRS)

Butler, T. G.

1971-01-01

Program uses finite element displacement method for solving linear response of large, three-dimensional structures subject to static, dynamic, thermal, and random loadings. Program adapts to computers of different manufacture, permits up-dating and extention, allows interchange of output and input information between users, and is extensively documented.

Quadrilateral/hexahedral finite element mesh coarsening

DOEpatents

Staten, Matthew L; Dewey, Mark W; Scott, Michael A; Benzley, Steven E

2012-10-16

A technique for coarsening a finite element mesh ("FEM") is described. This technique includes identifying a coarsening region within the FEM to be coarsened. Perimeter chords running along perimeter boundaries of the coarsening region are identified. The perimeter chords are redirected to create an adaptive chord separating the coarsening region from a remainder of the FEM. The adaptive chord runs through mesh elements residing along the perimeter boundaries of the coarsening region. The adaptive chord is then extracted to coarsen the FEM.

Adaptive Low Dissipative High Order Filter Methods for Multiscale MHD Flows

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sjoegreen, Bjoern

2004-01-01

Adaptive low-dissipative high order filter finite difference methods for long time wave propagation of shock/turbulence/combustion compressible viscous MHD flows has been constructed. Several variants of the filter approach that cater to different flow types are proposed. These filters provide a natural and efficient way for the minimization of the divergence of the magnetic field [divergence of B] numerical error in the sense that no standard divergence cleaning is required. For certain 2-D MHD test problems, divergence free preservation of the magnetic fields of these filter schemes has been achieved.

Does reproduction compromise defense in woody plants?

Treesearch

Daniel A. Herms; William J. Mattson

1991-01-01

A general principle of adaptive allocation was proposed by Cody (1966) who hypothesized that 1) all living organisms have finite resources to partition among growth and competing physiological processes such as reproduction and defense; and 2) natural selection results in the evolution of unique resource allocation patterns that maximize fitness in different...

Viewpoints: diet and dietary adaptations in early hominins: the hard food perspective.

PubMed

Strait, David S; Constantino, Paul; Lucas, Peter W; Richmond, Brian G; Spencer, Mark A; Dechow, Paul C; Ross, Callum F; Grosse, Ian R; Wright, Barth W; Wood, Bernard A; Weber, Gerhard W; Wang, Qian; Byron, Craig; Slice, Dennis E; Chalk, Janine; Smith, Amanda L; Smith, Leslie C; Wood, Sarah; Berthaume, Michael; Benazzi, Stefano; Dzialo, Christine; Tamvada, Kelli; Ledogar, Justin A

2013-07-01

Recent biomechanical analyses examining the feeding adaptations of early hominins have yielded results consistent with the hypothesis that hard foods exerted a selection pressure that influenced the evolution of australopith morphology. However, this hypothesis appears inconsistent with recent reconstructions of early hominin diet based on dental microwear and stable isotopes. Thus, it is likely that either the diets of some australopiths included a high proportion of foods these taxa were poorly adapted to consume (i.e., foods that they would not have processed efficiently), or that aspects of what we thought we knew about the functional morphology of teeth must be wrong. Evaluation of these possibilities requires a recognition that analyses based on microwear, isotopes, finite element modeling, and enamel chips and cracks each test different types of hypotheses and allow different types of inferences. Microwear and isotopic analyses are best suited to reconstructing broad dietary patterns, but are limited in their ability to falsify specific hypotheses about morphological adaptation. Conversely, finite element analysis is a tool for evaluating the mechanical basis of form-function relationships, but says little about the frequency with which specific behaviors were performed or the particular types of food that were consumed. Enamel chip and crack analyses are means of both reconstructing diet and examining biomechanics. We suggest that current evidence is consistent with the hypothesis that certain derived australopith traits are adaptations for consuming hard foods, but that australopiths had generalized diets that could include high proportions of foods that were both compliant and tough. Copyright © 2013 Wiley Periodicals, Inc.

Determination of cellular strains by combined atomic force microscopy and finite element modeling.

PubMed Central

Charras, Guillaume T; Horton, Mike A

2002-01-01

Many organs adapt to their mechanical environment as a result of physiological change or disease. Cells are both the detectors and effectors of this process. Though many studies have been performed in vitro to investigate the mechanisms of detection and adaptation to mechanical strains, the cellular strains remain unknown and results from different stimulation techniques cannot be compared. By combining experimental determination of cell profiles and elasticities by atomic force microscopy with finite element modeling and computational fluid dynamics, we report the cellular strain distributions exerted by common whole-cell straining techniques and from micromanipulation techniques, hence enabling their comparison. Using data from our own analyses and experiments performed by others, we examine the threshold of activation for different signal transduction processes and the strain components that they may detect. We show that modulating cell elasticity, by increasing the F-actin content of the cytoskeleton, or cellular Poisson ratio are good strategies to resist fluid shear or hydrostatic pressure. We report that stray fluid flow in some substrate-stretch systems elicits significant cellular strains. In conclusion, this technique shows promise in furthering our understanding of the interplay among mechanical forces, strain detection, gene expression, and cellular adaptation in physiology and disease. PMID:12124270

Structural adaptations to diverse fighting styles in sexually selected weapons

PubMed Central

McCullough, Erin L.; Tobalske, Bret W.; Emlen, Douglas J.

2014-01-01

The shapes of sexually selected weapons differ widely among species, but the drivers of this diversity remain poorly understood. Existing explanations suggest weapon shapes reflect structural adaptations to different fighting styles, yet explicit tests of this hypothesis are lacking. We constructed finite element models of the horns of different rhinoceros beetle species to test whether functional specializations for increased performance under species-specific fighting styles could have contributed to the diversification of weapon form. We find that horns are both stronger and stiffer in response to species-typical fighting loads and that they perform more poorly under atypical fighting loads, which suggests weapons are structurally adapted to meet the functional demands of fighting. Our research establishes a critical link between weapon form and function, revealing one way male–male competition can drive the diversification of animal weapons. PMID:25201949

Structural adaptations to diverse fighting styles in sexually selected weapons.

PubMed

McCullough, Erin L; Tobalske, Bret W; Emlen, Douglas J

2014-10-07

The shapes of sexually selected weapons differ widely among species, but the drivers of this diversity remain poorly understood. Existing explanations suggest weapon shapes reflect structural adaptations to different fighting styles, yet explicit tests of this hypothesis are lacking. We constructed finite element models of the horns of different rhinoceros beetle species to test whether functional specializations for increased performance under species-specific fighting styles could have contributed to the diversification of weapon form. We find that horns are both stronger and stiffer in response to species-typical fighting loads and that they perform more poorly under atypical fighting loads, which suggests weapons are structurally adapted to meet the functional demands of fighting. Our research establishes a critical link between weapon form and function, revealing one way male-male competition can drive the diversification of animal weapons.

Effect of randomness on multi-frequency aeroelastic responses resolved by Unsteady Adaptive Stochastic Finite Elements

NASA Astrophysics Data System (ADS)

Witteveen, Jeroen A. S.; Bijl, Hester

2009-10-01

The Unsteady Adaptive Stochastic Finite Elements (UASFE) method resolves the effect of randomness in numerical simulations of single-mode aeroelastic responses with a constant accuracy in time for a constant number of samples. In this paper, the UASFE framework is extended to multi-frequency responses and continuous structures by employing a wavelet decomposition pre-processing step to decompose the sampled multi-frequency signals into single-frequency components. The effect of the randomness on the multi-frequency response is then obtained by summing the results of the UASFE interpolation at constant phase for the different frequency components. Results for multi-frequency responses and continuous structures show a three orders of magnitude reduction of computational costs compared to crude Monte Carlo simulations in a harmonically forced oscillator, a flutter panel problem, and the three-dimensional transonic AGARD 445.6 wing aeroelastic benchmark subject to random fields and random parameters with various probability distributions.

An assessment of the adaptive unstructured tetrahedral grid, Euler Flow Solver Code FELISA

NASA Technical Reports Server (NTRS)

Djomehri, M. Jahed; Erickson, Larry L.

1994-01-01

A three-dimensional solution-adaptive Euler flow solver for unstructured tetrahedral meshes is assessed, and the accuracy and efficiency of the method for predicting sonic boom pressure signatures about simple generic models are demonstrated. Comparison of computational and wind tunnel data and enhancement of numerical solutions by means of grid adaptivity are discussed. The mesh generation is based on the advancing front technique. The FELISA code consists of two solvers, the Taylor-Galerkin and the Runge-Kutta-Galerkin schemes, both of which are spacially discretized by the usual Galerkin weighted residual finite-element methods but with different explicit time-marching schemes to steady state. The solution-adaptive grid procedure is based on either remeshing or mesh refinement techniques. An alternative geometry adaptive procedure is also incorporated.

Real-time adaptive finite element solution of time-dependent Kohn-Sham equation

NASA Astrophysics Data System (ADS)

Bao, Gang; Hu, Guanghui; Liu, Di

2015-01-01

In our previous paper (Bao et al., 2012 [1]), a general framework of using adaptive finite element methods to solve the Kohn-Sham equation has been presented. This work is concerned with solving the time-dependent Kohn-Sham equations. The numerical methods are studied in the time domain, which can be employed to explain both the linear and the nonlinear effects. A Crank-Nicolson scheme and linear finite element space are employed for the temporal and spatial discretizations, respectively. To resolve the trouble regions in the time-dependent simulations, a heuristic error indicator is introduced for the mesh adaptive methods. An algebraic multigrid solver is developed to efficiently solve the complex-valued system derived from the semi-implicit scheme. A mask function is employed to remove or reduce the boundary reflection of the wavefunction. The effectiveness of our method is verified by numerical simulations for both linear and nonlinear phenomena, in which the effectiveness of the mesh adaptive methods is clearly demonstrated.

CosmosDG: An hp -adaptive Discontinuous Galerkin Code for Hyper-resolved Relativistic MHD

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

Anninos, Peter; Lau, Cheuk; Bryant, Colton

We have extended Cosmos++, a multidimensional unstructured adaptive mesh code for solving the covariant Newtonian and general relativistic radiation magnetohydrodynamic (MHD) equations, to accommodate both discrete finite volume and arbitrarily high-order finite element structures. The new finite element implementation, called CosmosDG, is based on a discontinuous Galerkin (DG) formulation, using both entropy-based artificial viscosity and slope limiting procedures for the regularization of shocks. High-order multistage forward Euler and strong-stability preserving Runge–Kutta time integration options complement high-order spatial discretization. We have also added flexibility in the code infrastructure allowing for both adaptive mesh and adaptive basis order refinement to be performedmore » separately or simultaneously in a local (cell-by-cell) manner. We discuss in this report the DG formulation and present tests demonstrating the robustness, accuracy, and convergence of our numerical methods applied to special and general relativistic MHD, although we note that an equivalent capability currently also exists in CosmosDG for Newtonian systems.« less

CosmosDG: An hp-adaptive Discontinuous Galerkin Code for Hyper-resolved Relativistic MHD

NASA Astrophysics Data System (ADS)

Anninos, Peter; Bryant, Colton; Fragile, P. Chris; Holgado, A. Miguel; Lau, Cheuk; Nemergut, Daniel

2017-08-01

We have extended Cosmos++, a multidimensional unstructured adaptive mesh code for solving the covariant Newtonian and general relativistic radiation magnetohydrodynamic (MHD) equations, to accommodate both discrete finite volume and arbitrarily high-order finite element structures. The new finite element implementation, called CosmosDG, is based on a discontinuous Galerkin (DG) formulation, using both entropy-based artificial viscosity and slope limiting procedures for the regularization of shocks. High-order multistage forward Euler and strong-stability preserving Runge-Kutta time integration options complement high-order spatial discretization. We have also added flexibility in the code infrastructure allowing for both adaptive mesh and adaptive basis order refinement to be performed separately or simultaneously in a local (cell-by-cell) manner. We discuss in this report the DG formulation and present tests demonstrating the robustness, accuracy, and convergence of our numerical methods applied to special and general relativistic MHD, although we note that an equivalent capability currently also exists in CosmosDG for Newtonian systems.

Eulerian adaptive finite-difference method for high-velocity impact and penetration problems

NASA Astrophysics Data System (ADS)

Barton, P. T.; Deiterding, R.; Meiron, D.; Pullin, D.

2013-05-01

Owing to the complex processes involved, faithful prediction of high-velocity impact events demands a simulation method delivering efficient calculations based on comprehensively formulated constitutive models. Such an approach is presented herein, employing a weighted essentially non-oscillatory (WENO) method within an adaptive mesh refinement (AMR) framework for the numerical solution of hyperbolic partial differential equations. Applied widely in computational fluid dynamics, these methods are well suited to the involved locally non-smooth finite deformations, circumventing any requirement for artificial viscosity functions for shock capturing. Application of the methods is facilitated through using a model of solid dynamics based upon hyper-elastic theory comprising kinematic evolution equations for the elastic distortion tensor. The model for finite inelastic deformations is phenomenologically equivalent to Maxwell's model of tangential stress relaxation. Closure relations tailored to the expected high-pressure states are proposed and calibrated for the materials of interest. Sharp interface resolution is achieved by employing level-set functions to track boundary motion, along with a ghost material method to capture the necessary internal boundary conditions for material interactions and stress-free surfaces. The approach is demonstrated for the simulation of high velocity impacts of steel projectiles on aluminium target plates in two and three dimensions.

Analysing the mechanical performance and growth adaptation of Norway spruce using a non-linear finite-element model and experimental data.

PubMed

Lundström, T; Jonas, T; Volkwein, A

2008-01-01

Thirteen Norway spruce [Picea abies (L.) Karst.] trees of different size, age, and social status, and grown under varying conditions, were investigated to see how they react to complex natural static loading under summer and winter conditions, and how they have adapted their growth to such combinations of load and tree state. For this purpose a non-linear finite-element model and an extensive experimental data set were used, as well as a new formulation describing the degree to which the exploitation of the bending stress capacity is uniform. The three main findings were: material and geometric non-linearities play important roles when analysing tree deflections and critical loads; the strengths of the stem and the anchorage mutually adapt to the local wind acting on the tree crown in the forest canopy; and the radial stem growth follows a mechanically high-performance path because it adapts to prevailing as well as acute seasonal combinations of the tree state (e.g. frozen or unfrozen stem and anchorage) and load (e.g. wind and vertical and lateral snow pressure). Young trees appeared to adapt to such combinations in a more differentiated way than older trees. In conclusion, the mechanical performance of the Norway spruce studied was mostly very high, indicating that their overall growth had been clearly influenced by the external site- and tree-specific mechanical stress.

Higher-order adaptive finite-element methods for Kohn–Sham density functional theory

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

Motamarri, P.; Nowak, M.R.; Leiter, K.

2013-11-15

We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn–Sham density-functional theory (DFT). To this end, we develop an a priori mesh-adaption technique to construct a close to optimal finite-element discretization of the problem. We further propose an efficient solution strategy for solving the discrete eigenvalue problem by using spectral finite-elements in conjunction with Gauss–Lobatto quadrature, and a Chebyshev acceleration technique for computing the occupied eigenspace. The proposed approach has been observed to provide a staggering 100–200-fold computational advantage over the solution of a generalized eigenvalue problem. Using the proposedmore » solution procedure, we investigate the computational efficiency afforded by higher-order finite-element discretizations of the Kohn–Sham DFT problem. Our studies suggest that staggering computational savings—of the order of 1000-fold—relative to linear finite-elements can be realized, for both all-electron and local pseudopotential calculations, by using higher-order finite-element discretizations. On all the benchmark systems studied, we observe diminishing returns in computational savings beyond the sixth-order for accuracies commensurate with chemical accuracy, suggesting that the hexic spectral-element may be an optimal choice for the finite-element discretization of the Kohn–Sham DFT problem. A comparative study of the computational efficiency of the proposed higher-order finite-element discretizations suggests that the performance of finite-element basis is competing with the plane-wave discretization for non-periodic local pseudopotential calculations, and compares to the Gaussian basis for all-electron calculations to within an order of magnitude. Further, we demonstrate the capability of the proposed approach to compute the electronic structure of a metallic system containing 1688 atoms using modest computational resources, and good scalability of the present implementation up to 192 processors.« less

The multidimensional Self-Adaptive Grid code, SAGE, version 2

NASA Technical Reports Server (NTRS)

Davies, Carol B.; Venkatapathy, Ethiraj

1995-01-01

This new report on Version 2 of the SAGE code includes all the information in the original publication plus all upgrades and changes to the SAGE code since that time. The two most significant upgrades are the inclusion of a finite-volume option and the ability to adapt and manipulate zonal-matching multiple-grid files. In addition, the original SAGE code has been upgraded to Version 1.1 and includes all options mentioned in this report, with the exception of the multiple grid option and its associated features. Since Version 2 is a larger and more complex code, it is suggested (but not required) that Version 1.1 be used for single-grid applications. This document contains all the information required to run both versions of SAGE. The formulation of the adaption method is described in the first section of this document. The second section is presented in the form of a user guide that explains the input and execution of the code. The third section provides many examples. Successful application of the SAGE code in both two and three dimensions for the solution of various flow problems has proven the code to be robust, portable, and simple to use. Although the basic formulation follows the method of Nakahashi and Deiwert, many modifications have been made to facilitate the use of the self-adaptive grid method for complex grid structures. Modifications to the method and the simple but extensive input options make this a flexible and user-friendly code. The SAGE code can accommodate two-dimensional and three-dimensional, finite-difference and finite-volume, single grid, and zonal-matching multiple grid flow problems.

Adaptive multiresolution modeling of groundwater flow in heterogeneous porous media

NASA Astrophysics Data System (ADS)

Malenica, Luka; Gotovac, Hrvoje; Srzic, Veljko; Andric, Ivo

2016-04-01

Proposed methodology was originally developed by our scientific team in Split who designed multiresolution approach for analyzing flow and transport processes in highly heterogeneous porous media. The main properties of the adaptive Fup multi-resolution approach are: 1) computational capabilities of Fup basis functions with compact support capable to resolve all spatial and temporal scales, 2) multi-resolution presentation of heterogeneity as well as all other input and output variables, 3) accurate, adaptive and efficient strategy and 4) semi-analytical properties which increase our understanding of usually complex flow and transport processes in porous media. The main computational idea behind this approach is to separately find the minimum number of basis functions and resolution levels necessary to describe each flow and transport variable with the desired accuracy on a particular adaptive grid. Therefore, each variable is separately analyzed, and the adaptive and multi-scale nature of the methodology enables not only computational efficiency and accuracy, but it also describes subsurface processes closely related to their understood physical interpretation. The methodology inherently supports a mesh-free procedure, avoiding the classical numerical integration, and yields continuous velocity and flux fields, which is vitally important for flow and transport simulations. In this paper, we will show recent improvements within the proposed methodology. Since "state of the art" multiresolution approach usually uses method of lines and only spatial adaptive procedure, temporal approximation was rarely considered as a multiscale. Therefore, novel adaptive implicit Fup integration scheme is developed, resolving all time scales within each global time step. It means that algorithm uses smaller time steps only in lines where solution changes are intensive. Application of Fup basis functions enables continuous time approximation, simple interpolation calculations across different temporal lines and local time stepping control. Critical aspect of time integration accuracy is construction of spatial stencil due to accurate calculation of spatial derivatives. Since common approach applied for wavelets and splines uses a finite difference operator, we developed here collocation one including solution values and differential operator. In this way, new improved algorithm is adaptive in space and time enabling accurate solution for groundwater flow problems, especially in highly heterogeneous porous media with large lnK variances and different correlation length scales. In addition, differences between collocation and finite volume approaches are discussed. Finally, results show application of methodology to the groundwater flow problems in highly heterogeneous confined and unconfined aquifers.

In-memory integration of existing software components for parallel adaptive unstructured mesh workflows

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

Smith, Cameron W.; Granzow, Brian; Diamond, Gerrett

Unstructured mesh methods, like finite elements and finite volumes, support the effective analysis of complex physical behaviors modeled by partial differential equations over general threedimensional domains. The most reliable and efficient methods apply adaptive procedures with a-posteriori error estimators that indicate where and how the mesh is to be modified. Although adaptive meshes can have two to three orders of magnitude fewer elements than a more uniform mesh for the same level of accuracy, there are many complex simulations where the meshes required are so large that they can only be solved on massively parallel systems.

In-memory integration of existing software components for parallel adaptive unstructured mesh workflows

DOE PAGES

Smith, Cameron W.; Granzow, Brian; Diamond, Gerrett; ...

2017-01-01

Unstructured mesh methods, like finite elements and finite volumes, support the effective analysis of complex physical behaviors modeled by partial differential equations over general threedimensional domains. The most reliable and efficient methods apply adaptive procedures with a-posteriori error estimators that indicate where and how the mesh is to be modified. Although adaptive meshes can have two to three orders of magnitude fewer elements than a more uniform mesh for the same level of accuracy, there are many complex simulations where the meshes required are so large that they can only be solved on massively parallel systems.

Adaptive Critic Neural Network-Based Terminal Area Energy Management and Approach and Landing Guidance

NASA Technical Reports Server (NTRS)

Grantham, Katie

2003-01-01

Reusable Launch Vehicles (RLVs) have different mission requirements than the Space Shuttle, which is used for benchmark guidance design. Therefore, alternative Terminal Area Energy Management (TAEM) and Approach and Landing (A/L) Guidance schemes can be examined in the interest of cost reduction. A neural network based solution for a finite horizon trajectory optimization problem is presented in this paper. In this approach the optimal trajectory of the vehicle is produced by adaptive critic based neural networks, which were trained off-line to maintain a gradual glideslope.

A genuine nonlinear approach for controller design of a boiler-turbine system.

PubMed

Yang, Shizhong; Qian, Chunjiang; Du, Haibo

2012-05-01

This paper proposes a genuine nonlinear approach for controller design of a drum-type boiler-turbine system. Based on a second order nonlinear model, a finite-time convergent controller is first designed to drive the states to their setpoints in a finite time. In the case when the state variables are unmeasurable, the system will be regulated using a constant controller or an output feedback controller. An adaptive controller is also designed to stabilize the system since the model parameters may vary under different operating points. The novelty of the proposed controller design approach lies in fully utilizing the system nonlinearities instead of linearizing or canceling them. In addition, the newly developed techniques for finite-time convergent controller are used to guarantee fast convergence of the system. Simulations are conducted under different cases and the results are presented to illustrate the performance of the proposed controllers. Copyright © 2011 ISA. Published by Elsevier Ltd. All rights reserved.

Improved finite-element methods for rotorcraft structures

NASA Technical Reports Server (NTRS)

Hinnant, Howard E.

1991-01-01

An overview of the research directed at improving finite-element methods for rotorcraft airframes is presented. The development of a modification to the finite element method which eliminates interelement discontinuities is covered. The following subject areas are discussed: geometric entities, interelement continuity, dependent rotational degrees of freedom, and adaptive numerical integration. This new methodology is being implemented as an anisotropic, curvilinear, p-version, beam, shell, and brick finite element program.

A moving mesh finite difference method for equilibrium radiation diffusion equations

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

Yang, Xiaobo, E-mail: xwindyb@126.com; Huang, Weizhang, E-mail: whuang@ku.edu; Qiu, Jianxian, E-mail: jxqiu@xmu.edu.cn

2015-10-01

An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativitymore » of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.« less

Adaptive finite-volume WENO schemes on dynamically redistributed grids for compressible Euler equations

NASA Astrophysics Data System (ADS)

Pathak, Harshavardhana S.; Shukla, Ratnesh K.

2016-08-01

A high-order adaptive finite-volume method is presented for simulating inviscid compressible flows on time-dependent redistributed grids. The method achieves dynamic adaptation through a combination of time-dependent mesh node clustering in regions characterized by strong solution gradients and an optimal selection of the order of accuracy and the associated reconstruction stencil in a conservative finite-volume framework. This combined approach maximizes spatial resolution in discontinuous regions that require low-order approximations for oscillation-free shock capturing. Over smooth regions, high-order discretization through finite-volume WENO schemes minimizes numerical dissipation and provides excellent resolution of intricate flow features. The method including the moving mesh equations and the compressible flow solver is formulated entirely on a transformed time-independent computational domain discretized using a simple uniform Cartesian mesh. Approximations for the metric terms that enforce discrete geometric conservation law while preserving the fourth-order accuracy of the two-point Gaussian quadrature rule are developed. Spurious Cartesian grid induced shock instabilities such as carbuncles that feature in a local one-dimensional contact capturing treatment along the cell face normals are effectively eliminated through upwind flux calculation using a rotated Hartex-Lax-van Leer contact resolving (HLLC) approximate Riemann solver for the Euler equations in generalized coordinates. Numerical experiments with the fifth and ninth-order WENO reconstructions at the two-point Gaussian quadrature nodes, over a range of challenging test cases, indicate that the redistributed mesh effectively adapts to the dynamic flow gradients thereby improving the solution accuracy substantially even when the initial starting mesh is non-adaptive. The high adaptivity combined with the fifth and especially the ninth-order WENO reconstruction allows remarkably sharp capture of discontinuous propagating shocks with simultaneous resolution of smooth yet complex small scale unsteady flow features to an exceptional detail.

Biomechanical analysis comparing natural and alloplastic temporomandibular joint replacement using a finite element model.

PubMed

Mesnard, Michel; Ramos, Antonio; Ballu, Alex; Morlier, Julien; Cid, M; Simoes, J A

2011-04-01

Prosthetic materials and bone present quite different mechanical properties. Consequently, mandible reconstruction with metallic materials (or a mandible condyle implant) modifies the physiologic behavior of the mandible (stress, strain patterns, and condyle displacements). The changing of bone strain distribution results in an adaptation of the temporomandibular joint, including articular contacts. Using a validated finite element model, the natural mandible strains and condyle displacements were evaluated. Modifications of strains and displacements were then assessed for 2 different temporomandibular joint implants. Because materials and geometry play important key roles, mechanical properties of cortical bone were taken into account in models used in finite element analysis. The finite element model allowed verification of the worst loading configuration of the mandibular condyle. Replacing the natural condyle by 1 of the 2 tested implants, the results also show the importance of the implant geometry concerning biomechanical mandibular behavior. The implant geometry and stiffness influenced mainly strain distribution. The different forces applied to the mandible by the elevator muscles, teeth, and joint loads indicate that the finite element model is a relevant tool to optimize implant geometry or, in a subsequent study, to choose a more suitable distribution of the screws. Bone screws (number and position) have a significant influence on mandibular behavior and on implant stress pattern. Stress concentration and implant fracture must be avoided. Copyright © 2011 American Association of Oral and Maxillofacial Surgeons. Published by Elsevier Inc. All rights reserved.

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

DOE PAGES

Grayver, Alexander V.; Kolev, Tzanio V.

2015-11-01

Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, largemore » conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.« less

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

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

Grayver, Alexander V.; Kolev, Tzanio V.

Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, largemore » conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.« less

Adaptive twisting sliding mode algorithm for hypersonic reentry vehicle attitude control based on finite-time observer.

PubMed

Guo, Zongyi; Chang, Jing; Guo, Jianguo; Zhou, Jun

2018-06-01

This paper focuses on the adaptive twisting sliding mode control for the Hypersonic Reentry Vehicles (HRVs) attitude tracking issue. The HRV attitude tracking model is transformed into the error dynamics in matched structure, whereas an unmeasurable state is redefined by lumping the existing unmatched disturbance with the angular rate. Hence, an adaptive finite-time observer is used to estimate the unknown state. Then, an adaptive twisting algorithm is proposed for systems subject to disturbances with unknown bounds. The stability of the proposed observer-based adaptive twisting approach is guaranteed, and the case of noisy measurement is analyzed. Also, the developed control law avoids the aggressive chattering phenomenon of the existing adaptive twisting approaches because the adaptive gains decrease close to the disturbance once the trajectories reach the sliding surface. Finally, numerical simulations on the attitude control of the HRV are conducted to verify the effectiveness and benefit of the proposed approach. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

An adaptive multiblock high-order finite-volume method for solving the shallow-water equations on the sphere

DOE PAGES

McCorquodale, Peter; Ullrich, Paul; Johansen, Hans; ...

2015-09-04

We present a high-order finite-volume approach for solving the shallow-water equations on the sphere, using multiblock grids on the cubed-sphere. This approach combines a Runge--Kutta time discretization with a fourth-order accurate spatial discretization, and includes adaptive mesh refinement and refinement in time. Results of tests show fourth-order convergence for the shallow-water equations as well as for advection in a highly deformational flow. Hierarchical adaptive mesh refinement allows solution error to be achieved that is comparable to that obtained with uniform resolution of the most refined level of the hierarchy, but with many fewer operations.

Finite State Machine with Adaptive Electromyogram (EMG) Feature Extraction to Drive Meal Assistance Robot

NASA Astrophysics Data System (ADS)

Zhang, Xiu; Wang, Xingyu; Wang, Bei; Sugi, Takenao; Nakamura, Masatoshi

Surface electromyogram (EMG) from elbow, wrist and hand has been widely used as an input of multifunction prostheses for many years. However, for patients with high-level limb deficiencies, muscle activities in upper-limbs are not strong enough to be used as control signals. In this paper, EMG from lower-limbs is acquired and applied to drive a meal assistance robot. An onset detection method with adaptive threshold based on EMG power is proposed to recognize different muscle contractions. Predefined control commands are output by finite state machine (FSM), and applied to operate the robot. The performance of EMG control is compared with joystick control by both objective and subjective indices. The results show that FSM provides the user with an easy-performing control strategy, which successfully operates robots with complicated control commands by limited muscle motions. The high accuracy and comfortableness of the EMG-control meal assistance robot make it feasible for users with upper limbs motor disabilities.

Tsunami modelling with adaptively refined finite volume methods

USGS Publications Warehouse

LeVeque, R.J.; George, D.L.; Berger, M.J.

2011-01-01

Numerical modelling of transoceanic tsunami propagation, together with the detailed modelling of inundation of small-scale coastal regions, poses a number of algorithmic challenges. The depth-averaged shallow water equations can be used to reduce this to a time-dependent problem in two space dimensions, but even so it is crucial to use adaptive mesh refinement in order to efficiently handle the vast differences in spatial scales. This must be done in a 'wellbalanced' manner that accurately captures very small perturbations to the steady state of the ocean at rest. Inundation can be modelled by allowing cells to dynamically change from dry to wet, but this must also be done carefully near refinement boundaries. We discuss these issues in the context of Riemann-solver-based finite volume methods for tsunami modelling. Several examples are presented using the GeoClaw software, and sample codes are available to accompany the paper. The techniques discussed also apply to a variety of other geophysical flows. ?? 2011 Cambridge University Press.

Discrete maximum principle for the P1 - P0 weak Galerkin finite element approximations

NASA Astrophysics Data System (ADS)

Wang, Junping; Ye, Xiu; Zhai, Qilong; Zhang, Ran

2018-06-01

This paper presents two discrete maximum principles (DMP) for the numerical solution of second order elliptic equations arising from the weak Galerkin finite element method. The results are established by assuming an h-acute angle condition for the underlying finite element triangulations. The mathematical theory is based on the well-known De Giorgi technique adapted in the finite element context. Some numerical results are reported to validate the theory of DMP.

Design of a Modular Monolithic Implicit Solver for Multi-Physics Applications

NASA Technical Reports Server (NTRS)

Carton De Wiart, Corentin; Diosady, Laslo T.; Garai, Anirban; Burgess, Nicholas; Blonigan, Patrick; Ekelschot, Dirk; Murman, Scott M.

2018-01-01

The design of a modular multi-physics high-order space-time finite-element framework is presented together with its extension to allow monolithic coupling of different physics. One of the main objectives of the framework is to perform efficient high- fidelity simulations of capsule/parachute systems. This problem requires simulating multiple physics including, but not limited to, the compressible Navier-Stokes equations, the dynamics of a moving body with mesh deformations and adaptation, the linear shell equations, non-re effective boundary conditions and wall modeling. The solver is based on high-order space-time - finite element methods. Continuous, discontinuous and C1-discontinuous Galerkin methods are implemented, allowing one to discretize various physical models. Tangent and adjoint sensitivity analysis are also targeted in order to conduct gradient-based optimization, error estimation, mesh adaptation, and flow control, adding another layer of complexity to the framework. The decisions made to tackle these challenges are presented. The discussion focuses first on the "single-physics" solver and later on its extension to the monolithic coupling of different physics. The implementation of different physics modules, relevant to the capsule/parachute system, are also presented. Finally, examples of coupled computations are presented, paving the way to the simulation of the full capsule/parachute system.

Toward automatic finite element analysis

NASA Technical Reports Server (NTRS)

Kela, Ajay; Perucchio, Renato; Voelcker, Herbert

1987-01-01

Two problems must be solved if the finite element method is to become a reliable and affordable blackbox engineering tool. Finite element meshes must be generated automatically from computer aided design databases and mesh analysis must be made self-adaptive. The experimental system described solves both problems in 2-D through spatial and analytical substructuring techniques that are now being extended into 3-D.

Saccharomyces cerevisiae: a nomadic yeast with no niche?

PubMed

Goddard, Matthew R; Greig, Duncan

2015-05-01

Different species are usually thought to have specific adaptations, which allow them to occupy different ecological niches. But recent neutral ecology theory suggests that species diversity can simply be the result of random sampling, due to finite population sizes and limited dispersal. Neutral models predict that species are not necessarily adapted to specific niches, but are functionally equivalent across a range of habitats. Here, we evaluate the ecology of Saccharomyces cerevisiae, one of the most important microbial species in human history. The artificial collection, concentration and fermentation of large volumes of fruit for alcohol production produce an environment in which S. cerevisiae thrives, and therefore it is assumed that fruit is the ecological niche that S. cerevisiae inhabits and has adapted to. We find very little direct evidence that S. cerevisiae is adapted to fruit, or indeed to any other specific niche. We propose instead a neutral nomad model for S. cerevisiae, which we believe should be used as the starting hypothesis in attempting to unravel the ecology of this important microbe. © FEMS 2015.

On the mechanics of growing thin biological membranes

NASA Astrophysics Data System (ADS)

Rausch, Manuel K.; Kuhl, Ellen

2014-02-01

Despite their seemingly delicate appearance, thin biological membranes fulfill various crucial roles in the human body and can sustain substantial mechanical loads. Unlike engineering structures, biological membranes are able to grow and adapt to changes in their mechanical environment. Finite element modeling of biological growth holds the potential to better understand the interplay of membrane form and function and to reliably predict the effects of disease or medical intervention. However, standard continuum elements typically fail to represent thin biological membranes efficiently, accurately, and robustly. Moreover, continuum models are typically cumbersome to generate from surface-based medical imaging data. Here we propose a computational model for finite membrane growth using a classical midsurface representation compatible with standard shell elements. By assuming elastic incompressibility and membrane-only growth, the model a priori satisfies the zero-normal stress condition. To demonstrate its modular nature, we implement the membrane growth model into the general-purpose non-linear finite element package Abaqus/Standard using the concept of user subroutines. To probe efficiently and robustness, we simulate selected benchmark examples of growing biological membranes under different loading conditions. To demonstrate the clinical potential, we simulate the functional adaptation of a heart valve leaflet in ischemic cardiomyopathy. We believe that our novel approach will be widely applicable to simulate the adaptive chronic growth of thin biological structures including skin membranes, mucous membranes, fetal membranes, tympanic membranes, corneoscleral membranes, and heart valve membranes. Ultimately, our model can be used to identify diseased states, predict disease evolution, and guide the design of interventional or pharmaceutic therapies to arrest or revert disease progression.

On the mechanics of growing thin biological membranes

PubMed Central

Rausch, Manuel K.; Kuhl, Ellen

2013-01-01

Despite their seemingly delicate appearance, thin biological membranes fulfill various crucial roles in the human body and can sustain substantial mechanical loads. Unlike engineering structures, biological membranes are able to grow and adapt to changes in their mechanical environment. Finite element modeling of biological growth holds the potential to better understand the interplay of membrane form and function and to reliably predict the effects of disease or medical intervention. However, standard continuum elements typically fail to represent thin biological membranes efficiently, accurately, and robustly. Moreover, continuum models are typically cumbersome to generate from surface-based medical imaging data. Here we propose a computational model for finite membrane growth using a classical midsurface representation compatible with standard shell elements. By assuming elastic incompressibility and membrane-only growth, the model a priori satisfies the zero-normal stress condition. To demonstrate its modular nature, we implement the membrane growth model into the general-purpose non-linear finite element package Abaqus/Standard using the concept of user subroutines. To probe efficiently and robustness, we simulate selected benchmark examples of growing biological membranes under different loading conditions. To demonstrate the clinical potential, we simulate the functional adaptation of a heart valve leaflet in ischemic cardiomyopathy. We believe that our novel approach will be widely applicable to simulate the adaptive chronic growth of thin biological structures including skin membranes, mucous membranes, fetal membranes, tympanic membranes, corneoscleral membranes, and heart valve membranes. Ultimately, our model can be used to identify diseased states, predict disease evolution, and guide the design of interventional or pharmaceutic therapies to arrest or revert disease progression. PMID:24563551

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

NASA Technical Reports Server (NTRS)

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

1989-01-01

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

Generation of segmental chips in metal cutting modeled with the PFEM

NASA Astrophysics Data System (ADS)

Rodriguez Prieto, J. M.; Carbonell, J. M.; Cante, J. C.; Oliver, J.; Jonsén, P.

2018-06-01

The Particle Finite Element Method, a lagrangian finite element method based on a continuous Delaunay re-triangulation of the domain, is used to study machining of Ti6Al4V. In this work the method is revised and applied to study the influence of the cutting speed on the cutting force and the chip formation process. A parametric methodology for the detection and treatment of the rigid tool contact is presented. The adaptive insertion and removal of particles are developed and employed in order to sidestep the difficulties associated with mesh distortion, shear localization as well as for resolving the fine-scale features of the solution. The performance of PFEM is studied with a set of different two-dimensional orthogonal cutting tests. It is shown that, despite its Lagrangian nature, the proposed combined finite element-particle method is well suited for large deformation metal cutting problems with continuous chip and serrated chip formation.

Generation of segmental chips in metal cutting modeled with the PFEM

NASA Astrophysics Data System (ADS)

Rodriguez Prieto, J. M.; Carbonell, J. M.; Cante, J. C.; Oliver, J.; Jonsén, P.

2017-09-01

The Particle Finite Element Method, a lagrangian finite element method based on a continuous Delaunay re-triangulation of the domain, is used to study machining of Ti6Al4V. In this work the method is revised and applied to study the influence of the cutting speed on the cutting force and the chip formation process. A parametric methodology for the detection and treatment of the rigid tool contact is presented. The adaptive insertion and removal of particles are developed and employed in order to sidestep the difficulties associated with mesh distortion, shear localization as well as for resolving the fine-scale features of the solution. The performance of PFEM is studied with a set of different two-dimensional orthogonal cutting tests. It is shown that, despite its Lagrangian nature, the proposed combined finite element-particle method is well suited for large deformation metal cutting problems with continuous chip and serrated chip formation.

An adaptive approach to the physical annealing strategy for simulated annealing

NASA Astrophysics Data System (ADS)

Hasegawa, M.

2013-02-01

A new and reasonable method for adaptive implementation of simulated annealing (SA) is studied on two types of random traveling salesman problems. The idea is based on the previous finding on the search characteristics of the threshold algorithms, that is, the primary role of the relaxation dynamics in their finite-time optimization process. It is shown that the effective temperature for optimization can be predicted from the system's behavior analogous to the stabilization phenomenon occurring in the heating process starting from a quenched solution. The subsequent slow cooling near the predicted point draws out the inherent optimizing ability of finite-time SA in more straightforward manner than the conventional adaptive approach.

Hypermatrix scheme for finite element systems on CDC STAR-100 computer

NASA Technical Reports Server (NTRS)

Noor, A. K.; Voigt, S. J.

1975-01-01

A study is made of the adaptation of the hypermatrix (block matrix) scheme for solving large systems of finite element equations to the CDC STAR-100 computer. Discussion is focused on the organization of the hypermatrix computation using Cholesky decomposition and the mode of storage of the different submatrices to take advantage of the STAR pipeline (streaming) capability. Consideration is also given to the associated data handling problems and the means of balancing the I/Q and cpu times in the solution process. Numerical examples are presented showing anticipated gain in cpu speed over the CDC 6600 to be obtained by using the proposed algorithms on the STAR computer.

An adaptive wing for a small-aircraft application with a configuration of fibre Bragg grating sensors

NASA Astrophysics Data System (ADS)

Mieloszyk, M.; Krawczuk, M.; Zak, A.; Ostachowicz, W.

2010-08-01

In this paper a concept of an adaptive wing for small-aircraft applications with an array of fibre Bragg grating (FBG) sensors has been presented and discussed. In this concept the shape of the wing can be controlled and altered thanks to the wing design and the use of integrated shape memory alloy actuators. The concept has been tested numerically by the use of the finite element method. For numerical calculations the commercial finite element package ABAQUS® has been employed. A finite element model of the wing has been prepared in order to estimate the values of the wing twisting angles and distributions of the twist for various activation scenarios. Based on the results of numerical analysis the locations and numbers of the FBG sensors have also been determined. The results of numerical calculations obtained by the authors confirmed the usefulness of the assumed wing control strategy. Based on them and the concept developed of the adaptive wing, a wing demonstration stand has been designed and built. The stand has been used to verify experimentally the performance of the adaptive wing and the usefulness of the FBG sensors for evaluation of the wing condition.

H-P adaptive methods for finite element analysis of aerothermal loads in high-speed flows

NASA Technical Reports Server (NTRS)

Chang, H. J.; Bass, J. M.; Tworzydlo, W.; Oden, J. T.

1993-01-01

The commitment to develop the National Aerospace Plane and Maneuvering Reentry Vehicles has generated resurgent interest in the technology required to design structures for hypersonic flight. The principal objective of this research and development effort has been to formulate and implement a new class of computational methodologies for accurately predicting fine scale phenomena associated with this class of problems. The initial focus of this effort was to develop optimal h-refinement and p-enrichment adaptive finite element methods which utilize a-posteriori estimates of the local errors to drive the adaptive methodology. Over the past year this work has specifically focused on two issues which are related to overall performance of a flow solver. These issues include the formulation and implementation (in two dimensions) of an implicit/explicit flow solver compatible with the hp-adaptive methodology, and the design and implementation of computational algorithm for automatically selecting optimal directions in which to enrich the mesh. These concepts and algorithms have been implemented in a two-dimensional finite element code and used to solve three hypersonic flow benchmark problems (Holden Mach 14.1, Edney shock on shock interaction Mach 8.03, and the viscous backstep Mach 4.08).

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

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

Static shape control for adaptive wings

NASA Astrophysics Data System (ADS)

Austin, Fred; Rossi, Michael J.; van Nostrand, William; Knowles, Gareth; Jameson, Antony

1994-09-01

A theoretical method was developed and experimentally validated, to control the static shape of flexible structures by employing internal translational actuators. A finite element model of the structure, without the actuators present, is employed to obtain the multiple-input, multiple-output control-system gain matrices for actuator-load control as well as actuator-displacement control. The method is applied to the quasistatic problem of maintaining an optimum-wing cross section during various transonic-cruise flight conditions to obtain significant reductions in the shock-induced drag. Only small, potentially achievable, adaptive modifications to the profile are required. The adaptive-wing concept employs actuators as truss elements of active ribs to reshape the wing cross section by deforming the structure. Finite element analyses of an adaptive-rib model verify the controlled-structure theory. Experiments on the model were conducted, and arbitrarily selected deformed shapes were accurately achieved.

The evolution of recombination rates in finite populations during ecological speciation.

PubMed

Reeve, James; Ortiz-Barrientos, Daniel; Engelstädter, Jan

2016-10-26

Recombination can impede ecological speciation with gene flow by mixing locally adapted genotypes with maladapted migrant genotypes from a divergent population. In such a scenario, suppression of recombination can be selectively favoured. However, in finite populations evolving under the influence of random genetic drift, recombination can also facilitate adaptation by reducing Hill-Robertson interference between loci under selection. In this case, increased recombination rates can be favoured. Although these two major effects on recombination have been studied individually, their joint effect on ecological speciation with gene flow remains unexplored. Using a mathematical model, we investigated the evolution of recombination rates in two finite populations that exchange migrants while adapting to contrasting environments. Our results indicate a two-step dynamic where increased recombination is first favoured (in response to the Hill-Robertson effect), and then disfavoured, as the cost of recombining locally with maladapted migrant genotypes increases over time (the maladaptive gene flow effect). In larger populations, a stronger initial benefit for recombination was observed, whereas high migration rates intensify the long-term cost of recombination. These dynamics may have important implications for our understanding of the conditions that facilitate incipient speciation with gene flow and the evolution of recombination in finite populations. © 2016 The Author(s).

A novel adaptive algorithm for 3D finite element analysis to model extracortical bone growth.

PubMed

Cheong, Vee San; Blunn, Gordon W; Coathup, Melanie J; Fromme, Paul

2018-02-01

Extracortical bone growth with osseointegration of bone onto the shaft of massive bone tumour implants is an important clinical outcome for long-term implant survival. A new computational algorithm combining geometrical shape changes and bone adaptation in 3D Finite Element simulations has been developed, using a soft tissue envelope mesh, a novel concept of osteoconnectivity, and bone remodelling theory. The effects of varying the initial tissue density, spatial influence function and time step were investigated. The methodology demonstrated good correspondence to radiological results for a segmental prosthesis.

Interactive Finite Elements for General Engine Dynamics Analysis

NASA Technical Reports Server (NTRS)

Adams, M. L.; Padovan, J.; Fertis, D. G.

1984-01-01

General nonlinear finite element codes were adapted for the purpose of analyzing the dynamics of gas turbine engines. In particular, this adaptation required the development of a squeeze-film damper element software package and its implantation into a representative current generation code. The ADINA code was selected because of prior use of it and familiarity with its internal structure and logic. This objective was met and the results indicate that such use of general purpose codes is viable alternative to specialized codes for general dynamics analysis of engines.

An Analysis Technique/Automated Tool for Comparing and Tracking Analysis Modes of Different Finite Element Models

NASA Technical Reports Server (NTRS)

Towner, Robert L.; Band, Jonathan L.

2012-01-01

An analysis technique was developed to compare and track mode shapes for different Finite Element Models. The technique may be applied to a variety of structural dynamics analyses, including model reduction validation (comparing unreduced and reduced models), mode tracking for various parametric analyses (e.g., launch vehicle model dispersion analysis to identify sensitivities to modal gain for Guidance, Navigation, and Control), comparing models of different mesh fidelity (e.g., a coarse model for a preliminary analysis compared to a higher-fidelity model for a detailed analysis) and mode tracking for a structure with properties that change over time (e.g., a launch vehicle from liftoff through end-of-burn, with propellant being expended during the flight). Mode shapes for different models are compared and tracked using several numerical indicators, including traditional Cross-Orthogonality and Modal Assurance Criteria approaches, as well as numerical indicators obtained by comparing modal strain energy and kinetic energy distributions. This analysis technique has been used to reliably identify correlated mode shapes for complex Finite Element Models that would otherwise be difficult to compare using traditional techniques. This improved approach also utilizes an adaptive mode tracking algorithm that allows for automated tracking when working with complex models and/or comparing a large group of models.

Finite-volume scheme for anisotropic diffusion

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

Es, Bram van, E-mail: bramiozo@gmail.com; FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, The Netherlands"1; Koren, Barry

In this paper, we apply a special finite-volume scheme, limited to smooth temperature distributions and Cartesian grids, to test the importance of connectivity of the finite volumes. The area of application is nuclear fusion plasma with field line aligned temperature gradients and extreme anisotropy. We apply the scheme to the anisotropic heat-conduction equation, and compare its results with those of existing finite-volume schemes for anisotropic diffusion. Also, we introduce a general model adaptation of the steady diffusion equation for extremely anisotropic diffusion problems with closed field lines.

Parallel goal-oriented adaptive finite element modeling for 3D electromagnetic exploration

NASA Astrophysics Data System (ADS)

Zhang, Y.; Key, K.; Ovall, J.; Holst, M.

2014-12-01

We present a parallel goal-oriented adaptive finite element method for accurate and efficient electromagnetic (EM) modeling of complex 3D structures. An unstructured tetrahedral mesh allows this approach to accommodate arbitrarily complex 3D conductivity variations and a priori known boundaries. The total electric field is approximated by the lowest order linear curl-conforming shape functions and the discretized finite element equations are solved by a sparse LU factorization. Accuracy of the finite element solution is achieved through adaptive mesh refinement that is performed iteratively until the solution converges to the desired accuracy tolerance. Refinement is guided by a goal-oriented error estimator that uses a dual-weighted residual method to optimize the mesh for accurate EM responses at the locations of the EM receivers. As a result, the mesh refinement is highly efficient since it only targets the elements where the inaccuracy of the solution corrupts the response at the possibly distant locations of the EM receivers. We compare the accuracy and efficiency of two approaches for estimating the primary residual error required at the core of this method: one uses local element and inter-element residuals and the other relies on solving a global residual system using a hierarchical basis. For computational efficiency our method follows the Bank-Holst algorithm for parallelization, where solutions are computed in subdomains of the original model. To resolve the load-balancing problem, this approach applies a spectral bisection method to divide the entire model into subdomains that have approximately equal error and the same number of receivers. The finite element solutions are then computed in parallel with each subdomain carrying out goal-oriented adaptive mesh refinement independently. We validate the newly developed algorithm by comparison with controlled-source EM solutions for 1D layered models and with 2D results from our earlier 2D goal oriented adaptive refinement code named MARE2DEM. We demonstrate the performance and parallel scaling of this algorithm on a medium-scale computing cluster with a marine controlled-source EM example that includes a 3D array of receivers located over a 3D model that includes significant seafloor bathymetry variations and a heterogeneous subsurface.

About an adaptively weighted Kaplan-Meier estimate.

PubMed

Plante, Jean-François

2009-09-01

The minimum averaged mean squared error nonparametric adaptive weights use data from m possibly different populations to infer about one population of interest. The definition of these weights is based on the properties of the empirical distribution function. We use the Kaplan-Meier estimate to let the weights accommodate right-censored data and use them to define the weighted Kaplan-Meier estimate. The proposed estimate is smoother than the usual Kaplan-Meier estimate and converges uniformly in probability to the target distribution. Simulations show that the performances of the weighted Kaplan-Meier estimate on finite samples exceed that of the usual Kaplan-Meier estimate. A case study is also presented.

Adaptively-refined overlapping grids for the numerical solution of systems of hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Brislawn, Kristi D.; Brown, David L.; Chesshire, Geoffrey S.; Saltzman, Jeffrey S.

1995-01-01

Adaptive mesh refinement (AMR) in conjunction with higher-order upwind finite-difference methods have been used effectively on a variety of problems in two and three dimensions. In this paper we introduce an approach for resolving problems that involve complex geometries in which resolution of boundary geometry is important. The complex geometry is represented by using the method of overlapping grids, while local resolution is obtained by refining each component grid with the AMR algorithm, appropriately generalized for this situation. The CMPGRD algorithm introduced by Chesshire and Henshaw is used to automatically generate the overlapping grid structure for the underlying mesh.

Adaptive Identification and Control of Flow-Induced Cavity Oscillations

NASA Technical Reports Server (NTRS)

Kegerise, M. A.; Cattafesta, L. N.; Ha, C.

2002-01-01

Progress towards an adaptive self-tuning regulator (STR) for the cavity tone problem is discussed in this paper. Adaptive system identification algorithms were applied to an experimental cavity-flow tested as a prerequisite to control. In addition, a simple digital controller and a piezoelectric bimorph actuator were used to demonstrate multiple tone suppression. The control tests at Mach numbers of 0.275, 0.40, and 0.60 indicated approx. = 7dB tone reductions at multiple frequencies. Several different adaptive system identification algorithms were applied at a single freestream Mach number of 0.275. Adaptive finite-impulse response (FIR) filters of orders up to N = 100 were found to be unsuitable for modeling the cavity flow dynamics. Adaptive infinite-impulse response (IIR) filters of comparable order better captured the system dynamics. Two recursive algorithms, the least-mean square (LMS) and the recursive-least square (RLS), were utilized to update the adaptive filter coefficients. Given the sample-time requirements imposed by the cavity flow dynamics, the computational simplicity of the least mean squares (LMS) algorithm is advantageous for real-time control.

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

NASA Astrophysics Data System (ADS)

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

2013-04-01

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

Modeling dam-break flows using finite volume method on unstructured grid

USDA-ARS?s Scientific Manuscript database

Two-dimensional shallow water models based on unstructured finite volume method and approximate Riemann solvers for computing the intercell fluxes have drawn growing attention because of their robustness, high adaptivity to complicated geometry and ability to simulate flows with mixed regimes and di...

A collocation--Galerkin finite element model of cardiac action potential propagation.

PubMed

Rogers, J M; McCulloch, A D

1994-08-01

A new computational method was developed for modeling the effects of the geometric complexity, nonuniform muscle fiber orientation, and material inhomogeneity of the ventricular wall on cardiac impulse propagation. The method was used to solve a modification to the FitzHugh-Nagumo system of equations. The geometry, local muscle fiber orientation, and material parameters of the domain were defined using linear Lagrange or cubic Hermite finite element interpolation. Spatial variations of time-dependent excitation and recovery variables were approximated using cubic Hermite finite element interpolation, and the governing finite element equations were assembled using the collocation method. To overcome the deficiencies of conventional collocation methods on irregular domains, Galerkin equations for the no-flux boundary conditions were used instead of collocation equations for the boundary degrees-of-freedom. The resulting system was evolved using an adaptive Runge-Kutta method. Converged two-dimensional simulations of normal propagation showed that this method requires less CPU time than a traditional finite difference discretization. The model also reproduced several other physiologic phenomena known to be important in arrhythmogenesis including: Wenckebach periodicity, slowed propagation and unidirectional block due to wavefront curvature, reentry around a fixed obstacle, and spiral wave reentry. In a new result, we observed wavespeed variations and block due to nonuniform muscle fiber orientation. The findings suggest that the finite element method is suitable for studying normal and pathological cardiac activation and has significant advantages over existing techniques.

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

Guo, Z.; Department of Applied Mathematics and Mechanics, University of Science and Technology Beijing, Beijing 100083; Lin, P.

In this paper, we investigate numerically a diffuse interface model for the Navier–Stokes equation with fluid–fluid interface when the fluids have different densities [48]. Under minor reformulation of the system, we show that there is a continuous energy law underlying the system, assuming that all variables have reasonable regularities. It is shown in the literature that an energy law preserving method will perform better for multiphase problems. Thus for the reformulated system, we design a C{sup 0} finite element method and a special temporal scheme where the energy law is preserved at the discrete level. Such a discrete energy lawmore » (almost the same as the continuous energy law) for this variable density two-phase flow model has never been established before with C{sup 0} finite element. A Newton method is introduced to linearise the highly non-linear system of our discretization scheme. Some numerical experiments are carried out using the adaptive mesh to investigate the scenario of coalescing and rising drops with differing density ratio. The snapshots for the evolution of the interface together with the adaptive mesh at different times are presented to show that the evolution, including the break-up/pinch-off of the drop, can be handled smoothly by our numerical scheme. The discrete energy functional for the system is examined to show that the energy law at the discrete level is preserved by our scheme.« less

A Robust and Scalable Software Library for Parallel Adaptive Refinement on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Lou, John Z.; Norton, Charles D.; Cwik, Thomas A.

1999-01-01

The design and implementation of Pyramid, a software library for performing parallel adaptive mesh refinement (PAMR) on unstructured meshes, is described. This software library can be easily used in a variety of unstructured parallel computational applications, including parallel finite element, parallel finite volume, and parallel visualization applications using triangular or tetrahedral meshes. The library contains a suite of well-designed and efficiently implemented modules that perform operations in a typical PAMR process. Among these are mesh quality control during successive parallel adaptive refinement (typically guided by a local-error estimator), parallel load-balancing, and parallel mesh partitioning using the ParMeTiS partitioner. The Pyramid library is implemented in Fortran 90 with an interface to the Message-Passing Interface (MPI) library, supporting code efficiency, modularity, and portability. An EM waveguide filter application, adaptively refined using the Pyramid library, is illustrated.

Adaptive eigenspace method for inverse scattering problems in the frequency domain

NASA Astrophysics Data System (ADS)

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

2017-02-01

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

DOUAR: A new three-dimensional creeping flow numerical model for the solution of geological problems

NASA Astrophysics Data System (ADS)

Braun, Jean; Thieulot, Cédric; Fullsack, Philippe; DeKool, Marthijn; Beaumont, Christopher; Huismans, Ritske

2008-12-01

We present a new finite element code for the solution of the Stokes and energy (or heat transport) equations that has been purposely designed to address crustal-scale to mantle-scale flow problems in three dimensions. Although it is based on an Eulerian description of deformation and flow, the code, which we named DOUAR ('Earth' in Breton language), has the ability to track interfaces and, in particular, the free surface, by using a dual representation based on a set of particles placed on the interface and the computation of a level set function on the nodes of the finite element grid, thus ensuring accuracy and efficiency. The code also makes use of a new method to compute the dynamic Delaunay triangulation connecting the particles based on non-Euclidian, curvilinear measure of distance, ensuring that the density of particles remains uniform and/or dynamically adapted to the curvature of the interface. The finite element discretization is based on a non-uniform, yet regular octree division of space within a unit cube that allows efficient adaptation of the finite element discretization, i.e. in regions of strong velocity gradient or high interface curvature. The finite elements are cubes (the leaves of the octree) in which a q1- p0 interpolation scheme is used. Nodal incompatibilities across faces separating elements of differing size are dealt with by introducing linear constraints among nodal degrees of freedom. Discontinuities in material properties across the interfaces are accommodated by the use of a novel method (which we called divFEM) to integrate the finite element equations in which the elemental volume is divided by a local octree to an appropriate depth (resolution). A variety of rheologies have been implemented including linear, non-linear and thermally activated creep and brittle (or plastic) frictional deformation. A simple smoothing operator has been defined to avoid checkerboard oscillations in pressure that tend to develop when using a highly irregular octree discretization and the tri-linear (or q1- p0) finite element. A three-dimensional cloud of particles is used to track material properties that depend on the integrated history of deformation (the integrated strain, for example); its density is variable and dynamically adapted to the computed flow. The large system of algebraic equations that results from the finite element discretization and linearization of the basic partial differential equations is solved using a multi-frontal massively parallel direct solver that can efficiently factorize poorly conditioned systems resulting from the highly non-linear rheology and the presence of the free surface. The code is almost entirely parallelized. We present example results including the onset of a Rayleigh-Taylor instability, the indentation of a rigid-plastic material and the formation of a fold beneath a free eroding surface, that demonstrate the accuracy, efficiency and appropriateness of the new code to solve complex geodynamical problems in three dimensions.

A parallel finite element simulator for ion transport through three-dimensional ion channel systems.

PubMed

Tu, Bin; Chen, Minxin; Xie, Yan; Zhang, Linbo; Eisenberg, Bob; Lu, Benzhuo

2013-09-15

A parallel finite element simulator, ichannel, is developed for ion transport through three-dimensional ion channel systems that consist of protein and membrane. The coordinates of heavy atoms of the protein are taken from the Protein Data Bank and the membrane is represented as a slab. The simulator contains two components: a parallel adaptive finite element solver for a set of Poisson-Nernst-Planck (PNP) equations that describe the electrodiffusion process of ion transport, and a mesh generation tool chain for ion channel systems, which is an essential component for the finite element computations. The finite element method has advantages in modeling irregular geometries and complex boundary conditions. We have built a tool chain to get the surface and volume mesh for ion channel systems, which consists of a set of mesh generation tools. The adaptive finite element solver in our simulator is implemented using the parallel adaptive finite element package Parallel Hierarchical Grid (PHG) developed by one of the authors, which provides the capability of doing large scale parallel computations with high parallel efficiency and the flexibility of choosing high order elements to achieve high order accuracy. The simulator is applied to a real transmembrane protein, the gramicidin A (gA) channel protein, to calculate the electrostatic potential, ion concentrations and I - V curve, with which both primitive and transformed PNP equations are studied and their numerical performances are compared. To further validate the method, we also apply the simulator to two other ion channel systems, the voltage dependent anion channel (VDAC) and α-Hemolysin (α-HL). The simulation results agree well with Brownian dynamics (BD) simulation results and experimental results. Moreover, because ionic finite size effects can be included in PNP model now, we also perform simulations using a size-modified PNP (SMPNP) model on VDAC and α-HL. It is shown that the size effects in SMPNP can effectively lead to reduced current in the channel, and the results are closer to BD simulation results. Copyright © 2013 Wiley Periodicals, Inc.

The Quantized Geometry of Visual Space: The Coherent Computation of Depth, Form, and Lightness. Revised Version.

DTIC Science & Technology

1982-08-01

of sensitivity with background luminance, and the finitE capacity of visual short term memory are discussed in terms of a small set of ...binocular rivalry, reflectance rivalry, Fechner’s paradox, decrease of threshold contrast with increased number of cycles in a grating pattern, hysteresis...adaptation level tuning, Weber law modulation, shift of sensitivity with background luminance, and the finite capacity of visual

Finite-element time-domain modeling of electromagnetic data in general dispersive medium using adaptive Padé series

NASA Astrophysics Data System (ADS)

Cai, Hongzhu; Hu, Xiangyun; Xiong, Bin; Zhdanov, Michael S.

2017-12-01

The induced polarization (IP) method has been widely used in geophysical exploration to identify the chargeable targets such as mineral deposits. The inversion of the IP data requires modeling the IP response of 3D dispersive conductive structures. We have developed an edge-based finite-element time-domain (FETD) modeling method to simulate the electromagnetic (EM) fields in 3D dispersive medium. We solve the vector Helmholtz equation for total electric field using the edge-based finite-element method with an unstructured tetrahedral mesh. We adopt the backward propagation Euler method, which is unconditionally stable, with semi-adaptive time stepping for the time domain discretization. We use the direct solver based on a sparse LU decomposition to solve the system of equations. We consider the Cole-Cole model in order to take into account the frequency-dependent conductivity dispersion. The Cole-Cole conductivity model in frequency domain is expanded using a truncated Padé series with adaptive selection of the center frequency of the series for early and late time. This approach can significantly increase the accuracy of FETD modeling.

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

NASA Technical Reports Server (NTRS)

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

1996-01-01

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

A framework for grand scale parallelization of the combined finite discrete element method in 2d

NASA Astrophysics Data System (ADS)

Lei, Z.; Rougier, E.; Knight, E. E.; Munjiza, A.

2014-09-01

Within the context of rock mechanics, the Combined Finite-Discrete Element Method (FDEM) has been applied to many complex industrial problems such as block caving, deep mining techniques (tunneling, pillar strength, etc.), rock blasting, seismic wave propagation, packing problems, dam stability, rock slope stability, rock mass strength characterization problems, etc. The reality is that most of these were accomplished in a 2D and/or single processor realm. In this work a hardware independent FDEM parallelization framework has been developed using the Virtual Parallel Machine for FDEM, (V-FDEM). With V-FDEM, a parallel FDEM software can be adapted to different parallel architecture systems ranging from just a few to thousands of cores.

Adaptive Grid Generation for Numerical Solution of Partial Differential Equations.

DTIC Science & Technology

1983-12-01

numerical solution of fluid dynamics problems is presented. However, the method is applicable to the numer- ical evaluation of any partial differential...emphasis is being placed on numerical solution of the governing differential equations by finite difference methods . In the past two decades, considerable...original equations presented in that paper. The solution of the second problem is more difficult. 2 The method of Thompson et al. provides control for

Self-consistent field theory simulations of polymers on arbitrary domains

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

Ouaknin, Gaddiel, E-mail: gaddielouaknin@umail.ucsb.edu; Laachi, Nabil; Delaney, Kris

2016-12-15

We introduce a framework for simulating the mesoscale self-assembly of block copolymers in arbitrary confined geometries subject to Neumann boundary conditions. We employ a hybrid finite difference/volume approach to discretize the mean-field equations on an irregular domain represented implicitly by a level-set function. The numerical treatment of the Neumann boundary conditions is sharp, i.e. it avoids an artificial smearing in the irregular domain boundary. This strategy enables the study of self-assembly in confined domains and enables the computation of physically meaningful quantities at the domain interface. In addition, we employ adaptive grids encoded with Quad-/Oc-trees in parallel to automatically refinemore » the grid where the statistical fields vary rapidly as well as at the boundary of the confined domain. This approach results in a significant reduction in the number of degrees of freedom and makes the simulations in arbitrary domains using effective boundary conditions computationally efficient in terms of both speed and memory requirement. Finally, in the case of regular periodic domains, where pseudo-spectral approaches are superior to finite differences in terms of CPU time and accuracy, we use the adaptive strategy to store chain propagators, reducing the memory footprint without loss of accuracy in computed physical observables.« less

Acoustic reverse-time migration using GPU card and POSIX thread based on the adaptive optimal finite-difference scheme and the hybrid absorbing boundary condition

NASA Astrophysics Data System (ADS)

Cai, Xiaohui; Liu, Yang; Ren, Zhiming

2018-06-01

Reverse-time migration (RTM) is a powerful tool for imaging geologically complex structures such as steep-dip and subsalt. However, its implementation is quite computationally expensive. Recently, as a low-cost solution, the graphic processing unit (GPU) was introduced to improve the efficiency of RTM. In the paper, we develop three ameliorative strategies to implement RTM on GPU card. First, given the high accuracy and efficiency of the adaptive optimal finite-difference (FD) method based on least squares (LS) on central processing unit (CPU), we study the optimal LS-based FD method on GPU. Second, we develop the CPU-based hybrid absorbing boundary condition (ABC) to the GPU-based one by addressing two issues of the former when introduced to GPU card: time-consuming and chaotic threads. Third, for large-scale data, the combinatorial strategy for optimal checkpointing and efficient boundary storage is introduced for the trade-off between memory and recomputation. To save the time of communication between host and disk, the portable operating system interface (POSIX) thread is utilized to create the other CPU core at the checkpoints. Applications of the three strategies on GPU with the compute unified device architecture (CUDA) programming language in RTM demonstrate their efficiency and validity.

Nonlinear Conservation Laws and Finite Volume Methods

NASA Astrophysics Data System (ADS)

Leveque, Randall J.

Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References

Adaptive-gain fast super-twisting sliding mode fault tolerant control for a reusable launch vehicle in reentry phase.

PubMed

Zhang, Yao; Tang, Shengjing; Guo, Jie

2017-11-01

In this paper, a novel adaptive-gain fast super-twisting (AGFST) sliding mode attitude control synthesis is carried out for a reusable launch vehicle subject to actuator faults and unknown disturbances. According to the fast nonsingular terminal sliding mode surface (FNTSMS) and adaptive-gain fast super-twisting algorithm, an adaptive fault tolerant control law for the attitude stabilization is derived to protect against the actuator faults and unknown uncertainties. Firstly, a second-order nonlinear control-oriented model for the RLV is established by feedback linearization method. And on the basis a fast nonsingular terminal sliding mode (FNTSM) manifold is designed, which provides fast finite-time global convergence and avoids singularity problem as well as chattering phenomenon. Based on the merits of the standard super-twisting (ST) algorithm and fast reaching law with adaption, a novel adaptive-gain fast super-twisting (AGFST) algorithm is proposed for the finite-time fault tolerant attitude control problem of the RLV without any knowledge of the bounds of uncertainties and actuator faults. The important feature of the AGFST algorithm includes non-overestimating the values of the control gains and faster convergence speed than the standard ST algorithm. A formal proof of the finite-time stability of the closed-loop system is derived using the Lyapunov function technique. An estimation of the convergence time and accurate expression of convergence region are also provided. Finally, simulations are presented to illustrate the effectiveness and superiority of the proposed control scheme. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Object-oriented philosophy in designing adaptive finite-element package for 3D elliptic deferential equations

NASA Astrophysics Data System (ADS)

Zhengyong, R.; Jingtian, T.; Changsheng, L.; Xiao, X.

2007-12-01

Although adaptive finite-element (AFE) analysis is becoming more and more focused in scientific and engineering fields, its efficient implementations are remain to be a discussed problem as its more complex procedures. In this paper, we propose a clear C++ framework implementation to show the powerful properties of Object-oriented philosophy (OOP) in designing such complex adaptive procedure. In terms of the modal functions of OOP language, the whole adaptive system is divided into several separate parts such as the mesh generation or refinement, a-posterior error estimator, adaptive strategy and the final post processing. After proper designs are locally performed on these separate modals, a connected framework of adaptive procedure is formed finally. Based on the general elliptic deferential equation, little efforts should be added in the adaptive framework to do practical simulations. To show the preferable properties of OOP adaptive designing, two numerical examples are tested. The first one is the 3D direct current resistivity problem in which the powerful framework is efficiently shown as only little divisions are added. And then, in the second induced polarization£¨IP£©exploration case, new adaptive procedure is easily added which adequately shows the strong extendibility and re-usage of OOP language. Finally we believe based on the modal framework adaptive implementation by OOP methodology, more advanced adaptive analysis system will be available in future.

Stable Direct Adaptive Control of Linear Infinite-dimensional Systems Using a Command Generator Tracker Approach

NASA Technical Reports Server (NTRS)

Balas, M. J.; Kaufman, H.; Wen, J.

1985-01-01

A command generator tracker approach to model following contol of linear distributed parameter systems (DPS) whose dynamics are described on infinite dimensional Hilbert spaces is presented. This method generates finite dimensional controllers capable of exponentially stable tracking of the reference trajectories when certain ideal trajectories are known to exist for the open loop DPS; we present conditions for the existence of these ideal trajectories. An adaptive version of this type of controller is also presented and shown to achieve (in some cases, asymptotically) stable finite dimensional control of the infinite dimensional DPS.

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

Besse, Nicolas; Latu, Guillaume; Ghizzo, Alain

In this paper we present a new method for the numerical solution of the relativistic Vlasov-Maxwell system on a phase-space grid using an adaptive semi-Lagrangian method. The adaptivity is performed through a wavelet multiresolution analysis, which gives a powerful and natural refinement criterion based on the local measurement of the approximation error and regularity of the distribution function. Therefore, the multiscale expansion of the distribution function allows to get a sparse representation of the data and thus save memory space and CPU time. We apply this numerical scheme to reduced Vlasov-Maxwell systems arising in laser-plasma physics. Interaction of relativistically strongmore » laser pulses with overdense plasma slabs is investigated. These Vlasov simulations revealed a rich variety of phenomena associated with the fast particle dynamics induced by electromagnetic waves as electron trapping, particle acceleration, and electron plasma wavebreaking. However, the wavelet based adaptive method that we developed here, does not yield significant improvements compared to Vlasov solvers on a uniform mesh due to the substantial overhead that the method introduces. Nonetheless they might be a first step towards more efficient adaptive solvers based on different ideas for the grid refinement or on a more efficient implementation. Here the Vlasov simulations are performed in a two-dimensional phase-space where the development of thin filaments, strongly amplified by relativistic effects requires an important increase of the total number of points of the phase-space grid as they get finer as time goes on. The adaptive method could be more useful in cases where these thin filaments that need to be resolved are a very small fraction of the hyper-volume, which arises in higher dimensions because of the surface-to-volume scaling and the essentially one-dimensional structure of the filaments. Moreover, the main way to improve the efficiency of the adaptive method is to increase the local character in phase-space of the numerical scheme, by considering multiscale reconstruction with more compact support and by replacing the semi-Lagrangian method with more local - in space - numerical scheme as compact finite difference schemes, discontinuous-Galerkin method or finite element residual schemes which are well suited for parallel domain decomposition techniques.« less

Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size.

PubMed

Schwalger, Tilo; Deger, Moritz; Gerstner, Wulfram

2017-04-01

Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacting populations at the mesoscopic scale starting from a microscopic model of randomly connected generalized integrate-and-fire neuron models. Each population consists of 50-2000 neurons of the same type but different populations account for different neuron types. The stochastic population equations that we find reveal how spike-history effects in single-neuron dynamics such as refractoriness and adaptation interact with finite-size fluctuations on the population level. Efficient integration of the stochastic mesoscopic equations reproduces the statistical behavior of the population activities obtained from microscopic simulations of a full spiking neural network model. The theory describes nonlinear emergent dynamics such as finite-size-induced stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. The mesoscopic equations are employed to rapidly integrate a model of a cortical microcircuit consisting of eight neuron types, which allows us to predict spontaneous population activities as well as evoked responses to thalamic input. Our theory establishes a general framework for modeling finite-size neural population dynamics based on single cell and synapse parameters and offers an efficient approach to analyzing cortical circuits and computations.

A freestream-preserving fourth-order finite-volume method in mapped coordinates with adaptive-mesh refinement

DOE PAGES

Guzik, Stephen M.; Gao, Xinfeng; Owen, Landon D.; ...

2015-12-20

We present a fourth-order accurate finite-volume method for solving time-dependent hyperbolic systems of conservation laws on mapped grids that are adaptively refined in space and time. Some novel considerations for formulating the semi-discrete system of equations in computational space are combined with detailed mechanisms for accommodating the adapting grids. Furthermore, these considerations ensure that conservation is maintained and that the divergence of a constant vector field is always zero (freestream-preservation property). The solution in time is advanced with a fourth-order Runge-Kutta method. A series of tests verifies that the expected accuracy is achieved in smooth flows and the solution ofmore » a Mach reflection problem demonstrates the effectiveness of the algorithm in resolving strong discontinuities.« less

Finite element analysis in fluids; Proceedings of the Seventh International Conference on Finite Element Methods in Flow Problems, University of Alabama, Huntsville, Apr. 3-7, 1989

NASA Technical Reports Server (NTRS)

Chung, T. J. (Editor); Karr, Gerald R. (Editor)

1989-01-01

Recent advances in computational fluid dynamics are examined in reviews and reports, with an emphasis on finite-element methods. Sections are devoted to adaptive meshes, atmospheric dynamics, combustion, compressible flows, control-volume finite elements, crystal growth, domain decomposition, EM-field problems, FDM/FEM, and fluid-structure interactions. Consideration is given to free-boundary problems with heat transfer, free surface flow, geophysical flow problems, heat and mass transfer, high-speed flow, incompressible flow, inverse design methods, MHD problems, the mathematics of finite elements, and mesh generation. Also discussed are mixed finite elements, multigrid methods, non-Newtonian fluids, numerical dissipation, parallel vector processing, reservoir simulation, seepage, shallow-water problems, spectral methods, supercomputer architectures, three-dimensional problems, and turbulent flows.

Parallel deterministic neutronics with AMR in 3D

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

Clouse, C.; Ferguson, J.; Hendrickson, C.

1997-12-31

AMTRAN, a three dimensional Sn neutronics code with adaptive mesh refinement (AMR) has been parallelized over spatial domains and energy groups and runs on the Meiko CS-2 with MPI message passing. Block refined AMR is used with linear finite element representations for the fluxes, which allows for a straight forward interpretation of fluxes at block interfaces with zoning differences. The load balancing algorithm assumes 8 spatial domains, which minimizes idle time among processors.

Three Dimensional Grid Generation for Complex Configurations - Recent Progress

DTIC Science & Technology

1988-03-01

Navier/Stokes finite difference calculations currently of interest. It has been amply demonstrated that the viability of a numerical solution depends...such as advanced fighters or logistic transports, where a multiblock mesh, for example, is necessary. There exist numerous reports and books on the...MESHES I 3.10 ADAPTIVE GRID SCHEMES 10 3.11 REFERENCES 12 4. CONTRIBUTIONS 13 4.1 SOLICITATION AND OVERVIEW 13 4.2 LESSONS LEARNED IN THE MESH

Strip Yield Model Numerical Application to Different Geometries and Loading Conditions

NASA Technical Reports Server (NTRS)

Hatamleh, Omar; Forman, Royce; Shivakumar, Venkataraman; Lyons, Jed

2006-01-01

A new numerical method based on the strip-yield analysis approach was developed for calculating the Crack Tip Opening Displacement (CTOD). This approach can be applied for different crack configurations having infinite and finite geometries, and arbitrary applied loading conditions. The new technique adapts the boundary element / dislocation density method to obtain crack-face opening displacements at any point on a crack, and succeeds by obtaining requisite values as a series of definite integrals, the functional parts of each being evaluated exactly in a closed form.

Axioms of adaptivity

PubMed Central

Carstensen, C.; Feischl, M.; Page, M.; Praetorius, D.

2014-01-01

This paper aims first at a simultaneous axiomatic presentation of the proof of optimal convergence rates for adaptive finite element methods and second at some refinements of particular questions like the avoidance of (discrete) lower bounds, inexact solvers, inhomogeneous boundary data, or the use of equivalent error estimators. Solely four axioms guarantee the optimality in terms of the error estimators. Compared to the state of the art in the temporary literature, the improvements of this article can be summarized as follows: First, a general framework is presented which covers the existing literature on optimality of adaptive schemes. The abstract analysis covers linear as well as nonlinear problems and is independent of the underlying finite element or boundary element method. Second, efficiency of the error estimator is neither needed to prove convergence nor quasi-optimal convergence behavior of the error estimator. In this paper, efficiency exclusively characterizes the approximation classes involved in terms of the best-approximation error and data resolution and so the upper bound on the optimal marking parameters does not depend on the efficiency constant. Third, some general quasi-Galerkin orthogonality is not only sufficient, but also necessary for the R-linear convergence of the error estimator, which is a fundamental ingredient in the current quasi-optimality analysis due to Stevenson 2007. Finally, the general analysis allows for equivalent error estimators and inexact solvers as well as different non-homogeneous and mixed boundary conditions. PMID:25983390

Algorithms for computing solvents of unilateral second-order matrix polynomials over prime finite fields using lambda-matrices

NASA Astrophysics Data System (ADS)

Burtyka, Filipp

2018-01-01

The paper considers algorithms for finding diagonalizable and non-diagonalizable roots (so called solvents) of monic arbitrary unilateral second-order matrix polynomial over prime finite field. These algorithms are based on polynomial matrices (lambda-matrices). This is an extension of existing general methods for computing solvents of matrix polynomials over field of complex numbers. We analyze how techniques for complex numbers can be adapted for finite field and estimate asymptotic complexity of the obtained algorithms.

Error analysis and correction of discrete solutions from finite element codes

NASA Technical Reports Server (NTRS)

Thurston, G. A.; Stein, P. A.; Knight, N. F., Jr.; Reissner, J. E.

1984-01-01

Many structures are an assembly of individual shell components. Therefore, results for stresses and deflections from finite element solutions for each shell component should agree with the equations of shell theory. This paper examines the problem of applying shell theory to the error analysis and the correction of finite element results. The general approach to error analysis and correction is discussed first. Relaxation methods are suggested as one approach to correcting finite element results for all or parts of shell structures. Next, the problem of error analysis of plate structures is examined in more detail. The method of successive approximations is adapted to take discrete finite element solutions and to generate continuous approximate solutions for postbuckled plates. Preliminary numerical results are included.

Modeling of heterogeneous elastic materials by the multiscale hp-adaptive finite element method

NASA Astrophysics Data System (ADS)

Klimczak, Marek; Cecot, Witold

2018-01-01

We present an enhancement of the multiscale finite element method (MsFEM) by combining it with the hp-adaptive FEM. Such a discretization-based homogenization technique is a versatile tool for modeling heterogeneous materials with fast oscillating elasticity coefficients. No assumption on periodicity of the domain is required. In order to avoid direct, so-called overkill mesh computations, a coarse mesh with effective stiffness matrices is used and special shape functions are constructed to account for the local heterogeneities at the micro resolution. The automatic adaptivity (hp-type at the macro resolution and h-type at the micro resolution) increases efficiency of computation. In this paper details of the modified MsFEM are presented and a numerical test performed on a Fichera corner domain is presented in order to validate the proposed approach.

Finite Element Analysis of Adaptive-Stiffening and Shape-Control SMA Hybrid Composites

NASA Technical Reports Server (NTRS)

Gao, Xiu-Jie; Turner, Travis L.; Burton, Deborah; Brinson, L. Catherine

2005-01-01

The usage of shape memory materials has extended rapidly to many fields, including medical devices, actuators, composites, structures and MEMS devices. For these various applications, shape memory alloys (SMAs) are available in various forms: bulk, wire, ribbon, thin film, and porous. In this work, the focus is on SMA hybrid composites with adaptive-stiffening or morphing functions. These composites are created by using SMA ribbons or wires embedded in a polymeric based composite panel/beam. Adaptive stiffening or morphing is activated via selective resistance heating or uniform thermal loads. To simulate the thermomechanical behavior of these composites, a SMA model was implemented using ABAQUS user element interface and finite element simulations of the systems were studied. Several examples are presented which show that the implemented model can be a very useful design and simulation tool for SMA hybrid composites.

On Accuracy of Adaptive Grid Methods for Captured Shocks

NASA Technical Reports Server (NTRS)

Yamaleev, Nail K.; Carpenter, Mark H.

2002-01-01

The accuracy of two grid adaptation strategies, grid redistribution and local grid refinement, is examined by solving the 2-D Euler equations for the supersonic steady flow around a cylinder. Second- and fourth-order linear finite difference shock-capturing schemes, based on the Lax-Friedrichs flux splitting, are used to discretize the governing equations. The grid refinement study shows that for the second-order scheme, neither grid adaptation strategy improves the numerical solution accuracy compared to that calculated on a uniform grid with the same number of grid points. For the fourth-order scheme, the dominant first-order error component is reduced by the grid adaptation, while the design-order error component drastically increases because of the grid nonuniformity. As a result, both grid adaptation techniques improve the numerical solution accuracy only on the coarsest mesh or on very fine grids that are seldom found in practical applications because of the computational cost involved. Similar error behavior has been obtained for the pressure integral across the shock. A simple analysis shows that both grid adaptation strategies are not without penalties in the numerical solution accuracy. Based on these results, a new grid adaptation criterion for captured shocks is proposed.

Parallel processors and nonlinear structural dynamics algorithms and software

NASA Technical Reports Server (NTRS)

Belytschko, Ted; Gilbertsen, Noreen D.; Neal, Mark O.; Plaskacz, Edward J.

1989-01-01

The adaptation of a finite element program with explicit time integration to a massively parallel SIMD (single instruction multiple data) computer, the CONNECTION Machine is described. The adaptation required the development of a new algorithm, called the exchange algorithm, in which all nodal variables are allocated to the element with an exchange of nodal forces at each time step. The architectural and C* programming language features of the CONNECTION Machine are also summarized. Various alternate data structures and associated algorithms for nonlinear finite element analysis are discussed and compared. Results are presented which demonstrate that the CONNECTION Machine is capable of outperforming the CRAY XMP/14.

A novel adaptive finite time controller for bilateral teleoperation system

NASA Astrophysics Data System (ADS)

Wang, Ziwei; Chen, Zhang; Liang, Bin; Zhang, Bo

2018-03-01

Most bilateral teleoperation researches focus on the system stability within time-delays. However, practical teleoperation tasks require high performances besides system stability, such as convergence rate and accuracy. This paper investigates bilateral teleoperation controller design with transient performances. To ensure the transient performances and system stability simultaneously, an adaptive non-singular fast terminal mode controller is proposed to achieve practical finite-time stability considering system uncertainties and time delays. In addition, a novel switching scheme is introduced, in which way the singularity problem of conventional terminal sliding manifold is avoided. Finally, numerical simulations demonstrate the effectiveness and validity of the proposed method.

Heating and Large Scale Dynamics of the Solar Corona

NASA Technical Reports Server (NTRS)

Schnack, Dalton D.

2000-01-01

The effort was concentrated in the areas: coronal heating mechanism, unstructured adaptive grid algorithms, numerical modeling of magnetic reconnection in the MRX experiment: effect of toroidal magnetic field and finite pressure, effect of OHMIC heating and vertical magnetic field, effect of dynamic MESH adaption.

A mass-conservative adaptive FAS multigrid solver for cell-centered finite difference methods on block-structured, locally-cartesian grids

NASA Astrophysics Data System (ADS)

Feng, Wenqiang; Guo, Zhenlin; Lowengrub, John S.; Wise, Steven M.

2018-01-01

We present a mass-conservative full approximation storage (FAS) multigrid solver for cell-centered finite difference methods on block-structured, locally cartesian grids. The algorithm is essentially a standard adaptive FAS (AFAS) scheme, but with a simple modification that comes in the form of a mass-conservative correction to the coarse-level force. This correction is facilitated by the creation of a zombie variable, analogous to a ghost variable, but defined on the coarse grid and lying under the fine grid refinement patch. We show that a number of different types of fine-level ghost cell interpolation strategies could be used in our framework, including low-order linear interpolation. In our approach, the smoother, prolongation, and restriction operations need never be aware of the mass conservation conditions at the coarse-fine interface. To maintain global mass conservation, we need only modify the usual FAS algorithm by correcting the coarse-level force function at points adjacent to the coarse-fine interface. We demonstrate through simulations that the solver converges geometrically, at a rate that is h-independent, and we show the generality of the solver, applying it to several nonlinear, time-dependent, and multi-dimensional problems. In several tests, we show that second-order asymptotic (h → 0) convergence is observed for the discretizations, provided that (1) at least linear interpolation of the ghost variables is employed, and (2) the mass conservation corrections are applied to the coarse-level force term.

Finite elements: Theory and application

NASA Technical Reports Server (NTRS)

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

1988-01-01

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

A numerical study of adaptive space and time discretisations for Gross–Pitaevskii equations

PubMed Central

Thalhammer, Mechthild; Abhau, Jochen

2012-01-01

As a basic principle, benefits of adaptive discretisations are an improved balance between required accuracy and efficiency as well as an enhancement of the reliability of numerical computations. In this work, the capacity of locally adaptive space and time discretisations for the numerical solution of low-dimensional nonlinear Schrödinger equations is investigated. The considered model equation is related to the time-dependent Gross–Pitaevskii equation arising in the description of Bose–Einstein condensates in dilute gases. The performance of the Fourier-pseudo spectral method constrained to uniform meshes versus the locally adaptive finite element method and of higher-order exponential operator splitting methods with variable time stepsizes is studied. Numerical experiments confirm that a local time stepsize control based on a posteriori local error estimators or embedded splitting pairs, respectively, is effective in different situations with an enhancement either in efficiency or reliability. As expected, adaptive time-splitting schemes combined with fast Fourier transform techniques are favourable regarding accuracy and efficiency when applied to Gross–Pitaevskii equations with a defocusing nonlinearity and a mildly varying regular solution. However, the numerical solution of nonlinear Schrödinger equations in the semi-classical regime becomes a demanding task. Due to the highly oscillatory and nonlinear nature of the problem, the spatial mesh size and the time increments need to be of the size of the decisive parameter 0<ε≪1, especially when it is desired to capture correctly the quantitative behaviour of the wave function itself. The required high resolution in space constricts the feasibility of numerical computations for both, the Fourier pseudo-spectral and the finite element method. Nevertheless, for smaller parameter values locally adaptive time discretisations facilitate to determine the time stepsizes sufficiently small in order that the numerical approximation captures correctly the behaviour of the analytical solution. Further illustrations for Gross–Pitaevskii equations with a focusing nonlinearity or a sharp Gaussian as initial condition, respectively, complement the numerical study. PMID:25550676

A numerical study of adaptive space and time discretisations for Gross-Pitaevskii equations.

PubMed

Thalhammer, Mechthild; Abhau, Jochen

2012-08-15

As a basic principle, benefits of adaptive discretisations are an improved balance between required accuracy and efficiency as well as an enhancement of the reliability of numerical computations. In this work, the capacity of locally adaptive space and time discretisations for the numerical solution of low-dimensional nonlinear Schrödinger equations is investigated. The considered model equation is related to the time-dependent Gross-Pitaevskii equation arising in the description of Bose-Einstein condensates in dilute gases. The performance of the Fourier-pseudo spectral method constrained to uniform meshes versus the locally adaptive finite element method and of higher-order exponential operator splitting methods with variable time stepsizes is studied. Numerical experiments confirm that a local time stepsize control based on a posteriori local error estimators or embedded splitting pairs, respectively, is effective in different situations with an enhancement either in efficiency or reliability. As expected, adaptive time-splitting schemes combined with fast Fourier transform techniques are favourable regarding accuracy and efficiency when applied to Gross-Pitaevskii equations with a defocusing nonlinearity and a mildly varying regular solution. However, the numerical solution of nonlinear Schrödinger equations in the semi-classical regime becomes a demanding task. Due to the highly oscillatory and nonlinear nature of the problem, the spatial mesh size and the time increments need to be of the size of the decisive parameter [Formula: see text], especially when it is desired to capture correctly the quantitative behaviour of the wave function itself. The required high resolution in space constricts the feasibility of numerical computations for both, the Fourier pseudo-spectral and the finite element method. Nevertheless, for smaller parameter values locally adaptive time discretisations facilitate to determine the time stepsizes sufficiently small in order that the numerical approximation captures correctly the behaviour of the analytical solution. Further illustrations for Gross-Pitaevskii equations with a focusing nonlinearity or a sharp Gaussian as initial condition, respectively, complement the numerical study.

A multigrid method for steady Euler equations on unstructured adaptive grids

NASA Technical Reports Server (NTRS)

Riemslagh, Kris; Dick, Erik

1993-01-01

A flux-difference splitting type algorithm is formulated for the steady Euler equations on unstructured grids. The polynomial flux-difference splitting technique is used. A vertex-centered finite volume method is employed on a triangular mesh. The multigrid method is in defect-correction form. A relaxation procedure with a first order accurate inner iteration and a second-order correction performed only on the finest grid, is used. A multi-stage Jacobi relaxation method is employed as a smoother. Since the grid is unstructured a Jacobi type is chosen. The multi-staging is necessary to provide sufficient smoothing properties. The domain is discretized using a Delaunay triangular mesh generator. Three grids with more or less uniform distribution of nodes but with different resolution are generated by successive refinement of the coarsest grid. Nodes of coarser grids appear in the finer grids. The multigrid method is started on these grids. As soon as the residual drops below a threshold value, an adaptive refinement is started. The solution on the adaptively refined grid is accelerated by a multigrid procedure. The coarser multigrid grids are generated by successive coarsening through point removement. The adaption cycle is repeated a few times. Results are given for the transonic flow over a NACA-0012 airfoil.

Parameter estimation in IMEX-trigonometrically fitted methods for the numerical solution of reaction-diffusion problems

NASA Astrophysics Data System (ADS)

D'Ambrosio, Raffaele; Moccaldi, Martina; Paternoster, Beatrice

2018-05-01

In this paper, an adapted numerical scheme for reaction-diffusion problems generating periodic wavefronts is introduced. Adapted numerical methods for such evolutionary problems are specially tuned to follow prescribed qualitative behaviors of the solutions, making the numerical scheme more accurate and efficient as compared with traditional schemes already known in the literature. Adaptation through the so-called exponential fitting technique leads to methods whose coefficients depend on unknown parameters related to the dynamics and aimed to be numerically computed. Here we propose a strategy for a cheap and accurate estimation of such parameters, which consists essentially in minimizing the leading term of the local truncation error whose expression is provided in a rigorous accuracy analysis. In particular, the presented estimation technique has been applied to a numerical scheme based on combining an adapted finite difference discretization in space with an implicit-explicit time discretization. Numerical experiments confirming the effectiveness of the approach are also provided.

The Simulation of Magnetorheological Elastomers Adaptive Tuned Dynamic Vibration Absorber for Automobile Engine Vibration Control

NASA Astrophysics Data System (ADS)

Zhang, X. C.; Zhang, X. Z.; Li, W. H.; Liu, B.; Gong, X. L.; Zhang, P. Q.

The aim of this article is to investigate the use of a Dynamic Vibration Absorber to control vibration of engine by using simulation. Traditional means of vibration control have involved the use of passive and more recently, active methods. This study is different in that it involves an adaptive component in the design of vibration absorber using magnetorheological elastomers (MREs) as the adaptive spring. MREs are kind of novel smart material whose shear modulus can be controlled by applied magnetic field. In this paper, the vibration mode of a simple model of automobile engine is simulated by Finite Element Method (FEM) analysis. Based on the analysis, the MREs Adaptive Tuned Dynamic Vibration Absorber (ATDVA) is presented to reduce the vibration of the engine. Simulation result indicate that the control frequency of ATDVA can be changed by modifing the shear modulus of MREs and the vibraion reduction efficiency of ATDVA are also evaluated by FEM analysis.

TranAir: A full-potential, solution-adaptive, rectangular grid code for predicting subsonic, transonic, and supersonic flows about arbitrary configurations. Theory document

NASA Technical Reports Server (NTRS)

Johnson, F. T.; Samant, S. S.; Bieterman, M. B.; Melvin, R. G.; Young, D. P.; Bussoletti, J. E.; Hilmes, C. L.

1992-01-01

A new computer program, called TranAir, for analyzing complex configurations in transonic flow (with subsonic or supersonic freestream) was developed. This program provides accurate and efficient simulations of nonlinear aerodynamic flows about arbitrary geometries with the ease and flexibility of a typical panel method program. The numerical method implemented in TranAir is described. The method solves the full potential equation subject to a set of general boundary conditions and can handle regions with differing total pressure and temperature. The boundary value problem is discretized using the finite element method on a locally refined rectangular grid. The grid is automatically constructed by the code and is superimposed on the boundary described by networks of panels; thus no surface fitted grid generation is required. The nonlinear discrete system arising from the finite element method is solved using a preconditioned Krylov subspace method embedded in an inexact Newton method. The solution is obtained on a sequence of successively refined grids which are either constructed adaptively based on estimated solution errors or are predetermined based on user inputs. Many results obtained by using TranAir to analyze aerodynamic configurations are presented.

Reconstruction de defauts a partir de donnees issues de capteurs a courants de foucault avec modele direct differentiel

NASA Astrophysics Data System (ADS)

Trillon, Adrien

Eddy current tomography can be employed to caracterize flaws in metal plates in steam generators of nuclear power plants. Our goal is to evaluate a map of the relative conductivity that represents the flaw. This nonlinear ill-posed problem is difficult to solve and a forward model is needed. First, we studied existing forward models to chose the one that is the most adapted to our case. Finite difference and finite element methods matched very good to our application. We adapted contrast source inversion (CSI) type methods to the chosen model and a new criterion was proposed. These methods are based on the minimization of the weighted errors of the model equations, coupling and observation. They allow an error on the equations. It appeared that reconstruction quality grows with the decay of the error on the coupling equation. We resorted to augmented Lagrangian techniques to constrain coupling equation and to avoid conditioning problems. In order to overcome the ill-posed character of the problem, prior information was introduced about the shape of the flaw and the values of the relative conductivity. Efficiency of the methods are illustrated with simulated flaws in 2D case.

Testing convergent and parallel adaptations in talpids humeral mechanical performance by means of geometric morphometrics and finite element analysis.

PubMed

Piras, P; Sansalone, G; Teresi, L; Kotsakis, T; Colangelo, P; Loy, A

2012-07-01

The shape and mechanical performance in Talpidae humeri were studied by means of Geometric Morphometrics and Finite Element Analysis, including both extinct and extant taxa. The aim of this study was to test whether the ability to dig, quantified by humerus mechanical performance, was characterized by convergent or parallel adaptations in different clades of complex tunnel digger within Talpidae, that is, Talpinae+Condylura (monophyletic) and some complex tunnel diggers not belonging to this clade. Our results suggest that the pattern underlying Talpidae humerus evolution is evolutionary parallelism. However, this insight changed to true convergence when we tested an alternative phylogeny based on molecular data, with Condylura moved to a more basal phylogenetic position. Shape and performance analyses, as well as specific comparative methods, provided strong evidence that the ability to dig complex tunnels reached a functional optimum in distantly related taxa. This was also confirmed by the lower phenotypic variance in complex tunnel digger taxa, compared to non-complex tunnel diggers. Evolutionary rates of phenotypic change showed a smooth deceleration in correspondence with the most recent common ancestor of the Talpinae+Condylura clade. Copyright © 2012 Wiley Periodicals, Inc.

Auto-adaptive finite element meshes

NASA Technical Reports Server (NTRS)

Richter, Roland; Leyland, Penelope

1995-01-01

Accurate capturing of discontinuities within compressible flow computations is achieved by coupling a suitable solver with an automatic adaptive mesh algorithm for unstructured triangular meshes. The mesh adaptation procedures developed rely on non-hierarchical dynamical local refinement/derefinement techniques, which hence enable structural optimization as well as geometrical optimization. The methods described are applied for a number of the ICASE test cases are particularly interesting for unsteady flow simulations.

Introducing a model of pairing based on base pair specific interactions between identical DNA sequences

NASA Astrophysics Data System (ADS)

(O' Lee, Dominic J.

2018-02-01

At present, there have been suggested two types of physical mechanism that may facilitate preferential pairing between DNA molecules, with identical or similar base pair texts, without separation of base pairs. One mechanism solely relies on base pair specific patterns of helix distortion being the same on the two molecules, discussed extensively in the past. The other mechanism proposes that there are preferential interactions between base pairs of the same composition. We introduce a model, built on this second mechanism, where both thermal stretching and twisting fluctuations are included, as well as the base pair specific helix distortions. Firstly, we consider an approximation for weak pairing interactions, or short molecules. This yields a dependence of the energy on the square root of the molecular length, which could explain recent experimental data. However, analysis suggests that this approximation is no longer valid at large DNA lengths. In a second approximation, for long molecules, we define two adaptation lengths for twisting and stretching, over which the pairing interaction can limit the accumulation of helix disorder. When the pairing interaction is sufficiently strong, both adaptation lengths are finite; however, as we reduce pairing strength, the stretching adaptation length remains finite but the torsional one becomes infinite. This second state persists to arbitrarily weak values of the pairing strength; suggesting that, if the molecules are long enough, the pairing energy scales as length. To probe differences between the two pairing mechanisms, we also construct a model of similar form. However, now, pairing between identical sequences solely relies on the intrinsic helix distortion patterns. Between the two models, we see interesting qualitative differences. We discuss our findings, and suggest new work to distinguish between the two mechanisms.

Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size

PubMed Central

Gerstner, Wulfram

2017-01-01

Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacting populations at the mesoscopic scale starting from a microscopic model of randomly connected generalized integrate-and-fire neuron models. Each population consists of 50–2000 neurons of the same type but different populations account for different neuron types. The stochastic population equations that we find reveal how spike-history effects in single-neuron dynamics such as refractoriness and adaptation interact with finite-size fluctuations on the population level. Efficient integration of the stochastic mesoscopic equations reproduces the statistical behavior of the population activities obtained from microscopic simulations of a full spiking neural network model. The theory describes nonlinear emergent dynamics such as finite-size-induced stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. The mesoscopic equations are employed to rapidly integrate a model of a cortical microcircuit consisting of eight neuron types, which allows us to predict spontaneous population activities as well as evoked responses to thalamic input. Our theory establishes a general framework for modeling finite-size neural population dynamics based on single cell and synapse parameters and offers an efficient approach to analyzing cortical circuits and computations. PMID:28422957

A viscoelastic model for dielectric elastomers based on a continuum mechanical formulation and its finite element implementation

NASA Astrophysics Data System (ADS)

Bueschel, A.; Klinkel, S.; Wagner, W.

2011-04-01

Smart materials are active and multifunctional materials, which play an important part for sensor and actuator applications. These materials have the potential to transform passive structures into adaptive systems. However, a prerequisite for the design and the optimization of these materials is, that reliable models exist, which incorporate the interaction between the different combinations of thermal, electrical, magnetic, optical and mechanical effects. Polymeric electroelastic materials, so-called electroactive polymer (EAP), own the characteristic to deform if an electric field is applied. EAP's possesses the benefit that they share the characteristic of polymers, these are lightweight, inexpensive, fracture tolerant, elastic, and the chemical and physical structure is well understood. However, the description "electroactive polymer" is a generic term for many kinds of different microscopic mechanisms and polymeric materials. Based on the laws of electromagnetism and elasticity, a visco-electroelastic model is developed and implemented into the finite element method (FEM). The presented three-dimensional solid element has eight nodes and trilinear interpolation functions for the displacement and the electric potential. The continuum mechanics model contains finite deformations, the time dependency and the nearly incompressible behavior of the material. To describe the possible, large time dependent deformations, a finite viscoelastic model with a split of the deformation gradient is used. Thereby the time dependent characteristic of polymeric materials is incorporated through the free energy function. The electromechanical interactions are considered by the electrostatic forces and inside the energy function.

Adaptive control of a manipulator with a flexible link

NASA Technical Reports Server (NTRS)

Yang, Y. P.; Gibson, J. S.

1988-01-01

An adaptive controller for a manipulator with one rigid link and one flexible link is presented. The performance and robustness of the controller are demonstrated by numerical simulation results. In the simulations, the manipulator moves in a gravitational field and a finite element model represents the flexible link.

The use of supercomputer modelling of high-temperature failure in pipe weldments to optimize weld and heat affected zone materials property selection

NASA Astrophysics Data System (ADS)

Wang, Z. P.; Hayhurst, D. R.

1994-07-01

The creep deformation and damage evolution in a pipe weldment has been modeled by using the finite-element continuum damage mechanics (CDM) method. The finite-element CDM computer program DAMAGE XX has been adapted to run with increased speed on a Cray XMP/416 supercomputer. Run times are sufficiently short (20 min) to permit many parametric studies to be carried out on vessel lifetimes for different weld and heat affected zone (HAZ) materials. Finite-element mesh sensitivity was studied first in order to select a mesh capable of correctly predicting experimentally observed results using at least possible computer time. A study was then made of the effect on the lifetime of a butt welded vessel of each of the commomly measured material parameters for the weld and HAZ materials. Forty different ferritic steel welded vessels were analyzed for a constant internal pressure of 45.5 MPa at a temperature of 565 C; each vessel having the same parent pipe material but different weld and HAZ materials. A lifetime improvement has been demonstrated of 30% over that obtained for the initial materials property data. A methodology for weldment design has been established which uses supercomputer-based CDM analysis techniques; it is quick to use, provides accurate results, and is a viable design tool.

An adaptive finite element method for the inequality-constrained Reynolds equation

NASA Astrophysics Data System (ADS)

Gustafsson, Tom; Rajagopal, Kumbakonam R.; Stenberg, Rolf; Videman, Juha

2018-07-01

We present a stabilized finite element method for the numerical solution of cavitation in lubrication, modeled as an inequality-constrained Reynolds equation. The cavitation model is written as a variable coefficient saddle-point problem and approximated by a residual-based stabilized method. Based on our recent results on the classical obstacle problem, we present optimal a priori estimates and derive novel a posteriori error estimators. The method is implemented as a Nitsche-type finite element technique and shown in numerical computations to be superior to the usually applied penalty methods.

3D CSEM inversion based on goal-oriented adaptive finite element method

NASA Astrophysics Data System (ADS)

Zhang, Y.; Key, K.

2016-12-01

We present a parallel 3D frequency domain controlled-source electromagnetic inversion code name MARE3DEM. Non-linear inversion of observed data is performed with the Occam variant of regularized Gauss-Newton optimization. The forward operator is based on the goal-oriented finite element method that efficiently calculates the responses and sensitivity kernels in parallel using a data decomposition scheme where independent modeling tasks contain different frequencies and subsets of the transmitters and receivers. To accommodate complex 3D conductivity variation with high flexibility and precision, we adopt the dual-grid approach where the forward mesh conforms to the inversion parameter grid and is adaptively refined until the forward solution converges to the desired accuracy. This dual-grid approach is memory efficient, since the inverse parameter grid remains independent from fine meshing generated around the transmitter and receivers by the adaptive finite element method. Besides, the unstructured inverse mesh efficiently handles multiple scale structures and allows for fine-scale model parameters within the region of interest. Our mesh generation engine keeps track of the refinement hierarchy so that the map of conductivity and sensitivity kernel between the forward and inverse mesh is retained. We employ the adjoint-reciprocity method to calculate the sensitivity kernels which establish a linear relationship between changes in the conductivity model and changes in the modeled responses. Our code uses a direcy solver for the linear systems, so the adjoint problem is efficiently computed by re-using the factorization from the primary problem. Further computational efficiency and scalability is obtained in the regularized Gauss-Newton portion of the inversion using parallel dense matrix-matrix multiplication and matrix factorization routines implemented with the ScaLAPACK library. We show the scalability, reliability and the potential of the algorithm to deal with complex geological scenarios by applying it to the inversion of synthetic marine controlled source EM data generated for a complex 3D offshore model with significant seafloor topography.

M-Adapting Low Order Mimetic Finite Differences for Dielectric Interface Problems

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

McGregor, Duncan A.; Gyrya, Vitaliy; Manzini, Gianmarco

2016-03-07

We consider a problem of reducing numerical dispersion for electromagnetic wave in the domain with two materials separated by a at interface in 2D with a factor of two di erence in wave speed. The computational mesh in the homogeneous parts of the domain away from the interface consists of square elements. Here the method construction is based on m-adaptation construction in homogeneous domain that leads to fourth-order numerical dispersion (vs. second order in non-optimized method). The size of the elements in two domains also di ers by a factor of two, so as to preserve the same value ofmore » Courant number in each. Near the interface where two meshes merge the mesh with larger elements consists of degenerate pentagons. We demonstrate that prior to m-adaptation the accuracy of the method falls from second to rst due to breaking of symmetry in the mesh. Next we develop m-adaptation framework for the interface region and devise an optimization criteria. We prove that for the interface problem m-adaptation cannot produce increase in method accuracy. This is in contrast to homogeneous medium where m-adaptation can increase accuracy by two orders.« less

ZZ-Type a posteriori error estimators for adaptive boundary element methods on a curve☆

PubMed Central

Feischl, Michael; Führer, Thomas; Karkulik, Michael; Praetorius, Dirk

2014-01-01

In the context of the adaptive finite element method (FEM), ZZ-error estimators named after Zienkiewicz and Zhu (1987) [52] are mathematically well-established and widely used in practice. In this work, we propose and analyze ZZ-type error estimators for the adaptive boundary element method (BEM). We consider weakly singular and hyper-singular integral equations and prove, in particular, convergence of the related adaptive mesh-refining algorithms. Throughout, the theoretical findings are underlined by numerical experiments. PMID:24748725

The nonlinear modified equation approach to analyzing finite difference schemes

NASA Technical Reports Server (NTRS)

Klopfer, G. H.; Mcrae, D. S.

1981-01-01

The nonlinear modified equation approach is taken in this paper to analyze the generalized Lax-Wendroff explicit scheme approximation to the unsteady one- and two-dimensional equations of gas dynamics. Three important applications of the method are demonstrated. The nonlinear modified equation analysis is used to (1) generate higher order accurate schemes, (2) obtain more accurate estimates of the discretization error for nonlinear systems of partial differential equations, and (3) generate an adaptive mesh procedure for the unsteady gas dynamic equations. Results are obtained for all three areas. For the adaptive mesh procedure, mesh point requirements for equal resolution of discontinuities were reduced by a factor of five for a 1-D shock tube problem solved by the explicit MacCormack scheme.

The Relation of Finite Element and Finite Difference Methods

NASA Technical Reports Server (NTRS)

Vinokur, M.

1976-01-01

Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.

Application of adaptive gridding to magnetohydrodynamic flows

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

Schnack, D.D.; Lotatti, I.; Satyanarayana, P.

1996-12-31

The numerical simulation of the primitive, three-dimensional, time-dependent, resistive MHD equations on an unstructured, adaptive poloidal mesh using the TRIM code has been reported previously. The toroidal coordinate is approximated pseudo-spectrally with finite Fourier series and Fast-Fourier Transforms. The finite-volume algorithm preserves the magnetic field as solenoidal to round-off error, and also conserves mass, energy, and magnetic flux exactly. A semi-implicit method is used to allow for large time steps on the unstructured mesh. This is important for tokamak calculations where the relevant time scale is determined by the poloidal Alfven time. This also allows the viscosity to be treatedmore » implicitly. A conjugate-gradient method with pre-conditioning is used for matrix inversion. Applications to the growth and saturation of ideal instabilities in several toroidal fusion systems has been demonstrated. Recently we have concentrated on the details of the mesh adaption algorithm used in TRIM. We present several two-dimensional results relating to the use of grid adaptivity to track the evolution of hydrodynamic and MHD structures. Examples of plasma guns, opening switches, and supersonic flow over a magnetized sphere are presented. Issues relating to mesh adaption criteria are discussed.« less

Parallel iterative methods for sparse linear and nonlinear equations

NASA Technical Reports Server (NTRS)

Saad, Youcef

1989-01-01

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

Investigation of smoothness-increasing accuracy-conserving filters for improving streamline integration through discontinuous fields.

PubMed

Steffen, Michael; Curtis, Sean; Kirby, Robert M; Ryan, Jennifer K

2008-01-01

Streamline integration of fields produced by computational fluid mechanics simulations is a commonly used tool for the investigation and analysis of fluid flow phenomena. Integration is often accomplished through the application of ordinary differential equation (ODE) integrators--integrators whose error characteristics are predicated on the smoothness of the field through which the streamline is being integrated--smoothness which is not available at the inter-element level of finite volume and finite element data. Adaptive error control techniques are often used to ameliorate the challenge posed by inter-element discontinuities. As the root of the difficulties is the discontinuous nature of the data, we present a complementary approach of applying smoothness-enhancing accuracy-conserving filters to the data prior to streamline integration. We investigate whether such an approach applied to uniform quadrilateral discontinuous Galerkin (high-order finite volume) data can be used to augment current adaptive error control approaches. We discuss and demonstrate through numerical example the computational trade-offs exhibited when one applies such a strategy.

A Modeling Approach for Burn Scar Assessment Using Natural Features and Elastic Property

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

Tsap, L V; Zhang, Y; Goldgof, D B

2004-04-02

A modeling approach is presented for quantitative burn scar assessment. Emphases are given to: (1) constructing a finite element model from natural image features with an adaptive mesh, and (2) quantifying the Young's modulus of scars using the finite element model and the regularization method. A set of natural point features is extracted from the images of burn patients. A Delaunay triangle mesh is then generated that adapts to the point features. A 3D finite element model is built on top of the mesh with the aid of range images providing the depth information. The Young's modulus of scars ismore » quantified with a simplified regularization functional, assuming that the knowledge of scar's geometry is available. The consistency between the Relative Elasticity Index and the physician's rating based on the Vancouver Scale (a relative scale used to rate burn scars) indicates that the proposed modeling approach has high potentials for image-based quantitative burn scar assessment.« less

Newmark local time stepping on high-performance computing architectures

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

Rietmann, Max, E-mail: max.rietmann@erdw.ethz.ch; Institute of Geophysics, ETH Zurich; Grote, Marcus, E-mail: marcus.grote@unibas.ch

In multi-scale complex media, finite element meshes often require areas of local refinement, creating small elements that can dramatically reduce the global time-step for wave-propagation problems due to the CFL condition. Local time stepping (LTS) algorithms allow an explicit time-stepping scheme to adapt the time-step to the element size, allowing near-optimal time-steps everywhere in the mesh. We develop an efficient multilevel LTS-Newmark scheme and implement it in a widely used continuous finite element seismic wave-propagation package. In particular, we extend the standard LTS formulation with adaptations to continuous finite element methods that can be implemented very efficiently with very strongmore » element-size contrasts (more than 100x). Capable of running on large CPU and GPU clusters, we present both synthetic validation examples and large scale, realistic application examples to demonstrate the performance and applicability of the method and implementation on thousands of CPU cores and hundreds of GPUs.« less

Development of an adaptive hp-version finite element method for computational optimal control

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Warner, Michael S.

1994-01-01

In this research effort, the usefulness of hp-version finite elements and adaptive solution-refinement techniques in generating numerical solutions to optimal control problems has been investigated. Under NAG-939, a general FORTRAN code was developed which approximated solutions to optimal control problems with control constraints and state constraints. Within that methodology, to get high-order accuracy in solutions, the finite element mesh would have to be refined repeatedly through bisection of the entire mesh in a given phase. In the current research effort, the order of the shape functions in each element has been made a variable, giving more flexibility in error reduction and smoothing. Similarly, individual elements can each be subdivided into many pieces, depending on the local error indicator, while other parts of the mesh remain coarsely discretized. The problem remains to reduce and smooth the error while still keeping computational effort reasonable enough to calculate time histories in a short enough time for on-board applications.

Modelling the oscillations of the thermocline in a lake by means of a fully consistent and conservative 3D finite-element model with a vertically adaptive mesh

NASA Astrophysics Data System (ADS)

Delandmeter, Philippe; Lambrechts, Jonathan; Vallaeys, Valentin; Naithani, Jaya; Remacle, Jean-François; Legat, Vincent; Deleersnijder, Eric

2017-04-01

Vertical discretisation is crucial in the modelling of lake thermocline oscillations. For finite element methods, a simple way to increase the resolution close to the oscillating thermocline is to use vertical adaptive coordinates. With an Arbitrary Lagrangian-Eulerian (ALE) formulation, the mesh can be adapted to increase the resolution in regions with strong shear or stratification. In such an application, consistency and conservativity must be strictly enforced. SLIM 3D, a discontinuous-Galerkin finite element model for shallow-water flows (www.climate.be/slim, e.g. Kärnä et al., 2013, Delandmeter et al., 2015), was designed to be strictly consistent and conservative in its discrete formulation. In this context, special care must be paid to the coupling of the external and internal modes of the model and the moving mesh algorithm. In this framework, the mesh can be adapted arbitrarily in the vertical direction. Two moving mesh algorithms were implemented: the first one computes an a-priori optimal mesh; the second one diffuses vertically the mesh (Burchard et al., 2004, Hofmeister et al., 2010). The criteria used to define the optimal mesh and the diffusion function are related to a suitable measure of shear and stratification. We will present in detail the design of the model and how the consistency and conservativity is obtained. Then we will apply it to both idealised benchmarks and the wind-forced thermocline oscillations in Lake Tanganyika (Naithani et al. 2002). References Tuomas Kärnä, Vincent Legat and Eric Deleersnijder. A baroclinic discontinuous Galerkin finite element model for coastal flows, Ocean Modelling, 61:1-20, 2013. Philippe Delandmeter, Stephen E Lewis, Jonathan Lambrechts, Eric Deleersnijder, Vincent Legat and Eric Wolanski. The transport and fate of riverine fine sediment exported to a semi-open system. Estuarine, Coastal and Shelf Science, 167:336-346, 2015. Hans Burchard and Jean-Marie Beckers. Non-uniform adaptive vertical grids in one-dimensional numerical ocean models. Ocean Modelling, 6:51-81, 2004. Richard Hofmeister, Hans Burchard and Jean-Marie Beckers. Non-uniform adaptive vertical grids for 3d numerical ocean models. Ocean Modelling, 33:70-86, 2010. Jaya Naithani, Eric Deleersnijder and Pierre-Denis Plisnier. Origin of intraseasonal variability in Lake Tanganyika. Geophysical Research Letters, 29(23), doi:10.1029/2002GL015843, 2002.

A tissue adaptation model based on strain-dependent collagen degradation and contact-guided cell traction.

PubMed

Heck, T A M; Wilson, W; Foolen, J; Cilingir, A C; Ito, K; van Donkelaar, C C

2015-03-18

Soft biological tissues adapt their collagen network to the mechanical environment. Collagen remodeling and cell traction are both involved in this process. The present study presents a collagen adaptation model which includes strain-dependent collagen degradation and contact-guided cell traction. Cell traction is determined by the prevailing collagen structure and is assumed to strive for tensional homeostasis. In addition, collagen is assumed to mechanically fail if it is over-strained. Care is taken to use principally measurable and physiologically meaningful relationships. This model is implemented in a fibril-reinforced biphasic finite element model for soft hydrated tissues. The versatility and limitations of the model are demonstrated by corroborating the predicted transient and equilibrium collagen adaptation under distinct mechanical constraints against experimental observations from the literature. These experiments include overloading of pericardium explants until failure, static uniaxial and biaxial loading of cell-seeded gels in vitro and shortening of periosteum explants. In addition, remodeling under hypothetical conditions is explored to demonstrate how collagen might adapt to small differences in constraints. Typical aspects of all essentially different experimental conditions are captured quantitatively or qualitatively. Differences between predictions and experiments as well as new insights that emerge from the present simulations are discussed. This model is anticipated to evolve into a mechanistic description of collagen adaptation, which may assist in developing load-regimes for functional tissue engineered constructs, or may be employed to improve our understanding of the mechanisms behind physiological and pathological collagen remodeling. Copyright © 2014 Elsevier Ltd. All rights reserved.

Higher and lowest order mixed finite element approximation of subsurface flow problems with solutions of low regularity

NASA Astrophysics Data System (ADS)

Bause, Markus

2008-02-01

In this work we study mixed finite element approximations of Richards' equation for simulating variably saturated subsurface flow and simultaneous reactive solute transport. Whereas higher order schemes have proved their ability to approximate reliably reactive solute transport (cf., e.g. [Bause M, Knabner P. Numerical simulation of contaminant biodegradation by higher order methods and adaptive time stepping. Comput Visual Sci 7;2004:61-78]), the Raviart- Thomas mixed finite element method ( RT0) with a first order accurate flux approximation is popular for computing the underlying water flow field (cf. [Bause M, Knabner P. Computation of variably saturated subsurface flow by adaptive mixed hybrid finite element methods. Adv Water Resour 27;2004:565-581, Farthing MW, Kees CE, Miller CT. Mixed finite element methods and higher order temporal approximations for variably saturated groundwater flow. Adv Water Resour 26;2003:373-394, Starke G. Least-squares mixed finite element solution of variably saturated subsurface flow problems. SIAM J Sci Comput 21;2000:1869-1885, Younes A, Mosé R, Ackerer P, Chavent G. A new formulation of the mixed finite element method for solving elliptic and parabolic PDE with triangular elements. J Comp Phys 149;1999:148-167, Woodward CS, Dawson CN. Analysis of expanded mixed finite element methods for a nonlinear parabolic equation modeling flow into variably saturated porous media. SIAM J Numer Anal 37;2000:701-724]). This combination might be non-optimal. Higher order techniques could increase the accuracy of the flow field calculation and thereby improve the prediction of the solute transport. Here, we analyse the application of the Brezzi- Douglas- Marini element ( BDM1) with a second order accurate flux approximation to elliptic, parabolic and degenerate problems whose solutions lack the regularity that is assumed in optimal order error analyses. For the flow field calculation a superiority of the BDM1 approach to the RT0 one is observed, which however is less significant for the accompanying solute transport.

The Distributed Lambda (?) Model (DLM): A 3-D, Finite-Element Muscle Model Based on Feldman's ? Model; Assessment of Orofacial Gestures

ERIC Educational Resources Information Center

Nazari, Mohammad Ali; Perrier, Pascal; Payan, Yohan

2013-01-01

Purpose: The authors aimed to design a distributed lambda model (DLM), which is well adapted to implement three-dimensional (3-D), finite-element descriptions of muscles. Method: A muscle element model was designed. Its stress-strain relationships included the active force-length characteristics of the ? model along the muscle fibers, together…

Sensitivity Analysis for Multidisciplinary Systems (SAMS)

DTIC Science & Technology

2016-12-01

support both mode-based structural representations and time-dependent, nonlinear finite element structural dynamics. This interim report describes...Adaptation, & Sensitivity Toolkit • Elasticity, heat transfer, & compressible flow • Adjoint solver for sensitivity analysis • High-order finite elements ...PROGRAM ELEMENT NUMBER 62201F 6. AUTHOR(S) Richard D. Snyder 5d. PROJECT NUMBER 2401 5e. TASK NUMBER N/A 5f. WORK UNIT NUMBER Q1FS 7

Adaptive computational methods for aerothermal heating analysis

NASA Technical Reports Server (NTRS)

Price, John M.; Oden, J. Tinsley

1988-01-01

The development of adaptive gridding techniques for finite-element analysis of fluid dynamics equations is described. The developmental work was done with the Euler equations with concentration on shock and inviscid flow field capturing. Ultimately this methodology is to be applied to a viscous analysis for the purpose of predicting accurate aerothermal loads on complex shapes subjected to high speed flow environments. The development of local error estimate strategies as a basis for refinement strategies is discussed, as well as the refinement strategies themselves. The application of the strategies to triangular elements and a finite-element flux-corrected-transport numerical scheme are presented. The implementation of these strategies in the GIM/PAGE code for 2-D and 3-D applications is documented and demonstrated.

Hybrid simulation combining two space-time discretization of the discrete-velocity Boltzmann equation

NASA Astrophysics Data System (ADS)

Horstmann, Jan Tobias; Le Garrec, Thomas; Mincu, Daniel-Ciprian; Lévêque, Emmanuel

2017-11-01

Despite the efficiency and low dissipation of the stream-collide scheme of the discrete-velocity Boltzmann equation, which is nowadays implemented in many lattice Boltzmann solvers, a major drawback exists over alternative discretization schemes, i.e. finite-volume or finite-difference, that is the limitation to Cartesian uniform grids. In this paper, an algorithm is presented that combines the positive features of each scheme in a hybrid lattice Boltzmann method. In particular, the node-based streaming of the distribution functions is coupled with a second-order finite-volume discretization of the advection term of the Boltzmann equation under the Bhatnagar-Gross-Krook approximation. The algorithm is established on a multi-domain configuration, with the individual schemes being solved on separate sub-domains and connected by an overlapping interface of at least 2 grid cells. A critical parameter in the coupling is the CFL number equal to unity, which is imposed by the stream-collide algorithm. Nevertheless, a semi-implicit treatment of the collision term in the finite-volume formulation allows us to obtain a stable solution for this condition. The algorithm is validated in the scope of three different test cases on a 2D periodic mesh. It is shown that the accuracy of the combined discretization schemes agrees with the order of each separate scheme involved. The overall numerical error of the hybrid algorithm in the macroscopic quantities is contained between the error of the two individual algorithms. Finally, we demonstrate how such a coupling can be used to adapt to anisotropic flows with some gradual mesh refinement in the FV domain.

Issues in the digital implementation of control compensators. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Moroney, P.

1979-01-01

Techniques developed for the finite-precision implementation of digital filters were used, adapted, and extended for digital feedback compensators, with particular emphasis on steady state, linear-quadratic-Gaussian compensators. Topics covered include: (1) the linear-quadratic-Gaussian problem; (2) compensator structures; (3) architectural issues: serialism, parallelism, and pipelining; (4) finite wordlength effects: quantization noise, quantizing the coefficients, and limit cycles; and (5) the optimization of structures.

Quality Assessment and Control of Finite Element Solutions.

DTIC Science & Technology

1986-05-01

solutions. However, some special-purpose and pilot finite element systems have implemented adaptive algorithms 17 p." for practical performance studies ...simulator (SAFES code) developed at the University of Wyoming (Ref. 148); and the PROBE system developed by NOETIC Technologies Corporation in St. Louis (Ref...displacements. Recent studies have demonstrated that the accuracy and rate of convergence of stresses (and strains) r. depend on how (and where) they

Edge equilibrium code for tokamaks

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

Li, Xujing; Zakharov, Leonid E.; Drozdov, Vladimir V.

2014-01-15

The edge equilibrium code (EEC) described in this paper is developed for simulations of the near edge plasma using the finite element method. It solves the Grad-Shafranov equation in toroidal coordinate and uses adaptive grids aligned with magnetic field lines. Hermite finite elements are chosen for the numerical scheme. A fast Newton scheme which is the same as implemented in the equilibrium and stability code (ESC) is applied here to adjust the grids.

Data-Adaptive Bias-Reduced Doubly Robust Estimation.

PubMed

Vermeulen, Karel; Vansteelandt, Stijn

2016-05-01

Doubly robust estimators have now been proposed for a variety of target parameters in the causal inference and missing data literature. These consistently estimate the parameter of interest under a semiparametric model when one of two nuisance working models is correctly specified, regardless of which. The recently proposed bias-reduced doubly robust estimation procedure aims to partially retain this robustness in more realistic settings where both working models are misspecified. These so-called bias-reduced doubly robust estimators make use of special (finite-dimensional) nuisance parameter estimators that are designed to locally minimize the squared asymptotic bias of the doubly robust estimator in certain directions of these finite-dimensional nuisance parameters under misspecification of both parametric working models. In this article, we extend this idea to incorporate the use of data-adaptive estimators (infinite-dimensional nuisance parameters), by exploiting the bias reduction estimation principle in the direction of only one nuisance parameter. We additionally provide an asymptotic linearity theorem which gives the influence function of the proposed doubly robust estimator under correct specification of a parametric nuisance working model for the missingness mechanism/propensity score but a possibly misspecified (finite- or infinite-dimensional) outcome working model. Simulation studies confirm the desirable finite-sample performance of the proposed estimators relative to a variety of other doubly robust estimators.

Numerical computation of transonic flows by finite-element and finite-difference methods

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Wellford, L. C.; Merkle, C. L.; Murman, E. M.

1978-01-01

Studies on applications of the finite element approach to transonic flow calculations are reported. Different discretization techniques of the differential equations and boundary conditions are compared. Finite element analogs of Murman's mixed type finite difference operators for small disturbance formulations were constructed and the time dependent approach (using finite differences in time and finite elements in space) was examined.

An HP Adaptive Discontinuous Galerkin Method for Hyperbolic Conservation Laws. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Bey, Kim S.

1994-01-01

This dissertation addresses various issues for model classes of hyperbolic conservation laws. The basic approach developed in this work employs a new family of adaptive, hp-version, finite element methods based on a special discontinuous Galerkin formulation for hyperbolic problems. The discontinuous Galerkin formulation admits high-order local approximations on domains of quite general geometry, while providing a natural framework for finite element approximations and for theoretical developments. The use of hp-versions of the finite element method makes possible exponentially convergent schemes with very high accuracies in certain cases; the use of adaptive hp-schemes allows h-refinement in regions of low regularity and p-enrichment to deliver high accuracy, while keeping problem sizes manageable and dramatically smaller than many conventional approaches. The use of discontinuous Galerkin methods is uncommon in applications, but the methods rest on a reasonable mathematical basis for low-order cases and has local approximation features that can be exploited to produce very efficient schemes, especially in a parallel, multiprocessor environment. The place of this work is to first and primarily focus on a model class of linear hyperbolic conservation laws for which concrete mathematical results, methodologies, error estimates, convergence criteria, and parallel adaptive strategies can be developed, and to then briefly explore some extensions to more general cases. Next, we provide preliminaries to the study and a review of some aspects of the theory of hyperbolic conservation laws. We also provide a review of relevant literature on this subject and on the numerical analysis of these types of problems.

Solid rocket booster internal flow analysis by highly accurate adaptive computational methods

NASA Technical Reports Server (NTRS)

Huang, C. Y.; Tworzydlo, W.; Oden, J. T.; Bass, J. M.; Cullen, C.; Vadaketh, S.

1991-01-01

The primary objective of this project was to develop an adaptive finite element flow solver for simulating internal flows in the solid rocket booster. Described here is a unique flow simulator code for analyzing highly complex flow phenomena in the solid rocket booster. New methodologies and features incorporated into this analysis tool are described.

Controlling Reflections from Mesh Refinement Interfaces in Numerical Relativity

NASA Technical Reports Server (NTRS)

Baker, John G.; Van Meter, James R.

2005-01-01

A leading approach to improving the accuracy on numerical relativity simulations of black hole systems is through fixed or adaptive mesh refinement techniques. We describe a generic numerical error which manifests as slowly converging, artificial reflections from refinement boundaries in a broad class of mesh-refinement implementations, potentially limiting the effectiveness of mesh- refinement techniques for some numerical relativity applications. We elucidate this numerical effect by presenting a model problem which exhibits the phenomenon, but which is simple enough that its numerical error can be understood analytically. Our analysis shows that the effect is caused by variations in finite differencing error generated across low and high resolution regions, and that its slow convergence is caused by the presence of dramatic speed differences among propagation modes typical of 3+1 relativity. Lastly, we resolve the problem, presenting a class of finite-differencing stencil modifications which eliminate this pathology in both our model problem and in numerical relativity examples.

Multistage Fuzzy Decision Making in Bilateral Negotiation with Finite Termination Times

NASA Astrophysics Data System (ADS)

Richter, Jan; Kowalczyk, Ryszard; Klusch, Matthias

In this paper we model the negotiation process as a multistage fuzzy decision problem where the agents preferences are represented by a fuzzy goal and fuzzy constraints. The opponent is represented by a fuzzy Markov decision process in the form of offer-response patterns which enables utilization of limited and uncertain information, e.g. the characteristics of the concession behaviour. We show that we can obtain adaptive negotiation strategies by only using the negotiation threads of two past cases to create and update the fuzzy transition matrix. The experimental evaluation demonstrates that our approach is adaptive towards different negotiation behaviours and that the fuzzy representation of the preferences and the transition matrix allows for application in many scenarios where the available information, preferences and constraints are soft or imprecise.

AP-Cloud: Adaptive particle-in-cloud method for optimal solutions to Vlasov–Poisson equation

DOE PAGES

Wang, Xingyu; Samulyak, Roman; Jiao, Xiangmin; ...

2016-04-19

We propose a new adaptive Particle-in-Cloud (AP-Cloud) method for obtaining optimal numerical solutions to the Vlasov–Poisson equation. Unlike the traditional particle-in-cell (PIC) method, which is commonly used for solving this problem, the AP-Cloud adaptively selects computational nodes or particles to deliver higher accuracy and efficiency when the particle distribution is highly non-uniform. Unlike other adaptive techniques for PIC, our method balances the errors in PDE discretization and Monte Carlo integration, and discretizes the differential operators using a generalized finite difference (GFD) method based on a weighted least square formulation. As a result, AP-Cloud is independent of the geometric shapes ofmore » computational domains and is free of artificial parameters. Efficient and robust implementation is achieved through an octree data structure with 2:1 balance. We analyze the accuracy and convergence order of AP-Cloud theoretically, and verify the method using an electrostatic problem of a particle beam with halo. Here, simulation results show that the AP-Cloud method is substantially more accurate and faster than the traditional PIC, and it is free of artificial forces that are typical for some adaptive PIC techniques.« less

A goal-based angular adaptivity method for thermal radiation modelling in non grey media

NASA Astrophysics Data System (ADS)

Soucasse, Laurent; Dargaville, Steven; Buchan, Andrew G.; Pain, Christopher C.

2017-10-01

This paper investigates for the first time a goal-based angular adaptivity method for thermal radiation transport, suitable for non grey media when the radiation field is coupled with an unsteady flow field through an energy balance. Anisotropic angular adaptivity is achieved by using a Haar wavelet finite element expansion that forms a hierarchical angular basis with compact support and does not require any angular interpolation in space. The novelty of this work lies in (1) the definition of a target functional to compute the goal-based error measure equal to the radiative source term of the energy balance, which is the quantity of interest in the context of coupled flow-radiation calculations; (2) the use of different optimal angular resolutions for each absorption coefficient class, built from a global model of the radiative properties of the medium. The accuracy and efficiency of the goal-based angular adaptivity method is assessed in a coupled flow-radiation problem relevant for air pollution modelling in street canyons. Compared to a uniform Haar wavelet expansion, the adapted resolution uses 5 times fewer angular basis functions and is 6.5 times quicker, given the same accuracy in the radiative source term.

AP-Cloud: Adaptive Particle-in-Cloud method for optimal solutions to Vlasov–Poisson equation

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

Wang, Xingyu; Samulyak, Roman, E-mail: roman.samulyak@stonybrook.edu; Computational Science Initiative, Brookhaven National Laboratory, Upton, NY 11973

We propose a new adaptive Particle-in-Cloud (AP-Cloud) method for obtaining optimal numerical solutions to the Vlasov–Poisson equation. Unlike the traditional particle-in-cell (PIC) method, which is commonly used for solving this problem, the AP-Cloud adaptively selects computational nodes or particles to deliver higher accuracy and efficiency when the particle distribution is highly non-uniform. Unlike other adaptive techniques for PIC, our method balances the errors in PDE discretization and Monte Carlo integration, and discretizes the differential operators using a generalized finite difference (GFD) method based on a weighted least square formulation. As a result, AP-Cloud is independent of the geometric shapes ofmore » computational domains and is free of artificial parameters. Efficient and robust implementation is achieved through an octree data structure with 2:1 balance. We analyze the accuracy and convergence order of AP-Cloud theoretically, and verify the method using an electrostatic problem of a particle beam with halo. Simulation results show that the AP-Cloud method is substantially more accurate and faster than the traditional PIC, and it is free of artificial forces that are typical for some adaptive PIC techniques.« less

AP-Cloud: Adaptive particle-in-cloud method for optimal solutions to Vlasov–Poisson equation

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

Wang, Xingyu; Samulyak, Roman; Jiao, Xiangmin

We propose a new adaptive Particle-in-Cloud (AP-Cloud) method for obtaining optimal numerical solutions to the Vlasov–Poisson equation. Unlike the traditional particle-in-cell (PIC) method, which is commonly used for solving this problem, the AP-Cloud adaptively selects computational nodes or particles to deliver higher accuracy and efficiency when the particle distribution is highly non-uniform. Unlike other adaptive techniques for PIC, our method balances the errors in PDE discretization and Monte Carlo integration, and discretizes the differential operators using a generalized finite difference (GFD) method based on a weighted least square formulation. As a result, AP-Cloud is independent of the geometric shapes ofmore » computational domains and is free of artificial parameters. Efficient and robust implementation is achieved through an octree data structure with 2:1 balance. We analyze the accuracy and convergence order of AP-Cloud theoretically, and verify the method using an electrostatic problem of a particle beam with halo. Here, simulation results show that the AP-Cloud method is substantially more accurate and faster than the traditional PIC, and it is free of artificial forces that are typical for some adaptive PIC techniques.« less

Adapting Surface Ground Motion Relations to Underground conditions: A case study for the Sudbury Neutrino Observatory in Sudbury, Ontario, Canada

NASA Astrophysics Data System (ADS)

Babaie Mahani, A.; Eaton, D. W.

2013-12-01

Ground Motion Prediction Equations (GMPEs) are widely used in Probabilistic Seismic Hazard Assessment (PSHA) to estimate ground-motion amplitudes at Earth's surface as a function of magnitude and distance. Certain applications, such as hazard assessment for caprock integrity in the case of underground storage of CO2, waste disposal sites, and underground pipelines, require subsurface estimates of ground motion; at present, such estimates depend upon theoretical modeling and simulations. The objective of this study is to derive correction factors for GMPEs to enable estimation of amplitudes in the subsurface. We use a semi-analytic approach along with finite-difference simulations of ground-motion amplitudes for surface and underground motions. Spectral ratios of underground to surface motions are used to calculate the correction factors. Two predictive methods are used. The first is a semi-analytic approach based on a quarter-wavelength method that is widely used for earthquake site-response investigations; the second is a numerical approach based on elastic finite-difference simulations of wave propagation. Both methods are evaluated using recordings of regional earthquakes by broadband seismometers installed at the surface and at depths of 1400 m and 2100 m in the Sudbury Neutrino Observatory, Canada. Overall, both methods provide a reasonable fit to the peaks and troughs observed in the ratios of real data. The finite-difference method, however, has the capability to simulate ground motion ratios more accurately than the semi-analytic approach.

A class of hybrid finite element methods for electromagnetics: A review

NASA Technical Reports Server (NTRS)

Volakis, J. L.; Chatterjee, A.; Gong, J.

1993-01-01

Integral equation methods have generally been the workhorse for antenna and scattering computations. In the case of antennas, they continue to be the prominent computational approach, but for scattering applications the requirement for large-scale computations has turned researchers' attention to near neighbor methods such as the finite element method, which has low O(N) storage requirements and is readily adaptable in modeling complex geometrical features and material inhomogeneities. In this paper, we review three hybrid finite element methods for simulating composite scatterers, conformal microstrip antennas, and finite periodic arrays. Specifically, we discuss the finite element method and its application to electromagnetic problems when combined with the boundary integral, absorbing boundary conditions, and artificial absorbers for terminating the mesh. Particular attention is given to large-scale simulations, methods, and solvers for achieving low memory requirements and code performance on parallel computing architectures.

MULTISCALE ADAPTIVE SMOOTHING MODELS FOR THE HEMODYNAMIC RESPONSE FUNCTION IN FMRI*

PubMed Central

Wang, Jiaping; Zhu, Hongtu; Fan, Jianqing; Giovanello, Kelly; Lin, Weili

2012-01-01

In the event-related functional magnetic resonance imaging (fMRI) data analysis, there is an extensive interest in accurately and robustly estimating the hemodynamic response function (HRF) and its associated statistics (e.g., the magnitude and duration of the activation). Most methods to date are developed in the time domain and they have utilized almost exclusively the temporal information of fMRI data without accounting for the spatial information. The aim of this paper is to develop a multiscale adaptive smoothing model (MASM) in the frequency domain by integrating the spatial and temporal information to adaptively and accurately estimate HRFs pertaining to each stimulus sequence across all voxels in a three-dimensional (3D) volume. We use two sets of simulation studies and a real data set to examine the finite sample performance of MASM in estimating HRFs. Our real and simulated data analyses confirm that MASM outperforms several other state-of-art methods, such as the smooth finite impulse response (sFIR) model. PMID:24533041

On-the-fly Numerical Surface Integration for Finite-Difference Poisson-Boltzmann Methods.

PubMed

Cai, Qin; Ye, Xiang; Wang, Jun; Luo, Ray

2011-11-01

Most implicit solvation models require the definition of a molecular surface as the interface that separates the solute in atomic detail from the solvent approximated as a continuous medium. Commonly used surface definitions include the solvent accessible surface (SAS), the solvent excluded surface (SES), and the van der Waals surface. In this study, we present an efficient numerical algorithm to compute the SES and SAS areas to facilitate the applications of finite-difference Poisson-Boltzmann methods in biomolecular simulations. Different from previous numerical approaches, our algorithm is physics-inspired and intimately coupled to the finite-difference Poisson-Boltzmann methods to fully take advantage of its existing data structures. Our analysis shows that the algorithm can achieve very good agreement with the analytical method in the calculation of the SES and SAS areas. Specifically, in our comprehensive test of 1,555 molecules, the average unsigned relative error is 0.27% in the SES area calculations and 1.05% in the SAS area calculations at the grid spacing of 1/2Å. In addition, a systematic correction analysis can be used to improve the accuracy for the coarse-grid SES area calculations, with the average unsigned relative error in the SES areas reduced to 0.13%. These validation studies indicate that the proposed algorithm can be applied to biomolecules over a broad range of sizes and structures. Finally, the numerical algorithm can also be adapted to evaluate the surface integral of either a vector field or a scalar field defined on the molecular surface for additional solvation energetics and force calculations.

Accuracy Improvement in Magnetic Field Modeling for an Axisymmetric Electromagnet

NASA Technical Reports Server (NTRS)

Ilin, Andrew V.; Chang-Diaz, Franklin R.; Gurieva, Yana L.; Il,in, Valery P.

2000-01-01

This paper examines the accuracy and calculation speed for the magnetic field computation in an axisymmetric electromagnet. Different numerical techniques, based on an adaptive nonuniform grid, high order finite difference approximations, and semi-analitical calculation of boundary conditions are considered. These techniques are being applied to the modeling of the Variable Specific Impulse Magnetoplasma Rocket. For high-accuracy calculations, a fourth-order scheme offers dramatic advantages over a second order scheme. For complex physical configurations of interest in plasma propulsion, a second-order scheme with nonuniform mesh gives the best results. Also, the relative advantages of various methods are described when the speed of computation is an important consideration.

Anisotropic mesh adaptation for marine ice-sheet modelling

NASA Astrophysics Data System (ADS)

Gillet-Chaulet, Fabien; Tavard, Laure; Merino, Nacho; Peyaud, Vincent; Brondex, Julien; Durand, Gael; Gagliardini, Olivier

2017-04-01

Improving forecasts of ice-sheets contribution to sea-level rise requires, amongst others, to correctly model the dynamics of the grounding line (GL), i.e. the line where the ice detaches from its underlying bed and goes afloat on the ocean. Many numerical studies, including the intercomparison exercises MISMIP and MISMIP3D, have shown that grid refinement in the GL vicinity is a key component to obtain reliable results. Improving model accuracy while maintaining the computational cost affordable has then been an important target for the development of marine icesheet models. Adaptive mesh refinement (AMR) is a method where the accuracy of the solution is controlled by spatially adapting the mesh size. It has become popular in models using the finite element method as they naturally deal with unstructured meshes, but block-structured AMR has also been successfully applied to model GL dynamics. The main difficulty with AMR is to find efficient and reliable estimators of the numerical error to control the mesh size. Here, we use the estimator proposed by Frey and Alauzet (2015). Based on the interpolation error, it has been found effective in practice to control the numerical error, and has some flexibility, such as its ability to combine metrics for different variables, that makes it attractive. Routines to compute the anisotropic metric defining the mesh size have been implemented in the finite element ice flow model Elmer/Ice (Gagliardini et al., 2013). The mesh adaptation is performed using the freely available library MMG (Dapogny et al., 2014) called from Elmer/Ice. Using a setup based on the inter-comparison exercise MISMIP+ (Asay-Davis et al., 2016), we study the accuracy of the solution when the mesh is adapted using various variables (ice thickness, velocity, basal drag, …). We show that combining these variables allows to reduce the number of mesh nodes by more than one order of magnitude, for the same numerical accuracy, when compared to uniform mesh refinement. For transient solutions where the GL is moving, we have implemented an algorithm where the computation is reiterated allowing to anticipate the GL displacement and to adapt the mesh to the transient solution. We discuss the performance and robustness of this algorithm.

Analytical approach to an integrate-and-fire model with spike-triggered adaptation

NASA Astrophysics Data System (ADS)

Schwalger, Tilo; Lindner, Benjamin

2015-12-01

The calculation of the steady-state probability density for multidimensional stochastic systems that do not obey detailed balance is a difficult problem. Here we present the analytical derivation of the stationary joint and various marginal probability densities for a stochastic neuron model with adaptation current. Our approach assumes weak noise but is valid for arbitrary adaptation strength and time scale. The theory predicts several effects of adaptation on the statistics of the membrane potential of a tonically firing neuron: (i) a membrane potential distribution with a convex shape, (ii) a strongly increased probability of hyperpolarized membrane potentials induced by strong and fast adaptation, and (iii) a maximized variability associated with the adaptation current at a finite adaptation time scale.

Edge Equilibrium Code (EEC) For Tokamaks

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

Li, Xujling

2014-02-24

The edge equilibrium code (EEC) described in this paper is developed for simulations of the near edge plasma using the finite element method. It solves the Grad-Shafranov equation in toroidal coordinate and uses adaptive grids aligned with magnetic field lines. Hermite finite elements are chosen for the numerical scheme. A fast Newton scheme which is the same as implemented in the equilibrium and stability code (ESC) is applied here to adjust the grids

Calcul numérique des ondes de surface par une méthode de projection avec un maillage eulérien adaptatif

NASA Astrophysics Data System (ADS)

Guillou, Sylvain; Barbry, Nathaly; Nguyen, Kim Dan

A non hydrostatic vertical two-dimensional numerical model is proposed to calculate free-surface flows. This model is based on resolving the full Navier-Stokes equations by a finite-difference method coupled with Chorin's projection method. An adaptative-Eulerian grid in the sigma-coordinate system is used. The model permits the calculation of surface-waves in estuarine and coastal zones. A benchmark test relative to the soliton propagation is realised to validate the model.

Software Testbed for Developing and Evaluating Integrated Autonomous Systems

DTIC Science & Technology

2015-03-01

EUROPA planning system for plan generation. The adaptive controller executes the new plan, using augmented, hierarchical finite state machines to...using the Internet Communications Engine ( ICE ), an object-oriented toolkit for building distributed applications. TABLE OF CONTENTS 1...ANML model is translated into the New Domain Definition Language (NDDL) and sent to NASA???s EUROPA planning system for plan generation. The adaptive

The finite layer method for modelling the sound transmission through double walls

NASA Astrophysics Data System (ADS)

Díaz-Cereceda, Cristina; Poblet-Puig, Jordi; Rodríguez-Ferran, Antonio

2012-10-01

The finite layer method (FLM) is presented as a discretisation technique for the computation of noise transmission through double walls. It combines a finite element method (FEM) discretisation in the direction perpendicular to the wall with trigonometric functions in the two in-plane directions. It is used for solving the Helmholtz equation at the cavity inside the double wall, while the wall leaves are modelled with the thin plate equation and solved with modal analysis. Other approaches to this problem are described here (and adapted where needed) in order to compare them with the FLM. They range from impedance models of the double wall behaviour to different numerical methods for solving the Helmholtz equation in the cavity. For the examples simulated in this work (impact noise and airborne sound transmission), the former are less accurate than the latter at low frequencies. The main advantage of FLM over the other discretisation techniques is the possibility of extending it to multilayered structures without changing the interpolation functions and with an affordable computational cost. This potential is illustrated with a calculation of the noise transmission through a multilayered structure: a double wall partially filled with absorbing material.

Sex differences, sexual selection, and ageing: an experimental evolution approach.

PubMed

Maklakov, Alexei A; Bonduriansky, Russell; Brooks, Robert C

2009-10-01

Life-history (LH) theory predicts that selection will optimize the trade-off between reproduction and somatic maintenance. Reproductive ageing and finite life span are direct consequences of such optimization. Sexual selection and conflict profoundly affect the reproductive strategies of the sexes and thus can play an important role in the evolution of life span and ageing. In theory, sexual selection can favor the evolution of either faster or slower ageing, but the evidence is equivocal. We used a novel selection experiment to investigate the potential of sexual selection to influence the adaptive evolution of age-specific LH traits. We selected replicate populations of the seed beetle Callosobruchus maculatus for age at reproduction ("Young" and "Old") either with or without sexual selection. We found that LH selection resulted in the evolution of age-specific reproduction and mortality but these changes were largely unaffected by sexual selection. Sexual selection depressed net reproductive performance and failed to promote adaptation. Nonetheless, the evolution of several traits differed between males and females. These data challenge the importance of current sexual selection in promoting rapid adaptation to environmental change but support the hypothesis that sex differences in LH-a historical signature of sexual selection-are key in shaping trait responses to novel selection.

Unconditionally stable finite-difference time-domain methods for modeling the Sagnac effect

NASA Astrophysics Data System (ADS)

Novitski, Roman; Scheuer, Jacob; Steinberg, Ben Z.

2013-02-01

We present two unconditionally stable finite-difference time-domain (FDTD) methods for modeling the Sagnac effect in rotating optical microsensors. The methods are based on the implicit Crank-Nicolson scheme, adapted to hold in the rotating system reference frame—the rotating Crank-Nicolson (RCN) methods. The first method (RCN-2) is second order accurate in space whereas the second method (RCN-4) is fourth order accurate. Both methods are second order accurate in time. We show that the RCN-4 scheme is more accurate and has better dispersion isotropy. The numerical results show good correspondence with the expression for the classical Sagnac resonant frequency splitting when using group refractive indices of the resonant modes of a microresonator. Also we show that the numerical results are consistent with the perturbation theory for the rotating degenerate microcavities. We apply our method to simulate the effect of rotation on an entire Coupled Resonator Optical Waveguide (CROW) consisting of a set of coupled microresonators. Preliminary results validate the formation of a rotation-induced gap at the center of a transfer function of a CROW.

Density-to-Potential Inversions to Guide Development of Exchange-Correlation Approximations at Finite Temperature

NASA Astrophysics Data System (ADS)

Jensen, Daniel; Wasserman, Adam; Baczewski, Andrew

The construction of approximations to the exchange-correlation potential for warm dense matter (WDM) is a topic of significant recent interest. In this work, we study the inverse problem of Kohn-Sham (KS) DFT as a means of guiding functional design at zero temperature and in WDM. Whereas the forward problem solves the KS equations to produce a density from a specified exchange-correlation potential, the inverse problem seeks to construct the exchange-correlation potential from specified densities. These two problems require different computational methods and convergence criteria despite sharing the same mathematical equations. We present two new inversion methods based on constrained variational and PDE-constrained optimization methods. We adapt these methods to finite temperature calculations to reveal the exchange-correlation potential's temperature dependence in WDM-relevant conditions. The different inversion methods presented are applied to both non-interacting and interacting model systems for comparison. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Security Administration under contract DE-AC04-94.

Solving the Fluid Pressure Poisson Equation Using Multigrid-Evaluation and Improvements.

PubMed

Dick, Christian; Rogowsky, Marcus; Westermann, Rudiger

2016-11-01

In many numerical simulations of fluids governed by the incompressible Navier-Stokes equations, the pressure Poisson equation needs to be solved to enforce mass conservation. Multigrid solvers show excellent convergence in simple scenarios, yet they can converge slowly in domains where physically separated regions are combined at coarser scales. Moreover, existing multigrid solvers are tailored to specific discretizations of the pressure Poisson equation, and they cannot easily be adapted to other discretizations. In this paper we analyze the convergence properties of existing multigrid solvers for the pressure Poisson equation in different simulation domains, and we show how to further improve the multigrid convergence rate by using a graph-based extension to determine the coarse grid hierarchy. The proposed multigrid solver is generic in that it can be applied to different kinds of discretizations of the pressure Poisson equation, by using solely the specification of the simulation domain and pre-assembled computational stencils. We analyze the proposed solver in combination with finite difference and finite volume discretizations of the pressure Poisson equation. Our evaluations show that, despite the common assumption, multigrid schemes can exploit their potential even in the most complicated simulation scenarios, yet this behavior is obtained at the price of higher memory consumption.

Novel Multistatic Adaptive Microwave Imaging Methods for Early Breast Cancer Detection

NASA Astrophysics Data System (ADS)

Xie, Yao; Guo, Bin; Li, Jian; Stoica, Petre

2006-12-01

Multistatic adaptive microwave imaging (MAMI) methods are presented and compared for early breast cancer detection. Due to the significant contrast between the dielectric properties of normal and malignant breast tissues, developing microwave imaging techniques for early breast cancer detection has attracted much interest lately. MAMI is one of the microwave imaging modalities and employs multiple antennas that take turns to transmit ultra-wideband (UWB) pulses while all antennas are used to receive the reflected signals. MAMI can be considered as a special case of the multi-input multi-output (MIMO) radar with the multiple transmitted waveforms being either UWB pulses or zeros. Since the UWB pulses transmitted by different antennas are displaced in time, the multiple transmitted waveforms are orthogonal to each other. The challenge to microwave imaging is to improve resolution and suppress strong interferences caused by the breast skin, nipple, and so forth. The MAMI methods we investigate herein utilize the data-adaptive robust Capon beamformer (RCB) to achieve high resolution and interference suppression. We will demonstrate the effectiveness of our proposed methods for breast cancer detection via numerical examples with data simulated using the finite-difference time-domain method based on a 3D realistic breast model.

Spatio-temporal evolution of perturbations in ensembles initialized by bred, Lyapunov and singular vectors

NASA Astrophysics Data System (ADS)

Pazó, Diego; Rodríguez, Miguel A.; López, Juan M.

2010-05-01

We study the evolution of finite perturbations in the Lorenz ‘96 model, a meteorological toy model of the atmosphere. The initial perturbations are chosen to be aligned along different dynamic vectors: bred, Lyapunov, and singular vectors. Using a particular vector determines not only the amplification rate of the perturbation but also the spatial structure of the perturbation and its stability under the evolution of the flow. The evolution of perturbations is systematically studied by means of the so-called mean-variance of logarithms diagram that provides in a very compact way the basic information to analyse the spatial structure. We discuss the corresponding advantages of using those different vectors for preparing initial perturbations to be used in ensemble prediction systems, focusing on key properties: dynamic adaptation to the flow, robustness, equivalence between members of the ensemble, etc. Among all the vectors considered here, the so-called characteristic Lyapunov vectors are possibly optimal, in the sense that they are both perfectly adapted to the flow and extremely robust.

Spatio-temporal evolution of perturbations in ensembles initialized by bred, Lyapunov and singular vectors

NASA Astrophysics Data System (ADS)

Pazó, Diego; Rodríguez, Miguel A.; López, Juan M.

2010-01-01

We study the evolution of finite perturbations in the Lorenz `96 model, a meteorological toy model of the atmosphere. The initial perturbations are chosen to be aligned along different dynamic vectors: bred, Lyapunov, and singular vectors. Using a particular vector determines not only the amplification rate of the perturbation but also the spatial structure of the perturbation and its stability under the evolution of the flow. The evolution of perturbations is systematically studied by means of the so-called mean-variance of logarithms diagram that provides in a very compact way the basic information to analyse the spatial structure. We discuss the corresponding advantages of using those different vectors for preparing initial perturbations to be used in ensemble prediction systems, focusing on key properties: dynamic adaptation to the flow, robustness, equivalence between members of the ensemble, etc. Among all the vectors considered here, the so-called characteristic Lyapunov vectors are possibly optimal, in the sense that they are both perfectly adapted to the flow and extremely robust.

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

NASA Astrophysics Data System (ADS)

Wu, Chin-Tien

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

Implementation of a flexible and scalable particle-in-cell method for massively parallel computations in the mantle convection code ASPECT

NASA Astrophysics Data System (ADS)

Gassmöller, Rene; Bangerth, Wolfgang

2016-04-01

Particle-in-cell methods have a long history and many applications in geodynamic modelling of mantle convection, lithospheric deformation and crustal dynamics. They are primarily used to track material information, the strain a material has undergone, the pressure-temperature history a certain material region has experienced, or the amount of volatiles or partial melt present in a region. However, their efficient parallel implementation - in particular combined with adaptive finite-element meshes - is complicated due to the complex communication patterns and frequent reassignment of particles to cells. Consequently, many current scientific software packages accomplish this efficient implementation by specifically designing particle methods for a single purpose, like the advection of scalar material properties that do not evolve over time (e.g., for chemical heterogeneities). Design choices for particle integration, data storage, and parallel communication are then optimized for this single purpose, making the code relatively rigid to changing requirements. Here, we present the implementation of a flexible, scalable and efficient particle-in-cell method for massively parallel finite-element codes with adaptively changing meshes. Using a modular plugin structure, we allow maximum flexibility of the generation of particles, the carried tracer properties, the advection and output algorithms, and the projection of properties to the finite-element mesh. We present scaling tests ranging up to tens of thousands of cores and tens of billions of particles. Additionally, we discuss efficient load-balancing strategies for particles in adaptive meshes with their strengths and weaknesses, local particle-transfer between parallel subdomains utilizing existing communication patterns from the finite element mesh, and the use of established parallel output algorithms like the HDF5 library. Finally, we show some relevant particle application cases, compare our implementation to a modern advection-field approach, and demonstrate under which conditions which method is more efficient. We implemented the presented methods in ASPECT (aspect.dealii.org), a freely available open-source community code for geodynamic simulations. The structure of the particle code is highly modular, and segregated from the PDE solver, and can thus be easily transferred to other programs, or adapted for various application cases.

Residual interference and wind tunnel wall adaption

NASA Technical Reports Server (NTRS)

Mokry, Miroslav

1989-01-01

Measured flow variables near the test section boundaries, used to guide adjustments of the walls in adaptive wind tunnels, can also be used to quantify the residual interference. Because of a finite number of wall control devices (jacks, plenum compartments), the finite test section length, and the approximation character of adaptation algorithms, the unconfined flow conditions are not expected to be precisely attained even in the fully adapted stage. The procedures for the evaluation of residual wall interference are essentially the same as those used for assessing the correction in conventional, non-adaptive wind tunnels. Depending upon the number of flow variables utilized, one can speak of one- or two-variable methods; in two dimensions also of Schwarz- or Cauchy-type methods. The one-variable methods use the measured static pressure and normal velocity at the test section boundary, but do not require any model representation. This is clearly of an advantage for adaptive wall test section, which are often relatively small with respect to the test model, and for the variety of complex flows commonly encountered in wind tunnel testing. For test sections with flexible walls the normal component of velocity is given by the shape of the wall, adjusted for the displacement effect of its boundary layer. For ventilated test section walls it has to be measured by the Calspan pipes, laser Doppler velocimetry, or other appropriate techniques. The interface discontinuity method, also described, is a genuine residual interference assessment technique. It is specific to adaptive wall wind tunnels, where the computation results for the fictitious flow in the exterior of the test section are provided.

Neural network disturbance observer-based distributed finite-time formation tracking control for multiple unmanned helicopters.

PubMed

Wang, Dandan; Zong, Qun; Tian, Bailing; Shao, Shikai; Zhang, Xiuyun; Zhao, Xinyi

2018-02-01

The distributed finite-time formation tracking control problem for multiple unmanned helicopters is investigated in this paper. The control object is to maintain the positions of follower helicopters in formation with external interferences. The helicopter model is divided into a second order outer-loop subsystem and a second order inner-loop subsystem based on multiple-time scale features. Using radial basis function neural network (RBFNN) technique, we first propose a novel finite-time multivariable neural network disturbance observer (FMNNDO) to estimate the external disturbance and model uncertainty, where the neural network (NN) approximation errors can be dynamically compensated by adaptive law. Next, based on FMNNDO, a distributed finite-time formation tracking controller and a finite-time attitude tracking controller are designed using the nonsingular fast terminal sliding mode (NFTSM) method. In order to estimate the second derivative of the virtual desired attitude signal, a novel finite-time sliding mode integral filter is designed. Finally, Lyapunov analysis and multiple-time scale principle ensure the realization of control goal in finite-time. The effectiveness of the proposed FMNNDO and controllers are then verified by numerical simulations. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Hierarchical coarse-graining transform.

PubMed

Pancaldi, Vera; King, Peter R; Christensen, Kim

2009-03-01

We present a hierarchical transform that can be applied to Laplace-like differential equations such as Darcy's equation for single-phase flow in a porous medium. A finite-difference discretization scheme is used to set the equation in the form of an eigenvalue problem. Within the formalism suggested, the pressure field is decomposed into an average value and fluctuations of different kinds and at different scales. The application of the transform to the equation allows us to calculate the unknown pressure with a varying level of detail. A procedure is suggested to localize important features in the pressure field based only on the fine-scale permeability, and hence we develop a form of adaptive coarse graining. The formalism and method are described and demonstrated using two synthetic toy problems.

The fundamentals of adaptive grid movement

NASA Technical Reports Server (NTRS)

Eiseman, Peter R.

1990-01-01

Basic grid point movement schemes are studied. The schemes are referred to as adaptive grids. Weight functions and equidistribution in one dimension are treated. The specification of coefficients in the linear weight, attraction to a given grid or a curve, and evolutionary forces are considered. Curve by curve and finite volume methods are described. The temporal coupling of partial differential equations solvers and grid generators was discussed.

Analyzing the Adaptive Mesh Refinement (AMR) Characteristics of a High-Order 2D Cubed-Sphere Shallow-Water Model

DOE PAGES

Ferguson, Jared O.; Jablonowski, Christiane; Johansen, Hans; ...

2016-11-09

Adaptive mesh refinement (AMR) is a technique that has been featured only sporadically in atmospheric science literature. This study aims to demonstrate the utility of AMR for simulating atmospheric flows. Several test cases are implemented in a 2D shallow-water model on the sphere using the Chombo-AMR dynamical core. This high-order finite-volume model implements adaptive refinement in both space and time on a cubed-sphere grid using a mapped-multiblock mesh technique. The tests consist of the passive advection of a tracer around moving vortices, a steady-state geostrophic flow, an unsteady solid-body rotation, a gravity wave impinging on a mountain, and the interactionmore » of binary vortices. Both static and dynamic refinements are analyzed to determine the strengths and weaknesses of AMR in both complex flows with small-scale features and large-scale smooth flows. The different test cases required different AMR criteria, such as vorticity or height-gradient based thresholds, in order to achieve the best accuracy for cost. The simulations show that the model can accurately resolve key local features without requiring global high-resolution grids. The adaptive grids are able to track features of interest reliably without inducing noise or visible distortions at the coarse–fine interfaces. Finally and furthermore, the AMR grids keep any degradations of the large-scale smooth flows to a minimum.« less

Analyzing the Adaptive Mesh Refinement (AMR) Characteristics of a High-Order 2D Cubed-Sphere Shallow-Water Model

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

Ferguson, Jared O.; Jablonowski, Christiane; Johansen, Hans

Adaptive mesh refinement (AMR) is a technique that has been featured only sporadically in atmospheric science literature. This study aims to demonstrate the utility of AMR for simulating atmospheric flows. Several test cases are implemented in a 2D shallow-water model on the sphere using the Chombo-AMR dynamical core. This high-order finite-volume model implements adaptive refinement in both space and time on a cubed-sphere grid using a mapped-multiblock mesh technique. The tests consist of the passive advection of a tracer around moving vortices, a steady-state geostrophic flow, an unsteady solid-body rotation, a gravity wave impinging on a mountain, and the interactionmore » of binary vortices. Both static and dynamic refinements are analyzed to determine the strengths and weaknesses of AMR in both complex flows with small-scale features and large-scale smooth flows. The different test cases required different AMR criteria, such as vorticity or height-gradient based thresholds, in order to achieve the best accuracy for cost. The simulations show that the model can accurately resolve key local features without requiring global high-resolution grids. The adaptive grids are able to track features of interest reliably without inducing noise or visible distortions at the coarse–fine interfaces. Finally and furthermore, the AMR grids keep any degradations of the large-scale smooth flows to a minimum.« less

An extension of the finite cell method using boolean operations

NASA Astrophysics Data System (ADS)

Abedian, Alireza; Düster, Alexander

2017-05-01

In the finite cell method, the fictitious domain approach is combined with high-order finite elements. The geometry of the problem is taken into account by integrating the finite cell formulation over the physical domain to obtain the corresponding stiffness matrix and load vector. In this contribution, an extension of the FCM is presented wherein both the physical and fictitious domain of an element are simultaneously evaluated during the integration. In the proposed extension of the finite cell method, the contribution of the stiffness matrix over the fictitious domain is subtracted from the cell, resulting in the desired stiffness matrix which reflects the contribution of the physical domain only. This method results in an exponential rate of convergence for porous domain problems with a smooth solution and accurate integration. In addition, it reduces the computational cost, especially when applying adaptive integration schemes based on the quadtree/octree. Based on 2D and 3D problems of linear elastostatics, numerical examples serve to demonstrate the efficiency and accuracy of the proposed method.

Time-independent hybrid enrichment for finite element solution of transient conduction–radiation in diffusive grey media

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

Mohamed, M. Shadi, E-mail: m.s.mohamed@durham.ac.uk; Seaid, Mohammed; Trevelyan, Jon

2013-10-15

We investigate the effectiveness of the partition-of-unity finite element method for transient conduction–radiation problems in diffusive grey media. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary diffusion approximation to the radiation in grey media. The coupled equations are integrated in time using a semi-implicit method in the finite element framework. We show that for the considered problems, a combination of hyperbolic and exponential enrichment functions based on an approximation of the boundary layer leads to improved accuracy compared to the conventional finite element method. It is illustrated that this approach canmore » be more efficient than using h adaptivity to increase the accuracy of the finite element method near the boundary walls. The performance of the proposed partition-of-unity method is analyzed on several test examples for transient conduction–radiation problems in two space dimensions.« less

Advances and trends in structures and dynamics; Proceedings of the Symposium, Washington, DC, October 22-25, 1984

NASA Technical Reports Server (NTRS)

Noor, A. K. (Editor); Hayduk, R. J. (Editor)

1985-01-01

Among the topics discussed are developments in structural engineering hardware and software, computation for fracture mechanics, trends in numerical analysis and parallel algorithms, mechanics of materials, advances in finite element methods, composite materials and structures, determinations of random motion and dynamic response, optimization theory, automotive tire modeling methods and contact problems, the damping and control of aircraft structures, and advanced structural applications. Specific topics covered include structural design expert systems, the evaluation of finite element system architectures, systolic arrays for finite element analyses, nonlinear finite element computations, hierarchical boundary elements, adaptive substructuring techniques in elastoplastic finite element analyses, automatic tracking of crack propagation, a theory of rate-dependent plasticity, the torsional stability of nonlinear eccentric structures, a computation method for fluid-structure interaction, the seismic analysis of three-dimensional soil-structure interaction, a stress analysis for a composite sandwich panel, toughness criterion identification for unidirectional composite laminates, the modeling of submerged cable dynamics, and damping synthesis for flexible spacecraft structures.

Improving a complex finite-difference ground water flow model through the use of an analytic element screening model

USGS Publications Warehouse

Hunt, R.J.; Anderson, M.P.; Kelson, V.A.

1998-01-01

This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.

High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains

NASA Technical Reports Server (NTRS)

Fisher, Travis C.; Carpenter, Mark H.

2013-01-01

Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.

Fully-Implicit Navier-Stokes (FIN-S)

NASA Technical Reports Server (NTRS)

Kirk, Benjamin S.

2010-01-01

FIN-S is a SUPG finite element code for flow problems under active development at NASA Lyndon B. Johnson Space Center and within PECOS: a) The code is built on top of the libMesh parallel, adaptive finite element library. b) The initial implementation of the code targeted supersonic/hypersonic laminar calorically perfect gas flows & conjugate heat transfer. c) Initial extension to thermochemical nonequilibrium about 9 months ago. d) The technologies in FIN-S have been enhanced through a strongly collaborative research effort with Sandia National Labs.

Approaches to the automatic generation and control of finite element meshes

NASA Technical Reports Server (NTRS)

Shephard, Mark S.

1987-01-01

The algorithmic approaches being taken to the development of finite element mesh generators capable of automatically discretizing general domains without the need for user intervention are discussed. It is demonstrated that because of the modeling demands placed on a automatic mesh generator, all the approaches taken to date produce unstructured meshes. Consideration is also given to both a priori and a posteriori mesh control devices for automatic mesh generators as well as their integration with geometric modeling and adaptive analysis procedures.

Fission-Fusion Adaptivity in Finite Elements for Nonlinear Dynamics of Shells

DTIC Science & Technology

1988-11-30

where mesh refinement will prove useful. In fact, the deviation of a bilinear element from a smooth shell midsurface can be related to the angle between...comparisons with nonadaptive meshes. Conclusions and further discussions are given in Section 6. -5- 2. FINITE ELEMENT FORMULATION The shape of the midsurface ...8217 22 , and e3 is defined so that e, and e2 are tangent to the midsurface and rotate with the element; 2. for each node, a triad b i is defined so that

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

NASA Technical Reports Server (NTRS)

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

1976-01-01

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

Explosive synchronization coexists with classical synchronization in the Kuramoto model

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

Danziger, Michael M., E-mail: michael.danziger@biu.ac.il; Havlin, Shlomo; Moskalenko, Olga I.

2016-06-15

Explosive synchronization has recently been reported in a system of adaptively coupled Kuramoto oscillators, without any conditions on the frequency or degree of the nodes. Here, we find that, in fact, the explosive phase coexists with the standard phase of the Kuramoto oscillators. We determine this by extending the mean-field theory of adaptively coupled oscillators with full coupling to the case with partial coupling of a fraction f. This analysis shows that a metastable region exists for all finite values of f > 0, and therefore explosive synchronization is expected for any perturbation of adaptively coupling added to the standard Kuramoto model.more » We verify this theory with GPU-accelerated simulations on very large networks (N ∼ 10{sup 6}) and find that, in fact, an explosive transition with hysteresis is observed for all finite couplings. By demonstrating that explosive transitions coexist with standard transitions in the limit of f → 0, we show that this behavior is far more likely to occur naturally than was previously believed.« less

Lossy Wavefield Compression for Full-Waveform Inversion

NASA Astrophysics Data System (ADS)

Boehm, C.; Fichtner, A.; de la Puente, J.; Hanzich, M.

2015-12-01

We present lossy compression techniques, tailored to the inexact computation of sensitivity kernels, that significantly reduce the memory requirements of adjoint-based minimization schemes. Adjoint methods are a powerful tool to solve tomography problems in full-waveform inversion (FWI). Yet they face the challenge of massive memory requirements caused by the opposite directions of forward and adjoint simulations and the necessity to access both wavefields simultaneously during the computation of the sensitivity kernel. Thus, storage, I/O operations, and memory bandwidth become key topics in FWI. In this talk, we present strategies for the temporal and spatial compression of the forward wavefield. This comprises re-interpolation with coarse time steps and an adaptive polynomial degree of the spectral element shape functions. In addition, we predict the projection errors on a hierarchy of grids and re-quantize the residuals with an adaptive floating-point accuracy to improve the approximation. Furthermore, we use the first arrivals of adjoint waves to identify "shadow zones" that do not contribute to the sensitivity kernel at all. Updating and storing the wavefield within these shadow zones is skipped, which reduces memory requirements and computational costs at the same time. Compared to check-pointing, our approach has only a negligible computational overhead, utilizing the fact that a sufficiently accurate sensitivity kernel does not require a fully resolved forward wavefield. Furthermore, we use adaptive compression thresholds during the FWI iterations to ensure convergence. Numerical experiments on the reservoir scale and for the Western Mediterranean prove the high potential of this approach with an effective compression factor of 500-1000. Furthermore, it is computationally cheap and easy to integrate in both, finite-differences and finite-element wave propagation codes.

ICASE Semiannual Report, October 1, 1992 through March 31, 1993

DTIC Science & Technology

1993-06-01

NUMERICAL MATHEMATICS Saul Abarbanel Further results have been obtained regarding long time integration of high order compact finite difference schemes...overall accuracy. These problems are common to all numerical methods: finite differences , finite elements and spectral methods. It should be noted that...fourth order finite difference scheme. * In the same case, the D6 wavelets provide a sixth order finite difference , noncompact formula. * The wavelets

Neural adaptive control for vibration suppression in composite fin-tip of aircraft.

PubMed

Suresh, S; Kannan, N; Sundararajan, N; Saratchandran, P

2008-06-01

In this paper, we present a neural adaptive control scheme for active vibration suppression of a composite aircraft fin tip. The mathematical model of a composite aircraft fin tip is derived using the finite element approach. The finite element model is updated experimentally to reflect the natural frequencies and mode shapes very accurately. Piezo-electric actuators and sensors are placed at optimal locations such that the vibration suppression is a maximum. Model-reference direct adaptive neural network control scheme is proposed to force the vibration level within the minimum acceptable limit. In this scheme, Gaussian neural network with linear filters is used to approximate the inverse dynamics of the system and the parameters of the neural controller are estimated using Lyapunov based update law. In order to reduce the computational burden, which is critical for real-time applications, the number of hidden neurons is also estimated in the proposed scheme. The global asymptotic stability of the overall system is ensured using the principles of Lyapunov approach. Simulation studies are carried-out using sinusoidal force functions of varying frequency. Experimental results show that the proposed neural adaptive control scheme is capable of providing significant vibration suppression in the multiple bending modes of interest. The performance of the proposed scheme is better than the H(infinity) control scheme.

Human spaceflight and space adaptations: Computational simulation of gravitational unloading on the spine

NASA Astrophysics Data System (ADS)

Townsend, Molly T.; Sarigul-Klijn, Nesrin

2018-04-01

Living in reduced gravitational environments for a prolonged duration such, as a fly by mission to Mars or an extended stay at the international space station, affects the human body - in particular, the spine. As the spine adapts to spaceflight, morphological and physiological changes cause the mechanical integrity of the spinal column to be compromised, potentially endangering internal organs, nervous health, and human body mechanical function. Therefore, a high fidelity computational model and simulation of the whole human spine was created and validated for the purpose of investigating the mechanical integrity of the spine in crew members during exploratory space missions. A spaceflight exposed spine has been developed through the adaptation of a three-dimensional nonlinear finite element model with the updated Lagrangian formulation of a healthy ground-based human spine in vivo. Simulation of the porohyperelastic response of the intervertebral disc to mechanical unloading resulted in a model capable of accurately predicting spinal swelling/lengthening, spinal motion, and internal stress distribution. The curvature of this space adaptation exposed spine model was compared to a control terrestrial-based finite element model, indicating how the shape changed. Finally, the potential of injury sites to crew members are predicted for a typical 9 day mission.

A software platform for continuum modeling of ion channels based on unstructured mesh

NASA Astrophysics Data System (ADS)

Tu, B.; Bai, S. Y.; Chen, M. X.; Xie, Y.; Zhang, L. B.; Lu, B. Z.

2014-01-01

Most traditional continuum molecular modeling adopted finite difference or finite volume methods which were based on a structured mesh (grid). Unstructured meshes were only occasionally used, but an increased number of applications emerge in molecular simulations. To facilitate the continuum modeling of biomolecular systems based on unstructured meshes, we are developing a software platform with tools which are particularly beneficial to those approaches. This work describes the software system specifically for the simulation of a typical, complex molecular procedure: ion transport through a three-dimensional channel system that consists of a protein and a membrane. The platform contains three parts: a meshing tool chain for ion channel systems, a parallel finite element solver for the Poisson-Nernst-Planck equations describing the electrodiffusion process of ion transport, and a visualization program for continuum molecular modeling. The meshing tool chain in the platform, which consists of a set of mesh generation tools, is able to generate high-quality surface and volume meshes for ion channel systems. The parallel finite element solver in our platform is based on the parallel adaptive finite element package PHG which wass developed by one of the authors [1]. As a featured component of the platform, a new visualization program, VCMM, has specifically been developed for continuum molecular modeling with an emphasis on providing useful facilities for unstructured mesh-based methods and for their output analysis and visualization. VCMM provides a graphic user interface and consists of three modules: a molecular module, a meshing module and a numerical module. A demonstration of the platform is provided with a study of two real proteins, the connexin 26 and hemolysin ion channels.

Energy Losses Estimation During Pulsed-Laser Seam Welding

NASA Astrophysics Data System (ADS)

Sebestova, Hana; Havelkova, Martina; Chmelickova, Hana

2014-06-01

The finite-element tool SYSWELD (ESI Group, Paris, France) was adapted to simulate pulsed-laser seam welding. Besides temperature field distribution, one of the possible outputs of the welding simulation is the amount of absorbed power necessary to melt the required material volume including energy losses. Comparing absorbed or melting energy with applied laser energy, welding efficiencies can be calculated. This article presents achieved results of welding efficiency estimation based on the assimilation both experimental and simulation output data of the pulsed Nd:YAG laser bead on plate welding of 0.6-mm-thick AISI 304 stainless steel sheets using different beam powers.

Three-body unitarity in the finite volume

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

Mai, M.; Döring, M.

We present the physical interpretation of lattice QCD simulations, performed in a small volume, requires an extrapolation to the infinite volume. A method is proposed to perform such an extrapolation for three interacting particles at energies above threshold. For this, a recently formulated relativisticmore » $$3\\to 3$$ amplitude based on the isobar formulation is adapted to the finite volume. The guiding principle is two- and three-body unitarity that imposes the imaginary parts of the amplitude in the infinite volume. In turn, these imaginary parts dictate the leading power-law finite-volume effects. It is demonstrated that finite-volume poles arising from the singular interaction, from the external two-body sub-amplitudes, and from the disconnected topology cancel exactly leaving only the genuine three-body eigenvalues. Lastly, the corresponding quantization condition is derived for the case of three identical scalar-isoscalar particles and its numerical implementation is demonstrated.« less

Three-body unitarity in the finite volume

DOE PAGES

Mai, M.; Döring, M.

2017-12-18

We present the physical interpretation of lattice QCD simulations, performed in a small volume, requires an extrapolation to the infinite volume. A method is proposed to perform such an extrapolation for three interacting particles at energies above threshold. For this, a recently formulated relativisticmore » $$3\\to 3$$ amplitude based on the isobar formulation is adapted to the finite volume. The guiding principle is two- and three-body unitarity that imposes the imaginary parts of the amplitude in the infinite volume. In turn, these imaginary parts dictate the leading power-law finite-volume effects. It is demonstrated that finite-volume poles arising from the singular interaction, from the external two-body sub-amplitudes, and from the disconnected topology cancel exactly leaving only the genuine three-body eigenvalues. Lastly, the corresponding quantization condition is derived for the case of three identical scalar-isoscalar particles and its numerical implementation is demonstrated.« less

Analytical Modeling of a Novel Transverse Flux Machine for Direct Drive Wind Turbine Applications: Preprint

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

Hasan, IIftekhar; Husain, Tausif; Uddin, Md Wasi

2015-08-24

This paper presents a nonlinear analytical model of a novel double-sided flux concentrating Transverse Flux Machine (TFM) based on the Magnetic Equivalent Circuit (MEC) model. The analytical model uses a series-parallel combination of flux tubes to predict the flux paths through different parts of the machine including air gaps, permanent magnets, stator, and rotor. The two-dimensional MEC model approximates the complex three-dimensional flux paths of the TFM and includes the effects of magnetic saturation. The model is capable of adapting to any geometry that makes it a good alternative for evaluating prospective designs of TFM compared to finite element solversmore » that are numerically intensive and require more computation time. A single-phase, 1-kW, 400-rpm machine is analytically modeled, and its resulting flux distribution, no-load EMF, and torque are verified with finite element analysis. The results are found to be in agreement, with less than 5% error, while reducing the computation time by 25 times.« less

Analytical Modeling of a Novel Transverse Flux Machine for Direct Drive Wind Turbine Applications

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

Hasan, IIftekhar; Husain, Tausif; Uddin, Md Wasi

2015-09-02

This paper presents a nonlinear analytical model of a novel double sided flux concentrating Transverse Flux Machine (TFM) based on the Magnetic Equivalent Circuit (MEC) model. The analytical model uses a series-parallel combination of flux tubes to predict the flux paths through different parts of the machine including air gaps, permanent magnets (PM), stator, and rotor. The two-dimensional MEC model approximates the complex three-dimensional flux paths of the TFM and includes the effects of magnetic saturation. The model is capable of adapting to any geometry which makes it a good alternative for evaluating prospective designs of TFM as compared tomore » finite element solvers which are numerically intensive and require more computation time. A single phase, 1 kW, 400 rpm machine is analytically modeled and its resulting flux distribution, no-load EMF and torque, verified with Finite Element Analysis (FEA). The results are found to be in agreement with less than 5% error, while reducing the computation time by 25 times.« less

Application of finite elements heterogeneous multi-scale method to eddy currents non destructive testing of carbon composites material

NASA Astrophysics Data System (ADS)

Khebbab, Mohamed; Feliachi, Mouloud; El Hadi Latreche, Mohamed

2018-03-01

In this present paper, a simulation of eddy current non-destructive testing (EC NDT) on unidirectional carbon fiber reinforced polymer is performed; for this magneto-dynamic formulation in term of magnetic vector potential is solved using finite element heterogeneous multi-scale method (FE HMM). FE HMM has as goal to compute the homogenized solution without calculating the homogenized tensor explicitly, the solution is based only on the physical characteristic known in micro domain. This feature is well adapted to EC NDT to evaluate defect in carbon composite material in microscopic scale, where the defect detection is performed by coil impedance measurement; the measurement value is intimately linked to material characteristic in microscopic level. Based on this, our model can handle different defects such as: cracks, inclusion, internal electrical conductivity changes, heterogeneities, etc. The simulation results were compared with the solution obtained with homogenized material using mixture law, a good agreement was found.

Development of a solution adaptive unstructured scheme for quasi-3D inviscid flows through advanced turbomachinery cascades

NASA Technical Reports Server (NTRS)

Usab, William J., Jr.; Jiang, Yi-Tsann

1991-01-01

The objective of the present research is to develop a general solution adaptive scheme for the accurate prediction of inviscid quasi-three-dimensional flow in advanced compressor and turbine designs. The adaptive solution scheme combines an explicit finite-volume time-marching scheme for unstructured triangular meshes and an advancing front triangular mesh scheme with a remeshing procedure for adapting the mesh as the solution evolves. The unstructured flow solver has been tested on a series of two-dimensional airfoil configurations including a three-element analytic test case presented here. Mesh adapted quasi-three-dimensional Euler solutions are presented for three spanwise stations of the NASA rotor 67 transonic fan. Computed solutions are compared with available experimental data.

Modelling volumetric growth in a thick walled fibre reinforced artery

NASA Astrophysics Data System (ADS)

Eriksson, T. S. E.; Watton, P. N.; Luo, X. Y.; Ventikos, Y.

2014-12-01

A novel framework for simulating growth and remodelling (G&R) of a fibre-reinforced artery, including volumetric adaption, is proposed. We show how to implement this model into a finite element framework and propose and examine two underlying assumptions for modelling growth, namely constant individual density (CID) or adaptive individual density (AID). Moreover, we formulate a novel approach which utilises a combination of both AID and CID to simulate volumetric G&R for a tissue composed of several different constituents. We consider a special case of the G&R of an artery subjected to prescribed elastin degradation and we theorise on the assumptions and suitability of CID, AID and the mixed approach for modelling arterial biology. For simulating the volumetric changes that occur during aneurysm enlargement, we observe that it is advantageous to describe the growth of collagen using CID whilst it is preferable to model the atrophy of elastin using AID.

Stress Distribution During Deformation of Polycrystalline Aluminum by Molecular-Dynamics and Finite-Element Modeling

NASA Technical Reports Server (NTRS)

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

2004-01-01

In this paper, a multiscale modelling strategy is used to study the effect of grain-boundary sliding on stress localization in a polycrystalline microstructure with an uneven distribution of grain size. The development of the molecular dynamics (MD) analysis used to interrogate idealized grain microstructures with various types of grain boundaries and the multiscale modelling strategies for modelling large systems of grains is discussed. Both molecular-dynamics and finite-element (FE) simulations for idealized polycrystalline models of identical geometry are presented with the purpose of demonstrating the effectiveness of the adapted finite-element method using cohesive zone models to reproduce grain-boundary sliding and its effect on the stress distribution in a polycrystalline metal. The yield properties of the grain-boundary interface, used in the FE simulations, are extracted from a MD simulation on a bicrystal. The models allow for the study of the load transfer between adjacent grains of very different size through grain-boundary sliding during deformation. A large-scale FE simulation of 100 grains of a typical microstructure is then presented to reveal that the stress distribution due to grain-boundary sliding during uniform tensile strain can lead to stress localization of two to three times the background stress, thus suggesting a significant effect on the failure properties of the metal.

Effects of finite pulse width on two-dimensional Fourier transform electron spin resonance.

PubMed

Liang, Zhichun; Crepeau, Richard H; Freed, Jack H

2005-12-01

Two-dimensional (2D) Fourier transform ESR techniques, such as 2D-ELDOR, have considerably improved the resolution of ESR in studies of molecular dynamics in complex fluids such as liquid crystals and membrane vesicles and in spin labeled polymers and peptides. A well-developed theory based on the stochastic Liouville equation (SLE) has been successfully employed to analyze these experiments. However, one fundamental assumption has been utilized to simplify the complex analysis, viz. the pulses have been treated as ideal non-selective ones, which therefore provide uniform irradiation of the whole spectrum. In actual experiments, the pulses are of finite width causing deviations from the theoretical predictions, a problem that is exacerbated by experiments performed at higher frequencies. In the present paper we provide a method to deal with the full SLE including the explicit role of the molecular dynamics, the spin Hamiltonian and the radiation field during the pulse. The computations are rendered more manageable by utilizing the Trotter formula, which is adapted to handle this SLE in what we call a "Split Super-Operator" method. Examples are given for different motional regimes, which show how 2D-ELDOR spectra are affected by the finite pulse widths. The theory shows good agreement with 2D-ELDOR experiments performed as a function of pulse width.

Computer-Aided Engineering of Semiconductor Integrated Circuits

DTIC Science & Technology

1979-07-01

equation using a five point finite difference approximation. Section 4.3.6 describes the numerical techniques and iterative algorithms which are used...neighbor points. This is generally referred to as a five point finite difference scheme on a rectangular grid, as described below. The finite difference ...problems in steady state have been analyzed by the finite difference method [4. 16 ] [4.17 3 or finite element method [4. 18 3, [4. 19 3 as reported last

Parallel three-dimensional magnetotelluric inversion using adaptive finite-element method. Part I: theory and synthetic study

NASA Astrophysics Data System (ADS)

Grayver, Alexander V.

2015-07-01

This paper presents a distributed magnetotelluric inversion scheme based on adaptive finite-element method (FEM). The key novel aspect of the introduced algorithm is the use of automatic mesh refinement techniques for both forward and inverse modelling. These techniques alleviate tedious and subjective procedure of choosing a suitable model parametrization. To avoid overparametrization, meshes for forward and inverse problems were decoupled. For calculation of accurate electromagnetic (EM) responses, automatic mesh refinement algorithm based on a goal-oriented error estimator has been adopted. For further efficiency gain, EM fields for each frequency were calculated using independent meshes in order to account for substantially different spatial behaviour of the fields over a wide range of frequencies. An automatic approach for efficient initial mesh design in inverse problems based on linearized model resolution matrix was developed. To make this algorithm suitable for large-scale problems, it was proposed to use a low-rank approximation of the linearized model resolution matrix. In order to fill a gap between initial and true model complexities and resolve emerging 3-D structures better, an algorithm for adaptive inverse mesh refinement was derived. Within this algorithm, spatial variations of the imaged parameter are calculated and mesh is refined in the neighborhoods of points with the largest variations. A series of numerical tests were performed to demonstrate the utility of the presented algorithms. Adaptive mesh refinement based on the model resolution estimates provides an efficient tool to derive initial meshes which account for arbitrary survey layouts, data types, frequency content and measurement uncertainties. Furthermore, the algorithm is capable to deliver meshes suitable to resolve features on multiple scales while keeping number of unknowns low. However, such meshes exhibit dependency on an initial model guess. Additionally, it is demonstrated that the adaptive mesh refinement can be particularly efficient in resolving complex shapes. The implemented inversion scheme was able to resolve a hemisphere object with sufficient resolution starting from a coarse discretization and refining mesh adaptively in a fully automatic process. The code is able to harness the computational power of modern distributed platforms and is shown to work with models consisting of millions of degrees of freedom. Significant computational savings were achieved by using locally refined decoupled meshes.

Control of finite critical behaviour in a small-scale social system

NASA Astrophysics Data System (ADS)

Daniels, Bryan C.; Krakauer, David C.; Flack, Jessica C.

2017-02-01

Many adaptive systems sit near a tipping or critical point. For systems near a critical point small changes to component behaviour can induce large-scale changes in aggregate structure and function. Criticality can be adaptive when the environment is changing, but entails reduced robustness through sensitivity. This tradeoff can be resolved when criticality can be tuned. We address the control of finite measures of criticality using data on fight sizes from an animal society model system (Macaca nemestrina, n=48). We find that a heterogeneous, socially organized system, like homogeneous, spatial systems (flocks and schools), sits near a critical point; the contributions individuals make to collective phenomena can be quantified; there is heterogeneity in these contributions; and distance from the critical point (DFC) can be controlled through biologically plausible mechanisms exploiting heterogeneity. We propose two alternative hypotheses for why a system decreases the distance from the critical point.

Finite element simulation of adaptive aerospace structures with SMA actuators

NASA Astrophysics Data System (ADS)

Frautschi, Jason; Seelecke, Stefan

2003-07-01

The particular demands of aerospace engineering have spawned many of the developments in the field of adaptive structures. Shape memory alloys are particularly attractive as actuators in these types of structures due to their large strains, high specific work output and potential for structural integration. However, the requisite extensive physical testing has slowed development of potential applications and highlighted the need for a simulation tool for feasibility studies. In this paper we present an implementation of an extended version of the M'ller-Achenbach SMA model into a commercial finite element code suitable for such studies. Interaction between the SMA model and the solution algorithm for the global FE equations is thoroughly investigated with respect to the effect of tolerances and time step size on convergence, computational cost and accuracy. Finally, a simulation of a SMA-actuated flexible trailing edge of an aircraft wing modeled with beam elements is presented.

Enhancing Least-Squares Finite Element Methods Through a Quantity-of-Interest

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

Chaudhry, Jehanzeb Hameed; Cyr, Eric C.; Liu, Kuo

2014-12-18

Here, we introduce an approach that augments least-squares finite element formulations with user-specified quantities-of-interest. The method incorporates the quantity-of-interest into the least-squares functional and inherits the global approximation properties of the standard formulation as well as increased resolution of the quantity-of-interest. We establish theoretical properties such as optimality and enhanced convergence under a set of general assumptions. Central to the approach is that it offers an element-level estimate of the error in the quantity-of-interest. As a result, we introduce an adaptive approach that yields efficient, adaptively refined approximations. Several numerical experiments for a range of situations are presented to supportmore » the theory and highlight the effectiveness of our methodology. Notably, the results show that the new approach is effective at improving the accuracy per total computational cost.« less

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

PubMed

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

2011-01-01

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

A design tool for direct and non-stochastic calculations of near-field radiative transfer in complex structures: The NF-RT-FDTD algorithm

NASA Astrophysics Data System (ADS)

Didari, Azadeh; Pinar Mengüç, M.

2017-08-01

Advances in nanotechnology and nanophotonics are inextricably linked with the need for reliable computational algorithms to be adapted as design tools for the development of new concepts in energy harvesting, radiative cooling, nanolithography and nano-scale manufacturing, among others. In this paper, we provide an outline for such a computational tool, named NF-RT-FDTD, to determine the near-field radiative transfer between structured surfaces using Finite Difference Time Domain method. NF-RT-FDTD is a direct and non-stochastic algorithm, which accounts for the statistical nature of the thermal radiation and is easily applicable to any arbitrary geometry at thermal equilibrium. We present a review of the fundamental relations for far- and near-field radiative transfer between different geometries with nano-scale surface and volumetric features and gaps, and then we discuss the details of the NF-RT-FDTD formulation, its application to sample geometries and outline its future expansion to more complex geometries. In addition, we briefly discuss some of the recent numerical works for direct and indirect calculations of near-field thermal radiation transfer, including Scattering Matrix method, Finite Difference Time Domain method (FDTD), Wiener Chaos Expansion, Fluctuating Surface Current (FSC), Fluctuating Volume Current (FVC) and Thermal Discrete Dipole Approximations (TDDA).

Microclimatic modeling of the desert in the United Arab Emirates

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

Khalil, A.K.; Abdrabboh, M.A.; Kamel, K.A.

1996-10-01

The present study is concerned with the prediction of the weather parameters in the microclimate layer (less than 2 m above the ground surface) in the desert and sparsely vegetated areas in the United Arab Emirates. A survey was made of the weather data in these regions including solar radiation, wind speed, screen temperatures and relative humidity. Additionally, wind speed data were obtained at heights below two meters and surface albedo was recorded for various soil and vegetation conditions. A survey was also carried out for the different plant species in various areas of the U.A.E. Data on soil andmore » surface temperature were then analyzed. An energy balance model was formulated including incident short- and long-wave length radiation between earth and sky, convective heat transfer to/from earth surface, surface reflection of solar radiation and soil/plant evapotranspiration. An explicit one dimensional finite difference scheme was adapted to solve the resulting algebraic finite difference equations. The equation for surface nodes included thermal radiation as well as convection effects. The heat transfer coefficient was evaluated on the basis of wind speed and surface roughness at the site where the energy balance was set. Theoretical predictions of air and soil temperatures were accordingly compared to experimental measurements in selected sites, where reasonable agreements were observed.« less

Progress on the development of FullWave, a Hot and Cold Plasma Parallel Full Wave Code

NASA Astrophysics Data System (ADS)

Spencer, J. Andrew; Svidzinski, Vladimir; Zhao, Liangji; Kim, Jin-Soo

2017-10-01

FullWave is being developed at FAR-TECH, Inc. to simulate RF waves in hot inhomogeneous magnetized plasmas without making small orbit approximations. FullWave is based on a meshless formulation in configuration space on non-uniform clouds of computational points (CCP) adapted to better resolve plasma resonances, antenna structures and complex boundaries. The linear frequency domain 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 is calculated. The details of FullWave and some preliminary results will be presented, including: 1) a monitor function based on analytic solutions of the cold-plasma dispersion relation; 2) an adaptive CCP based on the monitor function; 3) construction of the finite differences for approximation of derivatives on adaptive CCP; 4) results of 2-D full wave simulations in the cold plasma model in tokamak geometry using the formulated approach for ECRH, ICRH and Lower Hybrid range of frequencies. Work is supported by the U.S. DOE SBIR program.

Highly accurate adaptive TOF determination method for ultrasonic thickness measurement

NASA Astrophysics Data System (ADS)

Zhou, Lianjie; Liu, Haibo; Lian, Meng; Ying, Yangwei; Li, Te; Wang, Yongqing

2018-04-01

Determining the time of flight (TOF) is very critical for precise ultrasonic thickness measurement. However, the relatively low signal-to-noise ratio (SNR) of the received signals would induce significant TOF determination errors. In this paper, an adaptive time delay estimation method has been developed to improve the TOF determination’s accuracy. An improved variable step size adaptive algorithm with comprehensive step size control function is proposed. Meanwhile, a cubic spline fitting approach is also employed to alleviate the restriction of finite sampling interval. Simulation experiments under different SNR conditions were conducted for performance analysis. Simulation results manifested the performance advantage of proposed TOF determination method over existing TOF determination methods. When comparing with the conventional fixed step size, and Kwong and Aboulnasr algorithms, the steady state mean square deviation of the proposed algorithm was generally lower, which makes the proposed algorithm more suitable for TOF determination. Further, ultrasonic thickness measurement experiments were performed on aluminum alloy plates with various thicknesses. They indicated that the proposed TOF determination method was more robust even under low SNR conditions, and the ultrasonic thickness measurement accuracy could be significantly improved.

Comparative evaluation of shock absorption ability of custom-fit mouthguards with new-generation polyolefin self-adapting mouthguards in three different maxillary anterior teeth alignments using Fiber Bragg Grating (FBG) sensors.

PubMed

Grewal, Navneet; Kumari, Foolan; Tiwari, Umesh

2015-08-01

Prevention of orofacial injuries is one of the biggest pre-occupations in sports dentistry. The custom-fitted mouthguard is considered the best choice for fit and protection when compared to over-the-counter commercial mouthguards. However, cost and time prohibit their mass production. It is therefore imperative to have an over-the-counter true mouth-formed mouthguard with comparable properties. The present in vitro experimental study was carried out to compare the shock absorption ability of EVA laminate mouthguards with self-adapting polyolefin material mouthguards in three different anterior teeth alignments. Finite element analysis (FEA) was performed to simulate the stress distribution due to impact on the respective mouthguards. Customized pendulum device with three interchangeable standard size impact objects was used. Response of grating was monitored using a FBG interrogation system. Shift in wavelength for each impact was measured. Three standardized jaw models were subjected to a total of 72 impact strikes with three different balls on two specified sites by releasing the objects from two different heights H1 24 cm and H2 48 cm. Two-way ANOVA was applied and comparative values computed. It was found that the percentage shock absorption ability of self-adapted polyolefin mouthguard was highly significant at <0.001 level in both regions. The influence of height on the shock absorption ability of both mouthguards was highly significant at P < 0.001. It was concluded that self-adapting polyolefin mouthguards fulfill similar protection requirement as custom-fit mouthguards and can be used for millions of athletes if properly fitted chairside by a dentist without requiring laboratory fabrication. © 2014 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

Functional Data Approximation on Bounded Domains using Polygonal Finite Elements.

PubMed

Cao, Juan; Xiao, Yanyang; Chen, Zhonggui; Wang, Wenping; Bajaj, Chandrajit

2018-07-01

We construct and analyze piecewise approximations of functional data on arbitrary 2D bounded domains using generalized barycentric finite elements, and particularly quadratic serendipity elements for planar polygons. We compare approximation qualities (precision/convergence) of these partition-of-unity finite elements through numerical experiments, using Wachspress coordinates, natural neighbor coordinates, Poisson coordinates, mean value coordinates, and quadratic serendipity bases over polygonal meshes on the domain. For a convex n -sided polygon, the quadratic serendipity elements have 2 n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, rather than the usual n ( n + 1)/2 basis functions to achieve quadratic convergence. Two greedy algorithms are proposed to generate Voronoi meshes for adaptive functional/scattered data approximations. Experimental results show space/accuracy advantages for these quadratic serendipity finite elements on polygonal domains versus traditional finite elements over simplicial meshes. Polygonal meshes and parameter coefficients of the quadratic serendipity finite elements obtained by our greedy algorithms can be further refined using an L 2 -optimization to improve the piecewise functional approximation. We conduct several experiments to demonstrate the efficacy of our algorithm for modeling features/discontinuities in functional data/image approximation.

Investigating the spectral characteristics of backscattering from heterogeneous spherical nuclei using broadband finite-difference time-domain simulations

NASA Astrophysics Data System (ADS)

Chao, Guo-Shan; Sung, Kung-Bin

2010-01-01

Reflectance spectra measured from epithelial tissue have been used to extract size distribution and refractive index of cell nuclei for noninvasive detection of precancerous changes. Despite many in vitro and in vivo experimental results, the underlying mechanism of sizing nuclei based on modeling nuclei as homogeneous spheres and fitting the measured data with Mie theory has not been fully explored. We describe the implementation of a three-dimensional finite-difference time-domain (FDTD) simulation tool using a Gaussian pulse as the light source to investigate the wavelength-dependent characteristics of backscattered light from a nuclear model consisting of a nucleolus and clumps of chromatin embedded in homogeneous nucleoplasm. The results show that small-sized heterogeneities within the nuclei generate about five times higher backscattering than homogeneous spheres. More interestingly, backscattering spectra from heterogeneous spherical nuclei show periodic oscillations similar to those from homogeneous spheres, leading to high accuracy of estimating the nuclear diameter by comparison with Mie theory. In addition to the application in light scattering spectroscopy, the reported FDTD method could be adapted to study the relations between measured spectral data and nuclear structures in other optical imaging and spectroscopic techniques for in vivo diagnosis.

Performance of Nonlinear Finite-Difference Poisson-Boltzmann Solvers

PubMed Central

Cai, Qin; Hsieh, Meng-Juei; Wang, Jun; Luo, Ray

2014-01-01

We implemented and optimized seven finite-difference solvers for the full nonlinear Poisson-Boltzmann equation in biomolecular applications, including four relaxation methods, one conjugate gradient method, and two inexact Newton methods. The performance of the seven solvers was extensively evaluated with a large number of nucleic acids and proteins. Worth noting is the inexact Newton method in our analysis. We investigated the role of linear solvers in its performance by incorporating the incomplete Cholesky conjugate gradient and the geometric multigrid into its inner linear loop. We tailored and optimized both linear solvers for faster convergence rate. In addition, we explored strategies to optimize the successive over-relaxation method to reduce its convergence failures without too much sacrifice in its convergence rate. Specifically we attempted to adaptively change the relaxation parameter and to utilize the damping strategy from the inexact Newton method to improve the successive over-relaxation method. Our analysis shows that the nonlinear methods accompanied with a functional-assisted strategy, such as the conjugate gradient method and the inexact Newton method, can guarantee convergence in the tested molecules. Especially the inexact Newton method exhibits impressive performance when it is combined with highly efficient linear solvers that are tailored for its special requirement. PMID:24723843

Moisture Transport in Composites during Repair Work,

DTIC Science & Technology

1983-09-01

4 * FINITE DIFFERENCE EQUATIONS. .. . . .. . .. .. .. .. .. 6 INI I A ANBOUNAAYYCONDITIONS................ 7 REASONABLE FIRST...DURING DRYING AND CURING . . . ........ 9 5 CONVERGENCE OF FINITE DIFFERENCE METHOD USING DIFFERENT At . . .. 12 6 CONVERGENCE OF FDA METHOD FOR SAME At...transport we will use a finite difference approach, changing the Fickian equation to a finite number of linear algebraic equations that can be solved by

Accuracy requirements of optical linear algebra processors in adaptive optics imaging systems.

PubMed

Downie, J D; Goodman, J W

1989-10-15

A ground-based adaptive optics imaging telescope system attempts to improve image quality by measuring and correcting for atmospherically induced wavefront aberrations. The necessary control computations during each cycle will take a finite amount of time, which adds to the residual error variance since the atmosphere continues to change during that time. Thus an optical processor may be well-suited for this task. This paper investigates this possibility by studying the accuracy requirements in a general optical processor that will make it competitive with, or superior to, a conventional digital computer for adaptive optics use.

Adaptive control and noise suppression by a variable-gain gradient algorithm

NASA Technical Reports Server (NTRS)

Merhav, S. J.; Mehta, R. S.

1987-01-01

An adaptive control system based on normalized LMS filters is investigated. The finite impulse response of the nonparametric controller is adaptively estimated using a given reference model. Specifically, the following issues are addressed: The stability of the closed loop system is analyzed and heuristically established. Next, the adaptation process is studied for piecewise constant plant parameters. It is shown that by introducing a variable-gain in the gradient algorithm, a substantial reduction in the LMS adaptation rate can be achieved. Finally, process noise at the plant output generally causes a biased estimate of the controller. By introducing a noise suppression scheme, this bias can be substantially reduced and the response of the adapted system becomes very close to that of the reference model. Extensive computer simulations validate these and demonstrate assertions that the system can rapidly adapt to random jumps in plant parameters.

How Do Tissues Respond and Adapt to Stresses Around a Prosthesis? A Primer on Finite Element Stress Analysis for Orthopaedic Surgeons

PubMed Central

Brand, Richard A; Stanford, Clark M; Swan, Colby C

2003-01-01

Joint implant design clearly affects long-term outcome. While many implant designs have been empirically-based, finite element analysis has the potential to identify beneficial and deleterious features prior to clinical trials. Finite element analysis is a powerful analytic tool allowing computation of the stress and strain distribution throughout an implant construct. Whether it is useful depends upon many assumptions and details of the model. Since ultimate failure is related to biological factors in addition to mechanical, and since the mechanical causes of failure are related to load history, rather than a few loading conditions, chief among them is whether the stresses or strains under limited loading conditions relate to outcome. Newer approaches can minimize this and the many other model limitations. If the surgeon is to critically and properly interpret the results in scientific articles and sales literature, he or she must have a fundamental understanding of finite element analysis. We outline here the major capabilities of finite element analysis, as well as the assumptions and limitations. PMID:14575244

Time-dependent density functional theory with twist-averaged boundary conditions

NASA Astrophysics Data System (ADS)

Schuetrumpf, B.; Nazarewicz, W.; Reinhard, P.-G.

2016-05-01

Background: Time-dependent density functional theory is widely used to describe excitations of many-fermion systems. In its many applications, three-dimensional (3D) coordinate-space representation is used, and infinite-domain calculations are limited to a finite volume represented by a spatial box. For finite quantum systems (atoms, molecules, nuclei, hadrons), the commonly used periodic or reflecting boundary conditions introduce spurious quantization of the continuum states and artificial reflections from boundary; hence, an incorrect treatment of evaporated particles. Purpose: The finite-volume artifacts for finite systems can be practically cured by invoking an absorbing potential in a certain boundary region sufficiently far from the described system. However, such absorption cannot be applied in the calculations of infinite matter (crystal electrons, quantum fluids, neutron star crust), which suffer from unphysical effects stemming from a finite computational box used. Here, twist-averaged boundary conditions (TABC) have been used successfully to diminish the finite-volume effects. In this work, we extend TABC to time-dependent modes. Method: We use the 3D time-dependent density functional framework with the Skyrme energy density functional. The practical calculations are carried out for small- and large-amplitude electric dipole and quadrupole oscillations of 16O. We apply and compare three kinds of boundary conditions: periodic, absorbing, and twist-averaged. Results: Calculations employing absorbing boundary conditions (ABC) and TABC are superior to those based on periodic boundary conditions. For low-energy excitations, TABC and ABC variants yield very similar results. With only four twist phases per spatial direction in TABC, one obtains an excellent reduction of spurious fluctuations. In the nonlinear regime, one has to deal with evaporated particles. In TABC, the floating nucleon gas remains in the box; the amount of nucleons in the gas is found to be roughly the same as the number of absorbed particles in ABC. Conclusion: We demonstrate that by using TABC, one can reduce finite-volume effects drastically without adding any additional parameters associated with absorption at large distances. Moreover, TABC are an obvious choice for time-dependent calculations for infinite systems. Since TABC calculations for different twists can be performed independently, the method is trivially adapted to parallel computing.

Simulation of Needle-Type Corona Electrodes by the Finite Element Method

NASA Astrophysics Data System (ADS)

Yang, Shiyou; José Márcio, Machado; Nancy Mieko, Abe; Angelo, Passaro

2007-12-01

This paper describes a software tool, called LEVSOFT, suitable for the electric field simulations of corona electrodes by the Finite Element Method (FEM). Special attention was paid to the user friendly construction of geometries with corners and sharp points, and to the fast generation of highly refined triangular meshes and field maps. The execution of self-adaptive meshes was also implemented. These customized features make the code attractive for the simulation of needle-type corona electrodes. Some case examples involving needle type electrodes are presented.

Comparison of finite-difference schemes for analysis of shells of revolution. [stress and free vibration analysis

NASA Technical Reports Server (NTRS)

Noor, A. K.; Stephens, W. B.

1973-01-01

Several finite difference schemes are applied to the stress and free vibration analysis of homogeneous isotropic and layered orthotropic shells of revolution. The study is based on a form of the Sanders-Budiansky first-approximation linear shell theory modified such that the effects of shear deformation and rotary inertia are included. A Fourier approach is used in which all the shell stress resultants and displacements are expanded in a Fourier series in the circumferential direction, and the governing equations reduce to ordinary differential equations in the meridional direction. While primary attention is given to finite difference schemes used in conjunction with first order differential equation formulation, comparison is made with finite difference schemes used with other formulations. These finite difference discretization models are compared with respect to simplicity of application, convergence characteristics, and computational efficiency. Numerical studies are presented for the effects of variations in shell geometry and lamination parameters on the accuracy and convergence of the solutions obtained by the different finite difference schemes. On the basis of the present study it is shown that the mixed finite difference scheme based on the first order differential equation formulation and two interlacing grids for the different fundamental unknowns combines a number of advantages over other finite difference schemes previously reported in the literature.

Robust adaptive uniform exact tracking control for uncertain Euler-Lagrange system

NASA Astrophysics Data System (ADS)

Yang, Yana; Hua, Changchun; Li, Junpeng; Guan, Xinping

2017-12-01

This paper offers a solution to the robust adaptive uniform exact tracking control for uncertain nonlinear Euler-Lagrange (EL) system. An adaptive finite-time tracking control algorithm is designed by proposing a novel nonsingular integral terminal sliding-mode surface. Moreover, a new adaptive parameter tuning law is also developed by making good use of the system tracking errors and the adaptive parameter estimation errors. Thus, both the trajectory tracking and the parameter estimation can be achieved in a guaranteed time adjusted arbitrarily based on practical demands, simultaneously. Additionally, the control result for the EL system proposed in this paper can be extended to high-order nonlinear systems easily. Finally, a test-bed 2-DOF robot arm is set-up to demonstrate the performance of the new control algorithm.

Robust partial integrated guidance and control for missiles via extended state observer.

PubMed

Wang, Qing; Ran, Maopeng; Dong, Chaoyang

2016-11-01

A novel extended state observer (ESO) based control is proposed for a class of nonlinear systems subject to multiple uncertainties, and then applied to partial integrated guidance and control (PIGC) design for a missile. The proposed control strategy incorporates both an ESO and an adaptive sliding mode control law. The multiple uncertainties are treated as an extended state of the plant, and then estimate them using the ESO and compensate for them in the control action, in real time. Based on the output of the ESO, the resulting adaptive sliding mode control law is inherently continuous and differentiable. Strict proof is given to show that the estimation error of the ESO can be arbitrarily small in a finite time. In addition, the adaptive sliding mode control law can achieve finite time convergence to a neighborhood of the origin, and the accurate expression of the convergent region is given. Finally, simulations are conducted on the planar missile-target engagement geometry. The effectiveness of the proposed control strategy in enhanced interception performance and improved robustness against multiple uncertainties are demonstrated. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Adaptive Multi-Layer LMS Controller Design and Application to Active Vibration Suppression on a Truss and Proposed Impact Analysis Technique

NASA Technical Reports Server (NTRS)

Barney, Timothy A.; Shin, Y. S.; Agrawal, B. N.

2001-01-01

This research develops an adaptive controller that actively suppresses a single frequency disturbance source at a remote position and tests the system on the NPS Space Truss. The experimental results are then compared to those predicted by an ANSYS finite element model. The NPS space truss is a 3.7-meter long truss that simulates a space-borne appendage with sensitive equipment mounted at its extremities. One of two installed piezoelectric actuators and an Adaptive Multi-Layer LMS control law were used to effectively eliminate an axial component of the vibrations induced by a linear proof mass actuator mounted at one end of the truss. Experimental and analytical results both demonstrate reductions to the level of system noise. Vibration reductions in excess of 50dB were obtained through experimentation and over 100dB using ANSYS, demonstrating the ability to model this system with a finite element model. This report also proposes a method to use distributed quartz accelerometers to evaluate the location, direction, and energy of impacts on the NPS space truss using the dSPACE data acquisition and processing system to capture the structural response and compare it to known reference Signals.

A cellular automaton - finite volume method for the simulation of dendritic and eutectic growth in binary alloys using an adaptive mesh refinement

NASA Astrophysics Data System (ADS)

Dobravec, Tadej; Mavrič, Boštjan; Šarler, Božidar

2017-11-01

A two-dimensional model to simulate the dendritic and eutectic growth in binary alloys is developed. A cellular automaton method is adopted to track the movement of the solid-liquid interface. The diffusion equation is solved in the solid and liquid phases by using an explicit finite volume method. The computational domain is divided into square cells that can be hierarchically refined or coarsened using an adaptive mesh based on the quadtree algorithm. Such a mesh refines the regions of the domain near the solid-liquid interface, where the highest concentration gradients are observed. In the regions where the lowest concentration gradients are observed the cells are coarsened. The originality of the work is in the novel, adaptive approach to the efficient and accurate solution of the posed multiscale problem. The model is verified and assessed by comparison with the analytical results of the Lipton-Glicksman-Kurz model for the steady growth of a dendrite tip and the Jackson-Hunt model for regular eutectic growth. Several examples of typical microstructures are simulated and the features of the method as well as further developments are discussed.

Adaptive extended-state observer-based fault tolerant attitude control for spacecraft with reaction wheels

NASA Astrophysics Data System (ADS)

Ran, Dechao; Chen, Xiaoqian; de Ruiter, Anton; Xiao, Bing

2018-04-01

This study presents an adaptive second-order sliding control scheme to solve the attitude fault tolerant control problem of spacecraft subject to system uncertainties, external disturbances and reaction wheel faults. A novel fast terminal sliding mode is preliminarily designed to guarantee that finite-time convergence of the attitude errors can be achieved globally. Based on this novel sliding mode, an adaptive second-order observer is then designed to reconstruct the system uncertainties and the actuator faults. One feature of the proposed observer is that the design of the observer does not necessitate any priori information of the upper bounds of the system uncertainties and the actuator faults. In view of the reconstructed information supplied by the designed observer, a second-order sliding mode controller is developed to accomplish attitude maneuvers with great robustness and precise tracking accuracy. Theoretical stability analysis proves that the designed fault tolerant control scheme can achieve finite-time stability of the closed-loop system, even in the presence of reaction wheel faults and system uncertainties. Numerical simulations are also presented to demonstrate the effectiveness and superiority of the proposed control scheme over existing methodologies.

Highly accurate adaptive finite element schemes for nonlinear hyperbolic problems

NASA Astrophysics Data System (ADS)

Oden, J. T.

1992-08-01

This document is a final report of research activities supported under General Contract DAAL03-89-K-0120 between the Army Research Office and the University of Texas at Austin from July 1, 1989 through June 30, 1992. The project supported several Ph.D. students over the contract period, two of which are scheduled to complete dissertations during the 1992-93 academic year. Research results produced during the course of this effort led to 6 journal articles, 5 research reports, 4 conference papers and presentations, 1 book chapter, and two dissertations (nearing completion). It is felt that several significant advances were made during the course of this project that should have an impact on the field of numerical analysis of wave phenomena. These include the development of high-order, adaptive, hp-finite element methods for elastodynamic calculations and high-order schemes for linear and nonlinear hyperbolic systems. Also, a theory of multi-stage Taylor-Galerkin schemes was developed and implemented in the analysis of several wave propagation problems, and was configured within a general hp-adaptive strategy for these types of problems. Further details on research results and on areas requiring additional study are given in the Appendix.

Progress in Computational Simulation of Earthquakes

NASA Technical Reports Server (NTRS)

Donnellan, Andrea; Parker, Jay; Lyzenga, Gregory; Judd, Michele; Li, P. Peggy; Norton, Charles; Tisdale, Edwin; Granat, Robert

2006-01-01

GeoFEST(P) is a computer program written for use in the QuakeSim project, which is devoted to development and improvement of means of computational simulation of earthquakes. GeoFEST(P) models interacting earthquake fault systems from the fault-nucleation to the tectonic scale. The development of GeoFEST( P) has involved coupling of two programs: GeoFEST and the Pyramid Adaptive Mesh Refinement Library. GeoFEST is a message-passing-interface-parallel code that utilizes a finite-element technique to simulate evolution of stress, fault slip, and plastic/elastic deformation in realistic materials like those of faulted regions of the crust of the Earth. The products of such simulations are synthetic observable time-dependent surface deformations on time scales from days to decades. Pyramid Adaptive Mesh Refinement Library is a software library that facilitates the generation of computational meshes for solving physical problems. In an application of GeoFEST(P), a computational grid can be dynamically adapted as stress grows on a fault. Simulations on workstations using a few tens of thousands of stress and displacement finite elements can now be expanded to multiple millions of elements with greater than 98-percent scaled efficiency on over many hundreds of parallel processors (see figure).

A total variation diminishing finite difference algorithm for sonic boom propagation models

NASA Technical Reports Server (NTRS)

Sparrow, Victor W.

1993-01-01

It is difficult to accurately model the rise phases of sonic boom waveforms with traditional finite difference algorithms because of finite difference phase dispersion. This paper introduces the concept of a total variation diminishing (TVD) finite difference method as a tool for accurately modeling the rise phases of sonic booms. A standard second order finite difference algorithm and its TVD modified counterpart are both applied to the one-way propagation of a square pulse. The TVD method clearly outperforms the non-TVD method, showing great potential as a new computational tool in the analysis of sonic boom propagation.

An accurate discontinuous Galerkin method for solving point-source Eikonal equation in 2-D heterogeneous anisotropic media

NASA Astrophysics Data System (ADS)

Le Bouteiller, P.; Benjemaa, M.; Métivier, L.; Virieux, J.

2018-03-01

Accurate numerical computation of wave traveltimes in heterogeneous media is of major interest for a large range of applications in seismics, such as phase identification, data windowing, traveltime tomography and seismic imaging. A high level of precision is needed for traveltimes and their derivatives in applications which require quantities such as amplitude or take-off angle. Even more challenging is the anisotropic case, where the general Eikonal equation is a quartic in the derivatives of traveltimes. Despite their efficiency on Cartesian meshes, finite-difference solvers are inappropriate when dealing with unstructured meshes and irregular topographies. Moreover, reaching high orders of accuracy generally requires wide stencils and high additional computational load. To go beyond these limitations, we propose a discontinuous-finite-element-based strategy which has the following advantages: (1) the Hamiltonian formalism is general enough for handling the full anisotropic Eikonal equations; (2) the scheme is suitable for any desired high-order formulation or mixing of orders (p-adaptivity); (3) the solver is explicit whatever Hamiltonian is used (no need to find the roots of the quartic); (4) the use of unstructured meshes provides the flexibility for handling complex boundary geometries such as topographies (h-adaptivity) and radiation boundary conditions for mimicking an infinite medium. The point-source factorization principles are extended to this discontinuous Galerkin formulation. Extensive tests in smooth analytical media demonstrate the high accuracy of the method. Simulations in strongly heterogeneous media illustrate the solver robustness to realistic Earth-sciences-oriented applications.

An Automation Framework for Neural Nets that Learn

ERIC Educational Resources Information Center

Kilmer, W. L.; Arbib, M. A.

1973-01-01

A discussion of several types of formal neurons, many of whose functions are modifiable by their own input stimuli. The language of finite automata is used to mathematicize the problem of adaptation sufficiently to remove some ambiguities of Brindley's approach. (Author)

Optimal design of composite hip implants using NASA technology

NASA Technical Reports Server (NTRS)

Blake, T. A.; Saravanos, D. A.; Davy, D. T.; Waters, S. A.; Hopkins, D. A.

1993-01-01

Using an adaptation of NASA software, we have investigated the use of numerical optimization techniques for the shape and material optimization of fiber composite hip implants. The original NASA inhouse codes, were originally developed for the optimization of aerospace structures. The adapted code, which was called OPORIM, couples numerical optimization algorithms with finite element analysis and composite laminate theory to perform design optimization using both shape and material design variables. The external and internal geometry of the implant and the surrounding bone is described with quintic spline curves. This geometric representation is then used to create an equivalent 2-D finite element model of the structure. Using laminate theory and the 3-D geometric information, equivalent stiffnesses are generated for each element of the 2-D finite element model, so that the 3-D stiffness of the structure can be approximated. The geometric information to construct the model of the femur was obtained from a CT scan. A variety of test cases were examined, incorporating several implant constructions and design variable sets. Typically the code was able to produce optimized shape and/or material parameters which substantially reduced stress concentrations in the bone adjacent of the implant. The results indicate that this technology can provide meaningful insight into the design of fiber composite hip implants.

Finite Volume Algorithms for Heat Conduction

DTIC Science & Technology

2010-05-01

scalar quantity). Although (3) is relatively easy to discretize by using finite differences , its form in generalized coordinates is not. Later, we...familiar with the finite difference method for discretizing differential equations. In fact, the Newton divided difference is the numerical analog for a...expression (8) for the average derivative matches the Newton divided difference formula, so for uniform one-dimensional meshes, the finite volume and

A Kirchhoff Approach to Seismic Modeling and Prestack Depth Migration

DTIC Science & Technology

1993-05-01

continuation of sources and geophones by finite difference (S-G finite - difference migration ), are relatively slow and dip-limited. Compared to S-G... finite - difference migration , the Kirchhoff integral implements prestack migration relatively efficiently and has no dip limitation. Liu .Mlodeling and...for modeling and migration . In this paper, a finite - difference algorithm is used to calculate traveltimes and amplitudes. With the help of

Evaluation of finite difference and FFT-based solutions of the transport of intensity equation.

PubMed

Zhang, Hongbo; Zhou, Wen-Jing; Liu, Ying; Leber, Donald; Banerjee, Partha; Basunia, Mahmudunnabi; Poon, Ting-Chung

2018-01-01

A finite difference method is proposed for solving the transport of intensity equation. Simulation results show that although slower than fast Fourier transform (FFT)-based methods, finite difference methods are able to reconstruct the phase with better accuracy due to relaxed assumptions for solving the transport of intensity equation relative to FFT methods. Finite difference methods are also more flexible than FFT methods in dealing with different boundary conditions.

Finite elements and finite differences for transonic flow calculations

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Murman, E. M.; Wellford, L. C.

1978-01-01

The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.

A finite difference method for off-fault plasticity throughout the earthquake cycle

NASA Astrophysics Data System (ADS)

Erickson, Brittany A.; Dunham, Eric M.; Khosravifar, Arash

2017-12-01

We have developed an efficient computational framework for simulating multiple earthquake cycles with off-fault plasticity. The method is developed for the classical antiplane problem of a vertical strike-slip fault governed by rate-and-state friction, with inertial effects captured through the radiation-damping approximation. Both rate-independent plasticity and viscoplasticity are considered, where stresses are constrained by a Drucker-Prager yield condition. The off-fault volume is discretized using finite differences and tectonic loading is imposed by displacing the remote side boundaries at a constant rate. Time-stepping combines an adaptive Runge-Kutta method with an incremental solution process which makes use of an elastoplastic tangent stiffness tensor and the return-mapping algorithm. Solutions are verified by convergence tests and comparison to a finite element solution. We quantify how viscosity, isotropic hardening, and cohesion affect the magnitude and off-fault extent of plastic strain that develops over many ruptures. If hardening is included, plastic strain saturates after the first event and the response during subsequent ruptures is effectively elastic. For viscoplasticity without hardening, however, successive ruptures continue to generate additional plastic strain. In all cases, coseismic slip in the shallow sub-surface is diminished compared to slip accumulated at depth during interseismic loading. The evolution of this slip deficit with each subsequent event, however, is dictated by the plasticity model. Integration of the off-fault plastic strain from the viscoplastic model reveals that a significant amount of tectonic offset is accommodated by inelastic deformation ( ∼ 0.1 m per rupture, or ∼ 10% of the tectonic deformation budget).

A comparative study of finite element and finite difference methods for Cauchy-Riemann type equations

NASA Technical Reports Server (NTRS)

Fix, G. J.; Rose, M. E.

1983-01-01

A least squares formulation of the system divu = rho, curlu = zeta is surveyed from the viewpoint of both finite element and finite difference methods. Closely related arguments are shown to establish convergence estimates.

Influence of technological factors on characteristics of hybrid fluid-film bearings

NASA Astrophysics Data System (ADS)

Koltsov, A.; Prosekova, A.; Rodichev, A.; Savin, L.

2017-08-01

The influence of the parameters of micro- and macrounevenness on the characteristics of a hybrid bearing with slotted throttling is considered in the present paper. The quantitative assumptions of calculation of pressure distribution, load capacity, lubricant flow rate and power loss due to friction in a radial hybrid bearing with slotted throttling are taken into account, considering the shape, dimensions and roughness of the support surfaces inaccuracies. Numerical simulation of processes in the lubricating layer is based on the finite-difference solution of the Reynolds equation using an uneven orthogonal computational grid with adaptive condensation. The results of computational and physical experiments are presented.

Efficient numerical method for solving Cauchy problem for the Gamma equation

NASA Astrophysics Data System (ADS)

Koleva, Miglena N.

2011-12-01

In this work we consider Cauchy problem for the so called Gamma equation, derived by transforming the fully nonlinear Black-Scholes equation for option price into a quasilinear parabolic equation for the second derivative (Greek) Γ = VSS of the option price V. We develop an efficient numerical method for solving the model problem concerning different volatility terms. Using suitable change of variables the problem is transformed on finite interval, keeping original behavior of the solution at the infinity. Then we construct Picard-Newton algorithm with adaptive mesh step in time, which can be applied also in the case of non-differentiable functions. Results of numerical simulations are given.

Computational Design of Tunable UV-Vis-IR Filters Based on Silver Nanoparticle Arrays

NASA Astrophysics Data System (ADS)

Waters, Michael; Shi, Guangsha; Kioupakis, Emmanouil

We propose design strategies to develop selective optical filters in the UV-Vis-IR spectrum using the surface plasmon response of silver nanoparticle arrays. Our finite-difference time-domain simulations allow us to rapidly evaluate many nanostructures comprising simple geometries while varying their shape, height, width, and spacing. Our results allow us to identify trends in the filtering spectra as well as the relative amount of absorption and reflection. Optical filtering with nanoparticles is applicable to any transparent substrate and can be easily adapted to existing manufacturing processes while keeping the total cost of materials low. This work was supported by Guardian Industries Corp.

Eliminating the zero spectrum in Fourier transform profilometry using empirical mode decomposition.

PubMed

Li, Sikun; Su, Xianyu; Chen, Wenjing; Xiang, Liqun

2009-05-01

Empirical mode decomposition is introduced into Fourier transform profilometry to extract the zero spectrum included in the deformed fringe pattern without the need for capturing two fringe patterns with pi phase difference. The fringe pattern is subsequently demodulated using a standard Fourier transform profilometry algorithm. With this method, the deformed fringe pattern is adaptively decomposed into a finite number of intrinsic mode functions that vary from high frequency to low frequency by means of an algorithm referred to as a sifting process. Then the zero spectrum is separated from the high-frequency components effectively. Experiments validate the feasibility of this method.

Elastic properties of external cortical bone in the craniofacial skeleton of the rhesus monkey.

PubMed

Wang, Qian; Dechow, Paul C

2006-11-01

Knowledge of elastic properties and of their variation in the cortical bone of the craniofacial skeleton is indispensable for creating accurate finite-element models to explore the biomechanics and adaptation of the skull in primates. In this study, we measured elastic properties of the external cortex of the rhesus monkey craniofacial skeleton, using an ultrasonic technique. Twenty-eight cylindrical cortical specimens were removed from each of six craniofacial skeletons of adult Macaca mulatta. Thickness, density, and a set of longitudinal and transverse ultrasonic velocities were measured on each specimen to allow calculation of the elastic properties in three dimensions, according to equations derived from Newton's second law and Hooke's law. The axes of maximum stiffness were determined by fitting longitudinal velocities measured along the perimeter of each cortical specimen to a sinusoidal function. Results showed significant differences in elastic properties between different functional areas of the rhesus cranium, and that many sites have a consistent orientation of maximum stiffness among specimens. Overall, the cortical bones of the rhesus monkey skull can be modeled as orthotropic in many regions, and as transversely isotropic in some regions, e.g., the supraorbital region. There are differences from human crania, suggesting that structural differences in skeletal form relate to differences in cortical material properties across species. These differences also suggest that we require more comparative data on elastic properties in primate craniofacial skeletons to explore effectively the functional significance of these differences, especially when these differences are elucidated through modeling approaches, such as finite-element modeling. (c) 2006 Wiley-Liss, Inc.

An efficicient data structure for three-dimensional vertex based finite volume method

NASA Astrophysics Data System (ADS)

Akkurt, Semih; Sahin, Mehmet

2017-11-01

A vertex based three-dimensional finite volume algorithm has been developed using an edge based data structure.The mesh data structure of the given algorithm is similar to ones that exist in the literature. However, the data structures are redesigned and simplied in order to fit requirements of the vertex based finite volume method. In order to increase the cache efficiency, the data access patterns for the vertex based finite volume method are investigated and these datas are packed/allocated in a way that they are close to each other in the memory. The present data structure is not limited with tetrahedrons, arbitrary polyhedrons are also supported in the mesh without putting any additional effort. Furthermore, the present data structure also supports adaptive refinement and coarsening. For the implicit and parallel implementation of the FVM algorithm, PETSc and MPI libraries are employed. The performance and accuracy of the present algorithm are tested for the classical benchmark problems by comparing the CPU time for the open source algorithms.

An atomic finite element model for biodegradable polymers. Part 1. Formulation of the finite elements.

PubMed

Gleadall, Andrew; Pan, Jingzhe; Ding, Lifeng; Kruft, Marc-Anton; Curcó, David

2015-11-01

Molecular dynamics (MD) simulations are widely used to analyse materials at the atomic scale. However, MD has high computational demands, which may inhibit its use for simulations of structures involving large numbers of atoms such as amorphous polymer structures. An atomic-scale finite element method (AFEM) is presented in this study with significantly lower computational demands than MD. Due to the reduced computational demands, AFEM is suitable for the analysis of Young's modulus of amorphous polymer structures. This is of particular interest when studying the degradation of bioresorbable polymers, which is the topic of an accompanying paper. AFEM is derived from the inter-atomic potential energy functions of an MD force field. The nonlinear MD functions were adapted to enable static linear analysis. Finite element formulations were derived to represent interatomic potential energy functions between two, three and four atoms. Validation of the AFEM was conducted through its application to atomic structures for crystalline and amorphous poly(lactide). Copyright © 2015 Elsevier Ltd. All rights reserved.

A staggered-grid finite-difference scheme optimized in the time–space domain for modeling scalar-wave propagation in geophysical problems

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

Tan, Sirui, E-mail: siruitan@hotmail.com; Huang, Lianjie, E-mail: ljh@lanl.gov

For modeling scalar-wave propagation in geophysical problems using finite-difference schemes, optimizing the coefficients of the finite-difference operators can reduce numerical dispersion. Most optimized finite-difference schemes for modeling seismic-wave propagation suppress only spatial but not temporal dispersion errors. We develop a novel optimized finite-difference scheme for numerical scalar-wave modeling to control dispersion errors not only in space but also in time. Our optimized scheme is based on a new stencil that contains a few more grid points than the standard stencil. We design an objective function for minimizing relative errors of phase velocities of waves propagating in all directions within amore » given range of wavenumbers. Dispersion analysis and numerical examples demonstrate that our optimized finite-difference scheme is computationally up to 2.5 times faster than the optimized schemes using the standard stencil to achieve the similar modeling accuracy for a given 2D or 3D problem. Compared with the high-order finite-difference scheme using the same new stencil, our optimized scheme reduces 50 percent of the computational cost to achieve the similar modeling accuracy. This new optimized finite-difference scheme is particularly useful for large-scale 3D scalar-wave modeling and inversion.« less

Limited Plasticity of Prismatic Visuomotor Adaptation

PubMed Central

Wischhusen, Sven; Fahle, Manfred

2017-01-01

Movements toward an object displaced optically through prisms adapt quickly, a striking example for the plasticity of neuronal visuomotor programs. We investigated the degree and time course of this system’s plasticity. Participants performed goal-directed throwing or pointing movements with terminal feedback before, during, and after wearing prism goggles shifting the visual world laterally either to the right or to the left. Prism adaptation was incomplete even after 240 throwing movements, still deviating significantly laterally by on average of 0.8° (CI = 0.20°) at the end of the adaptation period. The remaining lateral deviation was significant for pointing movements only with left shifting prisms. In both tasks, removal of the prisms led to an aftereffect which disappeared in the course of further training. This incomplete prism adaptation may be caused by movement variability combined with an adaptive neuronal control system exhibiting a finite capacity for evaluating movement errors. PMID:28473909

Quantum Transduction with Adaptive Control

NASA Astrophysics Data System (ADS)

Zhang, Mengzhen; Zou, Chang-Ling; Jiang, Liang

2018-01-01

Quantum transducers play a crucial role in hybrid quantum networks. A good quantum transducer can faithfully convert quantum signals from one mode to another with minimum decoherence. Most investigations of quantum transduction are based on the protocol of direct mode conversion. However, the direct protocol requires the matching condition, which in practice is not always feasible. Here we propose an adaptive protocol for quantum transducers, which can convert quantum signals without requiring the matching condition. The adaptive protocol only consists of Gaussian operations, feasible in various physical platforms. Moreover, we show that the adaptive protocol can be robust against imperfections associated with finite squeezing, thermal noise, and homodyne detection, and it can be implemented to realize quantum state transfer between microwave and optical modes.

Quantum Transduction with Adaptive Control.

PubMed

Zhang, Mengzhen; Zou, Chang-Ling; Jiang, Liang

2018-01-12

Quantum transducers play a crucial role in hybrid quantum networks. A good quantum transducer can faithfully convert quantum signals from one mode to another with minimum decoherence. Most investigations of quantum transduction are based on the protocol of direct mode conversion. However, the direct protocol requires the matching condition, which in practice is not always feasible. Here we propose an adaptive protocol for quantum transducers, which can convert quantum signals without requiring the matching condition. The adaptive protocol only consists of Gaussian operations, feasible in various physical platforms. Moreover, we show that the adaptive protocol can be robust against imperfections associated with finite squeezing, thermal noise, and homodyne detection, and it can be implemented to realize quantum state transfer between microwave and optical modes.

Accuracy requirements of optical linear algebra processors in adaptive optics imaging systems

NASA Technical Reports Server (NTRS)

Downie, John D.

1990-01-01

A ground-based adaptive optics imaging telescope system attempts to improve image quality by detecting and correcting for atmospherically induced wavefront aberrations. The required control computations during each cycle will take a finite amount of time. Longer time delays result in larger values of residual wavefront error variance since the atmosphere continues to change during that time. Thus an optical processor may be well-suited for this task. This paper presents a study of the accuracy requirements in a general optical processor that will make it competitive with, or superior to, a conventional digital computer for the adaptive optics application. An optimization of the adaptive optics correction algorithm with respect to an optical processor's degree of accuracy is also briefly discussed.

Application of a trigonometric finite difference procedure to numerical analysis of compressive and shear buckling of orthotropic panels

NASA Technical Reports Server (NTRS)

Stein, M.; Housner, J. D.

1978-01-01

A numerical analysis developed for the buckling of rectangular orthotropic layered panels under combined shear and compression is described. This analysis uses a central finite difference procedure based on trigonometric functions instead of using the conventional finite differences which are based on polynomial functions. Inasmuch as the buckle mode shape is usually trigonometric in nature, the analysis using trigonometric finite differences can be made to exhibit a much faster convergence rate than that using conventional differences. Also, the trigonometric finite difference procedure leads to difference equations having the same form as conventional finite differences; thereby allowing available conventional finite difference formulations to be converted readily to trigonometric form. For two-dimensional problems, the procedure introduces two numerical parameters into the analysis. Engineering approaches for the selection of these parameters are presented and the analysis procedure is demonstrated by application to several isotropic and orthotropic panel buckling problems. Among these problems is the shear buckling of stiffened isotropic and filamentary composite panels in which the stiffener is broken. Results indicate that a break may degrade the effect of the stiffener to the extent that the panel will not carry much more load than if the stiffener were absent.

Efficiency trade-offs of steady-state methods using FEM and FDM. [iterative solutions for nonlinear flow equations

NASA Technical Reports Server (NTRS)

Gartling, D. K.; Roache, P. J.

1978-01-01

The efficiency characteristics of finite element and finite difference approximations for the steady-state solution of the Navier-Stokes equations are examined. The finite element method discussed is a standard Galerkin formulation of the incompressible, steady-state Navier-Stokes equations. The finite difference formulation uses simple centered differences that are O(delta x-squared). Operation counts indicate that a rapidly converging Newton-Raphson-Kantorovitch iteration scheme is generally preferable over a Picard method. A split NOS Picard iterative algorithm for the finite difference method was most efficient.

Distributed parameter system coupled ARMA expansion identification and adaptive parallel IIR filtering - A unified problem statement. [Auto Regressive Moving-Average

NASA Technical Reports Server (NTRS)

Johnson, C. R., Jr.; Balas, M. J.

1980-01-01

A novel interconnection of distributed parameter system (DPS) identification and adaptive filtering is presented, which culminates in a common statement of coupled autoregressive, moving-average expansion or parallel infinite impulse response configuration adaptive parameterization. The common restricted complexity filter objectives are seen as similar to the reduced-order requirements of the DPS expansion description. The interconnection presents the possibility of an exchange of problem formulations and solution approaches not yet easily addressed in the common finite dimensional lumped-parameter system context. It is concluded that the shared problems raised are nevertheless many and difficult.

Mesh refinement in finite element analysis by minimization of the stiffness matrix trace

NASA Technical Reports Server (NTRS)

Kittur, Madan G.; Huston, Ronald L.

1989-01-01

Most finite element packages provide means to generate meshes automatically. However, the user is usually confronted with the problem of not knowing whether the mesh generated is appropriate for the problem at hand. Since the accuracy of the finite element results is mesh dependent, mesh selection forms a very important step in the analysis. Indeed, in accurate analyses, meshes need to be refined or rezoned until the solution converges to a value so that the error is below a predetermined tolerance. A-posteriori methods use error indicators, developed by using the theory of interpolation and approximation theory, for mesh refinements. Some use other criterions, such as strain energy density variation and stress contours for example, to obtain near optimal meshes. Although these methods are adaptive, they are expensive. Alternatively, a priori methods, until now available, use geometrical parameters, for example, element aspect ratio. Therefore, they are not adaptive by nature. An adaptive a-priori method is developed. The criterion is that the minimization of the trace of the stiffness matrix with respect to the nodal coordinates, leads to a minimization of the potential energy, and as a consequence provide a good starting mesh. In a few examples the method is shown to provide the optimal mesh. The method is also shown to be relatively simple and amenable to development of computer algorithms. When the procedure is used in conjunction with a-posteriori methods of grid refinement, it is shown that fewer refinement iterations and fewer degrees of freedom are required for convergence as opposed to when the procedure is not used. The mesh obtained is shown to have uniform distribution of stiffness among the nodes and elements which, as a consequence, leads to uniform error distribution. Thus the mesh obtained meets the optimality criterion of uniform error distribution.

The Benard problem: A comparison of finite difference and spectral collocation eigen value solutions

NASA Technical Reports Server (NTRS)

Skarda, J. Raymond Lee; Mccaughan, Frances E.; Fitzmaurice, Nessan

1995-01-01

The application of spectral methods, using a Chebyshev collocation scheme, to solve hydrodynamic stability problems is demonstrated on the Benard problem. Implementation of the Chebyshev collocation formulation is described. The performance of the spectral scheme is compared with that of a 2nd order finite difference scheme. An exact solution to the Marangoni-Benard problem is used to evaluate the performance of both schemes. The error of the spectral scheme is at least seven orders of magnitude smaller than finite difference error for a grid resolution of N = 15 (number of points used). The performance of the spectral formulation far exceeded the performance of the finite difference formulation for this problem. The spectral scheme required only slightly more effort to set up than the 2nd order finite difference scheme. This suggests that the spectral scheme may actually be faster to implement than higher order finite difference schemes.

Wavefront reconstruction from non-modulated pyramid wavefront sensor data using a singular value type expansion

NASA Astrophysics Data System (ADS)

Hutterer, Victoria; Ramlau, Ronny

2018-03-01

The new generation of extremely large telescopes includes adaptive optics systems to correct for atmospheric blurring. In this paper, we present a new method of wavefront reconstruction from non-modulated pyramid wavefront sensor data. The approach is based on a simplified sensor model represented as the finite Hilbert transform of the incoming phase. Due to the non-compactness of the finite Hilbert transform operator the classical theory for singular systems is not applicable. Nevertheless, we can express the Moore-Penrose inverse as a singular value type expansion with weighted Chebychev polynomials.

XFEM-based modeling of successive resections for preoperative image updating

NASA Astrophysics Data System (ADS)

Vigneron, Lara M.; Robe, Pierre A.; Warfield, Simon K.; Verly, Jacques G.

2006-03-01

We present a new method for modeling organ deformations due to successive resections. We use a biomechanical model of the organ, compute its volume-displacement solution based on the eXtended Finite Element Method (XFEM). The key feature of XFEM is that material discontinuities induced by every new resection can be handled without remeshing or mesh adaptation, as would be required by the conventional Finite Element Method (FEM). We focus on the application of preoperative image updating for image-guided surgery. Proof-of-concept demonstrations are shown for synthetic and real data in the context of neurosurgery.

Seakeeping with the semi-Lagrangian particle finite element method

NASA Astrophysics Data System (ADS)

Nadukandi, Prashanth; Servan-Camas, Borja; Becker, Pablo Agustín; Garcia-Espinosa, Julio

2017-07-01

The application of the semi-Lagrangian particle finite element method (SL-PFEM) for the seakeeping simulation of the wave adaptive modular vehicle under spray generating conditions is presented. The time integration of the Lagrangian advection is done using the explicit integration of the velocity and acceleration along the streamlines (X-IVAS). Despite the suitability of the SL-PFEM for the considered seakeeping application, small time steps were needed in the X-IVAS scheme to control the solution accuracy. A preliminary proposal to overcome this limitation of the X-IVAS scheme for seakeeping simulations is presented.

Neural-Net Processing of Characteristic Patterns From Electronic Holograms of Vibrating Blades

NASA Technical Reports Server (NTRS)

Decker, Arthur J.

1999-01-01

Finite-element-model-trained artificial neural networks can be used to process efficiently the characteristic patterns or mode shapes from electronic holograms of vibrating blades. The models used for routine design may not yet be sufficiently accurate for this application. This document discusses the creation of characteristic patterns; compares model generated and experimental characteristic patterns; and discusses the neural networks that transform the characteristic patterns into strain or damage information. The current potential to adapt electronic holography to spin rigs, wind tunnels and engines provides an incentive to have accurate finite element models lor training neural networks.

Computing Nash equilibria through computational intelligence methods

NASA Astrophysics Data System (ADS)

Pavlidis, N. G.; Parsopoulos, K. E.; Vrahatis, M. N.

2005-03-01

Nash equilibrium constitutes a central solution concept in game theory. The task of detecting the Nash equilibria of a finite strategic game remains a challenging problem up-to-date. This paper investigates the effectiveness of three computational intelligence techniques, namely, covariance matrix adaptation evolution strategies, particle swarm optimization, as well as, differential evolution, to compute Nash equilibria of finite strategic games, as global minima of a real-valued, nonnegative function. An issue of particular interest is to detect more than one Nash equilibria of a game. The performance of the considered computational intelligence methods on this problem is investigated using multistart and deflection.

Adaptive multi-resolution 3D Hartree-Fock-Bogoliubov solver for nuclear structure

NASA Astrophysics Data System (ADS)

Pei, J. C.; Fann, G. I.; Harrison, R. J.; Nazarewicz, W.; Shi, Yue; Thornton, S.

2014-08-01

Background: Complex many-body systems, such as triaxial and reflection-asymmetric nuclei, weakly bound halo states, cluster configurations, nuclear fragments produced in heavy-ion fusion reactions, cold Fermi gases, and pasta phases in neutron star crust, are all characterized by large sizes and complex topologies in which many geometrical symmetries characteristic of ground-state configurations are broken. A tool of choice to study such complex forms of matter is an adaptive multi-resolution wavelet analysis. This method has generated much excitement since it provides a common framework linking many diversified methodologies across different fields, including signal processing, data compression, harmonic analysis and operator theory, fractals, and quantum field theory. Purpose: To describe complex superfluid many-fermion systems, we introduce an adaptive pseudospectral method for solving self-consistent equations of nuclear density functional theory in three dimensions, without symmetry restrictions. Methods: The numerical method is based on the multi-resolution and computational harmonic analysis techniques with a multi-wavelet basis. The application of state-of-the-art parallel programming techniques include sophisticated object-oriented templates which parse the high-level code into distributed parallel tasks with a multi-thread task queue scheduler for each multi-core node. The internode communications are asynchronous. The algorithm is variational and is capable of solving coupled complex-geometric systems of equations adaptively, with functional and boundary constraints, in a finite spatial domain of very large size, limited by existing parallel computer memory. For smooth functions, user-defined finite precision is guaranteed. Results: The new adaptive multi-resolution Hartree-Fock-Bogoliubov (HFB) solver madness-hfb is benchmarked against a two-dimensional coordinate-space solver hfb-ax that is based on the B-spline technique and a three-dimensional solver hfodd that is based on the harmonic-oscillator basis expansion. Several examples are considered, including the self-consistent HFB problem for spin-polarized trapped cold fermions and the Skyrme-Hartree-Fock (+BCS) problem for triaxial deformed nuclei. Conclusions: The new madness-hfb framework has many attractive features when applied to nuclear and atomic problems involving many-particle superfluid systems. Of particular interest are weakly bound nuclear configurations close to particle drip lines, strongly elongated and dinuclear configurations such as those present in fission and heavy-ion fusion, and exotic pasta phases that appear in neutron star crust.

Conservative properties of finite difference schemes for incompressible flow

NASA Technical Reports Server (NTRS)

Morinishi, Youhei

1995-01-01

The purpose of this research is to construct accurate finite difference schemes for incompressible unsteady flow simulations such as LES (large-eddy simulation) or DNS (direct numerical simulation). In this report, conservation properties of the continuity, momentum, and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discretized equations. Existing finite difference schemes in staggered grid systems are checked for satisfaction of the requirements. Proper higher order accurate finite difference schemes in a staggered grid system are then proposed. Plane channel flow is simulated using the proposed fourth order accurate finite difference scheme and the results compared with those of the second order accurate Harlow and Welch algorithm.

T-matrix method in plasmonics: An overview

NASA Astrophysics Data System (ADS)

Khlebtsov, Nikolai G.

2013-07-01

Optical properties of isolated and coupled plasmonic nanoparticles (NPs) are of great interest for many applications in nanophotonics, nanobiotechnology, and nanomedicine owing to rapid progress in fabrication, characterization, and surface functionalization technologies. To simulate optical responses from plasmonic nanostructures, various electromagnetic analytical and numerical methods have been adapted, tested, and used during the past two decades. Currently, the most popular numerical techniques are those that do not suffer from geometrical and composition limitations, e.g., the discrete dipole approximation (DDA), the boundary (finite) element method (BEM, FEM), the finite difference time domain method (FDTDM), and others. However, the T-matrix method still has its own niche in plasmonic science because of its great numerical efficiency, especially for systems with randomly oriented particles and clusters. In this review, I consider the application of the T-matrix method to various plasmonic problems, including dipolar, multipolar, and anisotropic properties of metal NPs; sensing applications; surface enhanced Raman scattering; optics of 1D-3D nanoparticle assemblies; plasmonic particles and clusters near and on substrates; and manipulation of plasmonic NPs with laser tweezers.

ADAPTIVE FINITE ELEMENT MODELING TECHNIQUES FOR THE POISSON-BOLTZMANN EQUATION

PubMed Central

HOLST, MICHAEL; MCCAMMON, JAMES ANDREW; YU, ZEYUN; ZHOU, YOUNGCHENG; ZHU, YUNRONG

2011-01-01

We consider the design of an effective and reliable adaptive finite element method (AFEM) for the nonlinear Poisson-Boltzmann equation (PBE). We first examine the two-term regularization technique for the continuous problem recently proposed by Chen, Holst, and Xu based on the removal of the singular electrostatic potential inside biomolecules; this technique made possible the development of the first complete solution and approximation theory for the Poisson-Boltzmann equation, the first provably convergent discretization, and also allowed for the development of a provably convergent AFEM. However, in practical implementation, this two-term regularization exhibits numerical instability. Therefore, we examine a variation of this regularization technique which can be shown to be less susceptible to such instability. We establish a priori estimates and other basic results for the continuous regularized problem, as well as for Galerkin finite element approximations. We show that the new approach produces regularized continuous and discrete problems with the same mathematical advantages of the original regularization. We then design an AFEM scheme for the new regularized problem, and show that the resulting AFEM scheme is accurate and reliable, by proving a contraction result for the error. This result, which is one of the first results of this type for nonlinear elliptic problems, is based on using continuous and discrete a priori L∞ estimates to establish quasi-orthogonality. To provide a high-quality geometric model as input to the AFEM algorithm, we also describe a class of feature-preserving adaptive mesh generation algorithms designed specifically for constructing meshes of biomolecular structures, based on the intrinsic local structure tensor of the molecular surface. All of the algorithms described in the article are implemented in the Finite Element Toolkit (FETK), developed and maintained at UCSD. The stability advantages of the new regularization scheme are demonstrated with FETK through comparisons with the original regularization approach for a model problem. The convergence and accuracy of the overall AFEM algorithm is also illustrated by numerical approximation of electrostatic solvation energy for an insulin protein. PMID:21949541

3D numerical simulations of oblique droplet impact onto a deep liquid pool

NASA Astrophysics Data System (ADS)

Gelderblom, Hanneke; Reijers, Sten A.; Gielen, Marise; Sleutel, Pascal; Lohse, Detlef; Xie, Zhihua; Pain, Christopher C.; Matar, Omar K.

2017-11-01

We study the fluid dynamics of three-dimensional oblique droplet impact, which results in phenomena that include splashing and cavity formation. An adaptive, unstructured mesh modelling framework is employed here, which can modify and adapt unstructured meshes to better represent the underlying physics of droplet dynamics, and reduce computational effort without sacrificing accuracy. The numerical framework consists of a mixed control-volume and finite-element formulation, a volume-of-fluid-type method for the interface-capturing based on a compressive control-volume advection method. The framework also features second-order finite-element methods, and a force-balanced algorithm for the surface tension implementation, minimising the spurious velocities often found in many simulations involving capillary-driven flows. The numerical results generated using this framework are compared with high-speed images of the interfacial shapes of the deformed droplet, and the cavity formed upon impact, yielding good agreement. EPSRC, UK, MEMPHIS program Grant (EP/K003976/1), RAEng Research Chair (OKM).

A methodology for quadrilateral finite element mesh coarsening

DOE PAGES

Staten, Matthew L.; Benzley, Steven; Scott, Michael

2008-03-27

High fidelity finite element modeling of continuum mechanics problems often requires using all quadrilateral or all hexahedral meshes. The efficiency of such models is often dependent upon the ability to adapt a mesh to the physics of the phenomena. Adapting a mesh requires the ability to both refine and/or coarsen the mesh. The algorithms available to refine and coarsen triangular and tetrahedral meshes are very robust and efficient. However, the ability to locally and conformally refine or coarsen all quadrilateral and all hexahedral meshes presents many difficulties. Some research has been done on localized conformal refinement of quadrilateral and hexahedralmore » meshes. However, little work has been done on localized conformal coarsening of quadrilateral and hexahedral meshes. A general method which provides both localized conformal coarsening and refinement for quadrilateral meshes is presented in this paper. This method is based on restructuring the mesh with simplex manipulations to the dual of the mesh. Finally, this method appears to be extensible to hexahedral meshes in three dimensions.« less

A model-updating procedure to stimulate piezoelectric transducers accurately.

PubMed

Piranda, B; Ballandras, S; Steichen, W; Hecart, B

2001-09-01

The use of numerical calculations based on finite element methods (FEM) has yielded significant improvements in the simulation and design of piezoelectric transducers piezoelectric transducer utilized in acoustic imaging. However, the ultimate precision of such models is directly controlled by the accuracy of material characterization. The present work is dedicated to the development of a model-updating technique adapted to the problem of piezoelectric transducer. The updating process is applied using the experimental admittance of a given structure for which a finite element analysis is performed. The mathematical developments are reported and then applied to update the entries of a FEM of a two-layer structure (a PbZrTi-PZT-ridge glued on a backing) for which measurements were available. The efficiency of the proposed approach is demonstrated, yielding the definition of a new set of constants well adapted to predict the structure response accurately. Improvement of the proposed approach, consisting of the updating of material coefficients not only on the admittance but also on the impedance data, is finally discussed.

Developing parallel GeoFEST(P) using the PYRAMID AMR library

NASA Technical Reports Server (NTRS)

Norton, Charles D.; Lyzenga, Greg; Parker, Jay; Tisdale, Robert E.

2004-01-01

The PYRAMID parallel unstructured adaptive mesh refinement (AMR) library has been coupled with the GeoFEST geophysical finite element simulation tool to support parallel active tectonics simulations. Specifically, we have demonstrated modeling of coseismic and postseismic surface displacement due to a simulated Earthquake for the Landers system of interacting faults in Southern California. The new software demonstrated a 25-times resolution improvement and a 4-times reduction in time to solution over the sequential baseline milestone case. Simulations on workstations using a few tens of thousands of stress displacement finite elements can now be expanded to multiple millions of elements with greater than 98% scaled efficiency on various parallel platforms over many hundreds of processors. Our most recent work has demonstrated that we can dynamically adapt the computational grid as stress grows on a fault. In this paper, we will describe the major issues and challenges associated with coupling these two programs to create GeoFEST(P). Performance and visualization results will also be described.

A fiber orientation-adapted integration scheme for computing the hyperelastic Tucker average for short fiber reinforced composites

NASA Astrophysics Data System (ADS)

Goldberg, Niels; Ospald, Felix; Schneider, Matti

2017-10-01

In this article we introduce a fiber orientation-adapted integration scheme for Tucker's orientation averaging procedure applied to non-linear material laws, based on angular central Gaussian fiber orientation distributions. This method is stable w.r.t. fiber orientations degenerating into planar states and enables the construction of orthotropic hyperelastic energies for truly orthotropic fiber orientation states. We establish a reference scenario for fitting the Tucker average of a transversely isotropic hyperelastic energy, corresponding to a uni-directional fiber orientation, to microstructural simulations, obtained by FFT-based computational homogenization of neo-Hookean constituents. We carefully discuss ideas for accelerating the identification process, leading to a tremendous speed-up compared to a naive approach. The resulting hyperelastic material map turns out to be surprisingly accurate, simple to integrate in commercial finite element codes and fast in its execution. We demonstrate the capabilities of the extracted model by a finite element analysis of a fiber reinforced chain link.

Finite-time adaptive sliding mode force control for electro-hydraulic load simulator based on improved GMS friction model

NASA Astrophysics Data System (ADS)

Kang, Shuo; Yan, Hao; Dong, Lijing; Li, Changchun

2018-03-01

This paper addresses the force tracking problem of electro-hydraulic load simulator under the influence of nonlinear friction and uncertain disturbance. A nonlinear system model combined with the improved generalized Maxwell-slip (GMS) friction model is firstly derived to describe the characteristics of load simulator system more accurately. Then, by using particle swarm optimization (PSO) algorithm ​combined with the system hysteresis characteristic analysis, the GMS friction parameters are identified. To compensate for nonlinear friction and uncertain disturbance, a finite-time adaptive sliding mode control method is proposed based on the accurate system model. This controller has the ability to ensure that the system state moves along the nonlinear sliding surface to steady state in a short time as well as good dynamic properties under the influence of parametric uncertainties and disturbance, which further improves the force loading accuracy and rapidity. At the end of this work, simulation and experimental results are employed to demonstrate the effectiveness of the proposed sliding mode control strategy.

The finite cell method for polygonal meshes: poly-FCM

NASA Astrophysics Data System (ADS)

Duczek, Sascha; Gabbert, Ulrich

2016-10-01

In the current article, we extend the two-dimensional version of the finite cell method (FCM), which has so far only been used for structured quadrilateral meshes, to unstructured polygonal discretizations. Therefore, the adaptive quadtree-based numerical integration technique is reformulated and the notion of generalized barycentric coordinates is introduced. We show that the resulting polygonal (poly-)FCM approach retains the optimal rates of convergence if and only if the geometry of the structure is adequately resolved. The main advantage of the proposed method is that it inherits the ability of polygonal finite elements for local mesh refinement and for the construction of transition elements (e.g. conforming quadtree meshes without hanging nodes). These properties along with the performance of the poly-FCM are illustrated by means of several benchmark problems for both static and dynamic cases.

Utilising flags to reduce drag around a short finite circular cylinder

NASA Astrophysics Data System (ADS)

Javadi, Kh.; Kiani, F.; Tahaye Abadi, M.

2018-03-01

This paper utilises flags to decrease the drag around a short finite circular cylinder. Wall-adapted large eddy simulation and two-way fluid-structure interaction methods were applied to resolve unsteady turbulent flow structure. The far-field Reynolds number of the current configuration based on the cylinder diameter was chosen to be 20,000. In addition, the length-to-diameter ratio of the cylinder was assumed to be L/D = 2 whereas the flexible flag had a width-to-diameter ratio of W/D = 1.5. The results were compared with the regular short finite circular cylinder and the rigid flagged cylinder in our previous work. The results indicate that utilising flags inside the near-wake region of the cylinder reduces the pressure drag. The physical mechanism of this drag reduction is presented.

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

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

Challenges of Representing Sub-Grid Physics in an Adaptive Mesh Refinement Atmospheric Model

NASA Astrophysics Data System (ADS)

O'Brien, T. A.; Johansen, H.; Johnson, J. N.; Rosa, D.; Benedict, J. J.; Keen, N. D.; Collins, W.; Goodfriend, E.

2015-12-01

Some of the greatest potential impacts from future climate change are tied to extreme atmospheric phenomena that are inherently multiscale, including tropical cyclones and atmospheric rivers. Extremes are challenging to simulate in conventional climate models due to existing models' coarse resolutions relative to the native length-scales of these phenomena. Studying the weather systems of interest requires an atmospheric model with sufficient local resolution, and sufficient performance for long-duration climate-change simulations. To this end, we have developed a new global climate code with adaptive spatial and temporal resolution. The dynamics are formulated using a block-structured conservative finite volume approach suitable for moist non-hydrostatic atmospheric dynamics. By using both space- and time-adaptive mesh refinement, the solver focuses computational resources only where greater accuracy is needed to resolve critical phenomena. We explore different methods for parameterizing sub-grid physics, such as microphysics, macrophysics, turbulence, and radiative transfer. In particular, we contrast the simplified physics representation of Reed and Jablonowski (2012) with the more complex physics representation used in the System for Atmospheric Modeling of Khairoutdinov and Randall (2003). We also explore the use of a novel macrophysics parameterization that is designed to be explicitly scale-aware.

Adaptive hierarchical grid model of water-borne pollutant dispersion

NASA Astrophysics Data System (ADS)

Borthwick, A. G. L.; Marchant, R. D.; Copeland, G. J. M.

Water pollution by industrial and agricultural waste is an increasingly major public health issue. It is therefore important for water engineers and managers to be able to predict accurately the local behaviour of water-borne pollutants. This paper describes the novel and efficient coupling of dynamically adaptive hierarchical grids with standard solvers of the advection-diffusion equation. Adaptive quadtree grids are able to focus on regions of interest such as pollutant fronts, while retaining economy in the total number of grid elements through selective grid refinement. Advection is treated using Lagrangian particle tracking. Diffusion is solved separately using two grid-based methods; one is by explicit finite differences, the other a diffusion-velocity approach. Results are given in two dimensions for pure diffusion of an initially Gaussian plume, advection-diffusion of the Gaussian plume in the rotating flow field of a forced vortex, and the transport of species in a rectangular channel with side wall boundary layers. Close agreement is achieved with analytical solutions of the advection-diffusion equation and simulations from a Lagrangian random walk model. An application to Sepetiba Bay, Brazil is included to demonstrate the method with complex flows and topography.

Using adaptive grid in modeling rocket nozzle flow

NASA Technical Reports Server (NTRS)

Chow, Alan S.; Jin, Kang-Ren

1992-01-01

The mechanical behavior of a rocket motor internal flow field results in a system of nonlinear partial differential equations which cannot be solved analytically. However, this system of equations called the Navier-Stokes equations can be solved numerically. The accuracy and the convergence of the solution of the system of equations will depend largely on how precisely the sharp gradients in the domain of interest can be resolved. With the advances in computer technology, more sophisticated algorithms are available to improve the accuracy and convergence of the solutions. An adaptive grid generation is one of the schemes which can be incorporated into the algorithm to enhance the capability of numerical modeling. It is equivalent to putting intelligence into the algorithm to optimize the use of computer memory. With this scheme, the finite difference domain of the flow field called the grid does neither have to be very fine nor strategically placed at the location of sharp gradients. The grid is self adapting as the solution evolves. This scheme significantly improves the methodology of solving flow problems in rocket nozzles by taking the refinement part of grid generation out of the hands of computational fluid dynamics (CFD) specialists and place it into the computer algorithm itself.

Influence of Steering Control Devices Mounted in Cars for the Disabled on Passive Safety

NASA Astrophysics Data System (ADS)

Masiá, J.; Eixerés, B.; Dols, J. F.; Colomina, F. J.

2009-11-01

The purpose of this research is to analyze the influence of steering control devices for disabled people on passive safety. It is based on the advances made in the modelling and simulation of the driver position and in the suit verification test. The influence of these devices is studied through airbag deployment and/or its influence on driver safety. We characterize the different adaptations that are used in adapted cars that can be found mounted in vehicles in order to generating models that are verified by experimental test. A three dimensional design software package was used to develop the model. The simulations were generated using a dynamic simulation program employing LSDYNA finite elements. This program plots the geometry and assigns materials. The airbag is shaped, meshed and folded just as it is mounted in current vehicles. The thermodynamic model of expansion of gases is assigned and the contact interfaces are defined. Static tests were carried out on deployment of the airbag to contrast with and to validate the computational models and to measure the behaviour of the airbag when there are steering adaptations mounted in the vehicle.

A fast dynamic grid adaption scheme for meteorological flows

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

Fiedler, B.H.; Trapp, R.J.

1993-10-01

The continuous dynamic grid adaption (CDGA) technique is applied to a compressible, three-dimensional model of a rising thermal. The computational cost, per grid point per time step, of using CDGA instead of a fixed, uniform Cartesian grid is about 53% of the total cost of the model with CDGA. The use of general curvilinear coordinates contributes 11.7% to this total, calculating and moving the grid 6.1%, and continually updating the transformation relations 20.7%. Costs due to calculations that involve the gridpoint velocities (as well as some substantial unexplained costs) contribute the remaining 14.5%. A simple way to limit the costmore » of calculating the grid is presented. The grid is adapted by solving an elliptic equation for gridpoint coordinates on a coarse grid and then interpolating the full finite-difference grid. In this application, the additional costs per grid point of CDGA are shown to be easily offset by the savings resulting from the reduction in the required number of grid points. In simulation of the thermal costs are reduced by a factor of 3, as compared with those of a companion model with a fixed, uniform Cartesian grid. 8 refs., 8 figs.« less

Practical aspects of prestack depth migration with finite differences

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

Ober, C.C.; Oldfield, R.A.; Womble, D.E.

1997-07-01

Finite-difference, prestack, depth migrations offers significant improvements over Kirchhoff methods in imaging near or under salt structures. The authors have implemented a finite-difference prestack depth migration algorithm for use on massively parallel computers which is discussed. The image quality of the finite-difference scheme has been investigated and suggested improvements are discussed. In this presentation, the authors discuss an implicit finite difference migration code, called Salvo, that has been developed through an ACTI (Advanced Computational Technology Initiative) joint project. This code is designed to be efficient on a variety of massively parallel computers. It takes advantage of both frequency and spatialmore » parallelism as well as the use of nodes dedicated to data input/output (I/O). Besides giving an overview of the finite-difference algorithm and some of the parallelism techniques used, migration results using both Kirchhoff and finite-difference migration will be presented and compared. The authors start out with a very simple Cartoon model where one can intuitively see the multiple travel paths and some of the potential problems that will be encountered with Kirchhoff migration. More complex synthetic models as well as results from actual seismic data from the Gulf of Mexico will be shown.« less

Phase-space finite elements in a least-squares solution of the transport equation

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

Drumm, C.; Fan, W.; Pautz, S.

2013-07-01

The linear Boltzmann transport equation is solved using a least-squares finite element approximation in the space, angular and energy phase-space variables. The method is applied to both neutral particle transport and also to charged particle transport in the presence of an electric field, where the angular and energy derivative terms are handled with the energy/angular finite elements approximation, in a manner analogous to the way the spatial streaming term is handled. For multi-dimensional problems, a novel approach is used for the angular finite elements: mapping the surface of a unit sphere to a two-dimensional planar region and using a meshingmore » tool to generate a mesh. In this manner, much of the spatial finite-elements machinery can be easily adapted to handle the angular variable. The energy variable and the angular variable for one-dimensional problems make use of edge/beam elements, also building upon the spatial finite elements capabilities. The methods described here can make use of either continuous or discontinuous finite elements in space, angle and/or energy, with the use of continuous finite elements resulting in a smaller problem size and the use of discontinuous finite elements resulting in more accurate solutions for certain types of problems. The work described in this paper makes use of continuous finite elements, so that the resulting linear system is symmetric positive definite and can be solved with a highly efficient parallel preconditioned conjugate gradients algorithm. The phase-space finite elements capability has been built into the Sceptre code and applied to several test problems, including a simple one-dimensional problem with an analytic solution available, a two-dimensional problem with an isolated source term, showing how the method essentially eliminates ray effects encountered with discrete ordinates, and a simple one-dimensional charged-particle transport problem in the presence of an electric field. (authors)« less

Finite-Difference Solutions for Compressible Laminar Boundary-Layer Flows of a Dusty Gas over a Semi-Infinite Flat Plate.

DTIC Science & Technology

1986-08-01

AD-A174 952 FINITE - DIFFERENCE SOLUTIONS FOR CONPRESSIBLE LANINAR 1/2 BOUNDARY-LAYER FLOUS (U) TORONTO UNIV DOWNSVIEW (ONTARIO) INST FOR AEROSPACE...dilute dusty gas over a semi-infinite flat plate. Details are given of the impliit finite , difference schemes as well as the boundary conditions... FINITE - DIFFERENCE SOLUTIONS FOR COMPRESSIBLE LAMINAR BOUNDARY-LAYER FLOWS OF A DUSTY GAS OVER A SEMI-INFINITE FLAT PLATE by B. Y. Wang and I. I

An adaptively refined XFEM with virtual node polygonal elements for dynamic crack problems

NASA Astrophysics Data System (ADS)

Teng, Z. H.; Sun, F.; Wu, S. C.; Zhang, Z. B.; Chen, T.; Liao, D. M.

2018-02-01

By introducing the shape functions of virtual node polygonal (VP) elements into the standard extended finite element method (XFEM), a conforming elemental mesh can be created for the cracking process. Moreover, an adaptively refined meshing with the quadtree structure only at a growing crack tip is proposed without inserting hanging nodes into the transition region. A novel dynamic crack growth method termed as VP-XFEM is thus formulated in the framework of fracture mechanics. To verify the newly proposed VP-XFEM, both quasi-static and dynamic cracked problems are investigated in terms of computational accuracy, convergence, and efficiency. The research results show that the present VP-XFEM can achieve good agreement in stress intensity factor and crack growth path with the exact solutions or experiments. Furthermore, better accuracy, convergence, and efficiency of different models can be acquired, in contrast to standard XFEM and mesh-free methods. Therefore, VP-XFEM provides a suitable alternative to XFEM for engineering applications.

αAMG based on Weighted Matching for Systems of Elliptic PDEs Arising From Displacement and Mixed Methods

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

D'Ambra, P.; Vassilevski, P. S.

2014-05-30

Adaptive Algebraic Multigrid (or Multilevel) Methods (αAMG) are introduced to improve robustness and efficiency of classical algebraic multigrid methods in dealing with problems where no a-priori knowledge or assumptions on the near-null kernel of the underlined matrix are available. Recently we proposed an adaptive (bootstrap) AMG method, αAMG, aimed to obtain a composite solver with a desired convergence rate. Each new multigrid component relies on a current (general) smooth vector and exploits pairwise aggregation based on weighted matching in a matrix graph to define a new automatic, general-purpose coarsening process, which we refer to as “the compatible weighted matching”. Inmore » this work, we present results that broaden the applicability of our method to different finite element discretizations of elliptic PDEs. In particular, we consider systems arising from displacement methods in linear elasticity problems and saddle-point systems that appear in the application of the mixed method to Darcy problems.« less

Morphological and functional diversity in therizinosaur claws and the implications for theropod claw evolution.

PubMed

Lautenschlager, Stephan

2014-06-22

Therizinosaurs are a group of herbivorous theropod dinosaurs from the Cretaceous of North America and Asia, best known for their iconically large and elongate manual claws. However, among Therizinosauria, ungual morphology is highly variable, reflecting a general trend found in derived theropod dinosaurs (Maniraptoriformes). A combined approach of shape analysis to characterize changes in manual ungual morphology across theropods and finite-element analysis to assess the biomechanical properties of different ungual shapes in therizinosaurs reveals a functional diversity related to ungual morphology. While some therizinosaur taxa used their claws in a generalist fashion, other taxa were functionally adapted to use the claws as grasping hooks during foraging. Results further indicate that maniraptoriform dinosaurs deviated from the plesiomorphic theropod ungual morphology resulting in increased functional diversity. This trend parallels modifications of the cranial skeleton in derived theropods in response to dietary adaptation, suggesting that dietary diversification was a major driver for morphological and functional disparity in theropod evolution.

Service-oriented architecture for the ARGOS instrument control software

NASA Astrophysics Data System (ADS)

Borelli, J.; Barl, L.; Gässler, W.; Kulas, M.; Rabien, Sebastian

2012-09-01

The Advanced Rayleigh Guided ground layer Adaptive optic System, ARGOS, equips the Large Binocular Telescope (LBT) with a constellation of six rayleigh laser guide stars. By correcting atmospheric turbulence near the ground, the system is designed to increase the image quality of the multi-object spectrograph LUCIFER approximately by a factor of 3 over a field of 4 arc minute diameter. The control software has the critical task of orchestrating several devices, instruments, and high level services, including the already existing adaptive optic system and the telescope control software. All these components are widely distributed over the telescope, adding more complexity to the system design. The approach used by the ARGOS engineers is to write loosely coupled and distributed services under the control of different ownership systems, providing a uniform mechanism to offer, discover, interact and use these distributed capabilities. The control system counts with several finite state machines, vibration and flexure compensation loops, and safety mechanism, such as interlocks, aircraft, and satellite avoidance systems.

Large-eddy simulation of turbulent cavitating flow in a micro channel

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

Egerer, Christian P., E-mail: christian.egerer@aer.mw.tum.de; Hickel, Stefan; Schmidt, Steffen J.

2014-08-15

Large-eddy simulations (LES) of cavitating flow of a Diesel-fuel-like fluid in a generic throttle geometry are presented. Two-phase regions are modeled by a parameter-free thermodynamic equilibrium mixture model, and compressibility of the liquid and the liquid-vapor mixture is taken into account. The Adaptive Local Deconvolution Method (ALDM), adapted for cavitating flows, is employed for discretizing the convective terms of the Navier-Stokes equations for the homogeneous mixture. ALDM is a finite-volume-based implicit LES approach that merges physically motivated turbulence modeling and numerical discretization. Validation of the numerical method is performed for a cavitating turbulent mixing layer. Comparisons with experimental data ofmore » the throttle flow at two different operating conditions are presented. The LES with the employed cavitation modeling predicts relevant flow and cavitation features accurately within the uncertainty range of the experiment. The turbulence structure of the flow is further analyzed with an emphasis on the interaction between cavitation and coherent motion, and on the statistically averaged-flow evolution.« less

Actuators of 3-element unimorph deformable mirror

NASA Astrophysics Data System (ADS)

Fu, Tianyang; Ning, Yu; Du, Shaojun

2016-10-01

Kinds of wavefront aberrations exist among optical systems because of atmosphere disturbance, device displacement and a variety of thermal effects, which disturb the information of transmitting beam and restrain its energy. Deformable mirror(DM) is designed to adjust these wavefront aberrations. Bimorph DM becomes more popular and more applicable among adaptive optical(AO) systems with advantages in simple structure, low cost and flexible design compared to traditional discrete driving DM. The defocus aberration accounted for a large proportion of all wavefront aberrations, with a simpler surface and larger amplitude than others, so it is very useful to correct the defocus aberration effectively for beam controlling and aberration adjusting of AO system. In this study, we desired on correcting the 3rd and 10th Zernike modes, analyze the characteristic of the 3rd and 10th defocus aberration surface distribution, design 3-element actuators unimorph DM model study on its structure and deformation principle theoretically, design finite element models of different electrode configuration with different ring diameters, analyze and compare effects of different electrode configuration and different fixing mode to DM deformation capacity through COMSOL finite element software, compare fitting efficiency of DM models to the 3rd and 10th Zernike modes. We choose the inhomogeneous electrode distribution model with better result, get the influence function of every electrode and the voltage-PV relationship of the model. This unimorph DM is suitable for the AO system with a mainly defocus aberration.

Finite Mathematics and Discrete Mathematics: Is There a Difference?

ERIC Educational Resources Information Center

Johnson, Marvin L.

Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…

Micro-finite element analysis applied to high-resolution MRI reveals improved bone mechanical competence in the distal femur of female pre-professional dancers

PubMed Central

Rajapakse, C. S.; Diamond, M.; Honig, S.; Recht, M. P.; Weiss, D. S.; Regatte, R. R.

2013-01-01

Summary Micro-finite element analysis applied to high-resolution (0.234-mm length scale) MRI reveals greater whole and cancellous bone stiffness, but not greater cortical bone stiffness, in the distal femur of female dancers compared to controls. Greater whole bone stiffness appears to be mediated by cancellous, rather than cortical bone adaptation. Introduction The purpose of this study was to compare bone mechanical competence (stiffness) in the distal femur of female dancers compared to healthy, relatively inactive female controls. Methods This study had institutional review board approval. We recruited nine female modern dancers (25.7± 5.8 years, 1.63±0.06 m, 57.1±4.6 kg) and ten relatively inactive, healthy female controls matched for age, height, and weight (32.1±4.8 years, 1.6±0.04 m, 55.8±5.9 kg). We scanned the distal femur using a 7-T MRI scanner and a three-dimensional fast low-angle shot sequence (TR/TE= 31 ms/5.1 ms, 0.234 mm×0.234 mm×1 mm, 80 slices). We applied micro-finite element analysis to 10-mm-thick volumes of interest at the distal femoral diaphysis, metaphysis, and epiphysis to compute stiffness and cross-sectional area of whole, cortical, and cancellous bone, as well as cortical thickness. We applied two-tailed t-tests and ANCOVA to compare groups. Results Dancers demonstrated greater whole and cancellous bone stiffness and cross-sectional area at all locations (p< 0.05). Cortical bone stiffness, cross-sectional area, and thickness did not differ between groups (>0.08). At all locations, the percent of intact whole bone stiffness for cortical bone alone was lower in dancers (p<0.05). Adjustment for cancellous bone cross-sectional area eliminated significant differences in whole bone stiffness between groups (p>0.07), but adjustment for cortical bone cross-sectional area did not (p<0.03). Conclusions Modern dancers have greater whole and cancellous bone stiffness in the distal femur compared to controls. Elevated whole bone stiffness in dancers may be mediated via cancellous, rather than cortical bone adaptation. PMID:22893356

Improved methods of vibration analysis of pretwisted, airfoil blades

NASA Technical Reports Server (NTRS)

Subrahmanyam, K. B.; Kaza, K. R. V.

1984-01-01

Vibration analysis of pretwisted blades of asymmetric airfoil cross section is performed by using two mixed variational approaches. Numerical results obtained from these two methods are compared to those obtained from an improved finite difference method and also to those given by the ordinary finite difference method. The relative merits, convergence properties and accuracies of all four methods are studied and discussed. The effects of asymmetry and pretwist on natural frequencies and mode shapes are investigated. The improved finite difference method is shown to be far superior to the conventional finite difference method in several respects. Close lower bound solutions are provided by the improved finite difference method for untwisted blades with a relatively coarse mesh while the mixed methods have not indicated any specific bound.

Direct adaptive control of wind energy conversion systems using Gaussian networks.

PubMed

Mayosky, M A; Cancelo, I E

1999-01-01

Grid connected wind energy conversion systems (WECS) present interesting control demands, due to the intrinsic nonlinear characteristics of windmills and electric generators. In this paper a direct adaptive control strategy for WECS control is proposed. It is based on the combination of two control actions: a radial basis zfunction network-based adaptive controller, which drives the tracking error to zero with user specified dynamics, and a supervisory controller, based on crude bounds of the system's nonlinearities. The supervisory controller fires when the finite neural-network approximation properties cannot be guaranteed. The form of the supervisor control and the adaptation law for the neural controller are derived from a Lyapunov analysis of stability. The results are applied to a typical turbine/generator pair, showing the feasibility of the proposed solution.

Adaptive backstepping sliding mode control with fuzzy monitoring strategy for a kind of mechanical system.

PubMed

Song, Zhankui; Sun, Kaibiao

2014-01-01

A novel adaptive backstepping sliding mode control (ABSMC) law with fuzzy monitoring strategy is proposed for the tracking-control of a kind of nonlinear mechanical system. The proposed ABSMC scheme combining the sliding mode control and backstepping technique ensure that the occurrence of the sliding motion in finite-time and the trajectory of tracking-error converge to equilibrium point. To obtain a better perturbation rejection property, an adaptive control law is employed to compensate the lumped perturbation. Furthermore, we introduce fuzzy monitoring strategy to improve adaptive capacity and soften the control signal. The convergence and stability of the proposed control scheme are proved by using Lyaponov's method. Finally, numerical simulations demonstrate the effectiveness of the proposed control scheme. © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Shear Heating-Induced Thermal Pressurization During the Nucleation of Earthquakes

NASA Astrophysics Data System (ADS)

Schmitt, S. V.; Segall, P.

2008-12-01

Shear heating-induced thermal pressurization has long been posited as a weakening mechanism during earthquakes. It is often assumed that thermal pressurization does not become important until earthquakes become moderate to large in magnitude. Schmitt et al. [AGU, 2007] confirmed the estimate of Segall and Rice [JGR, 2006] that thermal pressurization becomes dominant during the quasi-static nucleation phase by conducting 2D numerical simulations that account for full thermomechanical coupling, with rate and state dependent friction. In that work, thermal pressurization becomes the dominant weakening mechanism at slip rates of 10-5 to 10-3 m/s, depending on the fault zone hydraulic diffusivity. Interestingly, the thermal pressurization process leads to a contraction of the nucleation zone, rather than the growing crack (aging law) or unidirectional slip pulse (slip law) associated with drained rate- and state-dependent frictional nucleation. The results of Schmitt et al. [AGU, 2007] had a shortcoming in that the principal slip surface was treated as a zero-width feature, while in reality it should be a finite-width shear zone. We address that shortcoming with a new set of numerical simulations. We assume a finite-width fault governed by rate and state friction with the radiation damping approximation to simulate inertial effects. Both thermal and hydraulic diffusion are computed via finite differences on separate, coupled grids that adaptively remesh to minimize computational expense while maintaining accuracy. New results suggest that the thermal pressurization effect is modestly reduced by including the finite thickness of the shear zone. Despite the reduction in the effect, the new results still indicate that (1) thermal pressurization is important before seismic slip and (2) thermal pressurization restricts growth of the nucleation zone.

Improving sub-grid scale accuracy of boundary features in regional finite-difference models

USGS Publications Warehouse

Panday, Sorab; Langevin, Christian D.

2012-01-01

As an alternative to grid refinement, the concept of a ghost node, which was developed for nested grid applications, has been extended towards improving sub-grid scale accuracy of flow to conduits, wells, rivers or other boundary features that interact with a finite-difference groundwater flow model. The formulation is presented for correcting the regular finite-difference groundwater flow equations for confined and unconfined cases, with or without Newton Raphson linearization of the nonlinearities, to include the Ghost Node Correction (GNC) for location displacement. The correction may be applied on the right-hand side vector for a symmetric finite-difference Picard implementation, or on the left-hand side matrix for an implicit but asymmetric implementation. The finite-difference matrix connectivity structure may be maintained for an implicit implementation by only selecting contributing nodes that are a part of the finite-difference connectivity. Proof of concept example problems are provided to demonstrate the improved accuracy that may be achieved through sub-grid scale corrections using the GNC schemes.

Finite-Time Attitude Tracking Control for Spacecraft Using Terminal Sliding Mode and Chebyshev Neural Network.

PubMed

An-Min Zou; Kumar, K D; Zeng-Guang Hou; Xi Liu

2011-08-01

A finite-time attitude tracking control scheme is proposed for spacecraft using terminal sliding mode and Chebyshev neural network (NN) (CNN). The four-parameter representations (quaternion) are used to describe the spacecraft attitude for global representation without singularities. The attitude state (i.e., attitude and velocity) error dynamics is transformed to a double integrator dynamics with a constraint on the spacecraft attitude. With consideration of this constraint, a novel terminal sliding manifold is proposed for the spacecraft. In order to guarantee that the output of the NN used in the controller is bounded by the corresponding bound of the approximated unknown function, a switch function is applied to generate a switching between the adaptive NN control and the robust controller. Meanwhile, a CNN, whose basis functions are implemented using only desired signals, is introduced to approximate the desired nonlinear function and bounded external disturbances online, and the robust term based on the hyperbolic tangent function is applied to counteract NN approximation errors in the adaptive neural control scheme. Most importantly, the finite-time stability in both the reaching phase and the sliding phase can be guaranteed by a Lyapunov-based approach. Finally, numerical simulations on the attitude tracking control of spacecraft in the presence of an unknown mass moment of inertia matrix, bounded external disturbances, and control input constraints are presented to demonstrate the performance of the proposed controller.

The CUBLAS and CULA based GPU acceleration of adaptive finite element framework for bioluminescence tomography.

PubMed

Zhang, Bo; Yang, Xiang; Yang, Fei; Yang, Xin; Qin, Chenghu; Han, Dong; Ma, Xibo; Liu, Kai; Tian, Jie

2010-09-13

In molecular imaging (MI), especially the optical molecular imaging, bioluminescence tomography (BLT) emerges as an effective imaging modality for small animal imaging. The finite element methods (FEMs), especially the adaptive finite element (AFE) framework, play an important role in BLT. The processing speed of the FEMs and the AFE framework still needs to be improved, although the multi-thread CPU technology and the multi CPU technology have already been applied. In this paper, we for the first time introduce a new kind of acceleration technology to accelerate the AFE framework for BLT, using the graphics processing unit (GPU). Besides the processing speed, the GPU technology can get a balance between the cost and performance. The CUBLAS and CULA are two main important and powerful libraries for programming on NVIDIA GPUs. With the help of CUBLAS and CULA, it is easy to code on NVIDIA GPU and there is no need to worry about the details about the hardware environment of a specific GPU. The numerical experiments are designed to show the necessity, effect and application of the proposed CUBLAS and CULA based GPU acceleration. From the results of the experiments, we can reach the conclusion that the proposed CUBLAS and CULA based GPU acceleration method can improve the processing speed of the AFE framework very much while getting a balance between cost and performance.

Plasma Theory and Simulation

DTIC Science & Technology

1988-06-30

equation using finite difference methods. The distribution function is represented by a large number of particles. The particle’s velocities change as a...Small angle Coulomb collisions The FP equation for describing small angle Coulomb collisions can be solved numerically using finite difference techniques...A finite Fourrier transform (FT) is made in z, then we can solve for each k using the following finite difference scheme [5]: 2{r 1 +l1 2 (,,+ 1 - fj

Controls for space structures

NASA Astrophysics Data System (ADS)

Balas, Mark

1991-11-01

Assembly and operation of large space structures (LSS) in orbit will require robot-assisted docking and berthing of partially-assembled structures. These operations require new solutions to the problems of controls. This is true because of large transient and persistent disturbances, controller-structure interaction with unmodeled modes, poorly known structure parameters, slow actuator/sensor dynamical behavior, and excitation of nonlinear structure vibrations during control and assembly. For on-orbit assembly, controllers must start with finite element models of LSS and adapt on line to the best operating points, without compromising stability. This is not easy to do, since there are often unmodeled dynamic interactions between the controller and the structure. The indirect adaptive controllers are based on parameter estimation. Due to the large number of modes in LSS, this approach leads to very high-order control schemes with consequent poor stability and performance. In contrast, direct model reference adaptive controllers operate to force the LSS to track the desirable behavior of a chosen model. These schemes produce simple control algorithms which are easy to implement on line. One problem with their use for LSS has been that the model must be the same dimension as the LSS - i.e., quite large. A control theory based on the command generator tracker (CGT) ideas of Sobel, Mabins, Kaufman and Wen, Balas to obtain very low-order models based on adaptive algorithms was developed. Closed-loop stability for both finite element models and distributed parameter models of LSS was proved. In addition, successful numerical simulations on several LSS databases were obtained. An adaptive controller based on our theory was also implemented on a flexible robotic manipulator at Martin Marietta Astronautics. Computation schemes for controller-structure interaction with unmodeled modes, the residual mode filters or RMF, were developed. The RMF theory was modified to compensate slow actuator/sensor dynamics. These new ideas are being applied to LSS simulations to demonstrate the ease with which one can incorporate slow actuator/sensor effects into our design. It was also shown that residual mode filter compensation can be modified for small nonlinearities to produce exponentially stable closed-loop control.

Controls for space structures

NASA Technical Reports Server (NTRS)

Balas, Mark

1991-01-01

Assembly and operation of large space structures (LSS) in orbit will require robot-assisted docking and berthing of partially-assembled structures. These operations require new solutions to the problems of controls. This is true because of large transient and persistent disturbances, controller-structure interaction with unmodeled modes, poorly known structure parameters, slow actuator/sensor dynamical behavior, and excitation of nonlinear structure vibrations during control and assembly. For on-orbit assembly, controllers must start with finite element models of LSS and adapt on line to the best operating points, without compromising stability. This is not easy to do, since there are often unmodeled dynamic interactions between the controller and the structure. The indirect adaptive controllers are based on parameter estimation. Due to the large number of modes in LSS, this approach leads to very high-order control schemes with consequent poor stability and performance. In contrast, direct model reference adaptive controllers operate to force the LSS to track the desirable behavior of a chosen model. These schemes produce simple control algorithms which are easy to implement on line. One problem with their use for LSS has been that the model must be the same dimension as the LSS - i.e., quite large. A control theory based on the command generator tracker (CGT) ideas of Sobel, Mabins, Kaufman and Wen, Balas to obtain very low-order models based on adaptive algorithms was developed. Closed-loop stability for both finite element models and distributed parameter models of LSS was proved. In addition, successful numerical simulations on several LSS databases were obtained. An adaptive controller based on our theory was also implemented on a flexible robotic manipulator at Martin Marietta Astronautics. Computation schemes for controller-structure interaction with unmodeled modes, the residual mode filters or RMF, were developed. The RMF theory was modified to compensate slow actuator/sensor dynamics. These new ideas are being applied to LSS simulations to demonstrate the ease with which one can incorporate slow actuator/sensor effects into our design. It was also shown that residual mode filter compensation can be modified for small nonlinearities to produce exponentially stable closed-loop control. A theory for disturbance accommodating controllers based on reduced order models of structures was developed, and stability results for these controllers in closed-loop with large-scale finite element models of structures were obtained.

Cultural Adaptation and Validation of the Cultural Self-Efficacy Scale for Colombian Nursing Professionals.

PubMed

Herrero-Hahn, Raquel; Rojas, Juan Guillermo; Ospina-Díaz, Juan Manuel; Montoya-Juárez, Rafael; Restrepo-Medrano, Juan Carlos; Hueso-Montoro, César

2017-03-01

The level of cultural self-efficacy indicates the degree of confidence nursing professionals possess for their ability to provide culturally competent care. Cultural adaptation and validation of the Cultural Self-Efficacy Scale was performed for nursing professionals in Colombia. A scale validation study was conducted. Cultural adaptation and validation of the Cultural Self-Efficacy Scale was performed using a sample of 190 nurses in Colombia, between September 2013 and April 2014. This sample was chosen via systematic random sampling from a finite population. The scale was culturally adapted. Cronbach's alpha for the revised scale was .978. Factor analysis revealed the existence of six factors grouped in three dimensions that explained 68% of the variance. The results demonstrated that the version of the Cultural Self-Efficacy Scale adapted to the Colombian context is a valid and reliable instrument for determining the level of cultural self-efficacy of nursing professionals.

A stochastic-field description of finite-size spiking neural networks

PubMed Central

Longtin, André

2017-01-01

Neural network dynamics are governed by the interaction of spiking neurons. Stochastic aspects of single-neuron dynamics propagate up to the network level and shape the dynamical and informational properties of the population. Mean-field models of population activity disregard the finite-size stochastic fluctuations of network dynamics and thus offer a deterministic description of the system. Here, we derive a stochastic partial differential equation (SPDE) describing the temporal evolution of the finite-size refractory density, which represents the proportion of neurons in a given refractory state at any given time. The population activity—the density of active neurons per unit time—is easily extracted from this refractory density. The SPDE includes finite-size effects through a two-dimensional Gaussian white noise that acts both in time and along the refractory dimension. For an infinite number of neurons the standard mean-field theory is recovered. A discretization of the SPDE along its characteristic curves allows direct simulations of the activity of large but finite spiking networks; this constitutes the main advantage of our approach. Linearizing the SPDE with respect to the deterministic asynchronous state allows the theoretical investigation of finite-size activity fluctuations. In particular, analytical expressions for the power spectrum and autocorrelation of activity fluctuations are obtained. Moreover, our approach can be adapted to incorporate multiple interacting populations and quasi-renewal single-neuron dynamics. PMID:28787447

Modeling the evolution of a ramp-flat-ramp thrust system: A geological application of DynEarthSol2D

NASA Astrophysics Data System (ADS)

Feng, L.; Choi, E.; Bartholomew, M. J.

2013-12-01

DynEarthSol2D (available at http://bitbucket.org/tan2/dynearthsol2) is a robust, adaptive, two-dimensional finite element code that solves the momentum balance and the heat equation in Lagrangian form using unstructured meshes. Verified in a number of benchmark problems, this solver uses contingent mesh adaptivity in places where shear strain is focused (localization) and a conservative mapping assisted by marker particles to preserve phase and facies boundaries during remeshing. We apply this cutting-edge geodynamic modeling tool to the evolution of a thrust fault with a ramp-flat-ramp geometry. The overall geometry of the fault is constrained by observations in the northern part of the southern Appalachian fold and thrust belt. Brittle crust is treated as a Mohr-Coulomb plastic material. The thrust fault is a zone of a finite thickness but has a lower cohesion and friction angle than its surrounding rocks. When an intervening flat separates two distinct sequential ramps crossing different stratigraphic intervals, the thrust system will experience more complex deformations than those from a single thrust fault ramp. The resultant deformations associated with sequential ramps would exhibit a spectrum of styles, of which two end members correspond to ';overprinting' and ';interference'. Reproducing these end-member styles as well as intermediate ones, our models show that the relative importance of overprinting versus interference is a sensitive function of initial fault geometry and hanging wall displacement. We further present stress and strain histories extracted from the models. If clearly distinguishable, they will guide the interpretation of field observations on thrust faults.

High Resolution DNS of Turbulent Flows using an Adaptive, Finite Volume Method

NASA Astrophysics Data System (ADS)

Trebotich, David

2014-11-01

We present a new computational capability for high resolution simulation of incompressible viscous flows. Our approach is based on cut cell methods where an irregular geometry such as a bluff body is intersected with a rectangular Cartesian grid resulting in cut cells near the boundary. In the cut cells we use a conservative discretization based on a discrete form of the divergence theorem to approximate fluxes for elliptic and hyperbolic terms in the Navier-Stokes equations. Away from the boundary the method reduces to a finite difference method. The algorithm is implemented in the Chombo software framework which supports adaptive mesh refinement and massively parallel computations. The code is scalable to 200,000 + processor cores on DOE supercomputers, resulting in DNS studies at unprecedented scale and resolution. For flow past a cylinder in transition (Re = 300) we observe a number of secondary structures in the far wake in 2D where the wake is over 120 cylinder diameters in length. These are compared with the more regularized wake structures in 3D at the same scale. For flow past a sphere (Re = 600) we resolve an arrowhead structure in the velocity in the near wake. The effectiveness of AMR is further highlighted in a simulation of turbulent flow (Re = 6000) in the contraction of an oil well blowout preventer. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Contract Number DE-AC02-05-CH11231.

Adaptation of an unstructured-mesh, finite-element ocean model to the simulation of ocean circulation beneath ice shelves

NASA Astrophysics Data System (ADS)

Kimura, Satoshi; Candy, Adam S.; Holland, Paul R.; Piggott, Matthew D.; Jenkins, Adrian

2013-07-01

Several different classes of ocean model are capable of representing floating glacial ice shelves. We describe the incorporation of ice shelves into Fluidity-ICOM, a nonhydrostatic finite-element ocean model with the capacity to utilize meshes that are unstructured and adaptive in three dimensions. This geometric flexibility offers several advantages over previous approaches. The model represents melting and freezing on all ice-shelf surfaces including vertical faces, treats the ice shelf topography as continuous rather than stepped, and does not require any smoothing of the ice topography or any of the additional parameterisations of the ocean mixed layer used in isopycnal or z-coordinate models. The model can also represent a water column that decreases to zero thickness at the 'grounding line', where the floating ice shelf is joined to its tributary ice streams. The model is applied to idealised ice-shelf geometries in order to demonstrate these capabilities. In these simple experiments, arbitrarily coarsening the mesh outside the ice-shelf cavity has little effect on the ice-shelf melt rate, while the mesh resolution within the cavity is found to be highly influential. Smoothing the vertical ice front results in faster flow along the smoothed ice front, allowing greater exchange with the ocean than in simulations with a realistic ice front. A vanishing water-column thickness at the grounding line has little effect in the simulations studied. We also investigate the response of ice shelf basal melting to variations in deep water temperature in the presence of salt stratification.

Application of 'steady' state finite element and transient finite difference theory to sound propagation in a variable duct - A comparison with experiment

NASA Technical Reports Server (NTRS)

Baumeister, K. J.; Eversman, W.; Astley, R. J.; White, J. W.

1981-01-01

Experimental data are presented for sound propagation in a simulated infinite hard wall duct with a large change in duct cross sectional area. The data are conveniently tabulated for further use. The 'steady' state finite element theory of Astley and Eversman (1981) and the transient finite difference theory of White (1981) are in good agreement with the data for both the axial and transverse pressure profiles and the axial phase angle. Therefore, numerical finite difference and finite element theories appear to be ideally suited for handling duct propagation problems which encounter large axial gradients in acoustic parameters. The measured energy reflection coefficient agrees with the values from the Astley-Eversman modal coupling model.

Adaptive approach for on-board impedance parameters and voltage estimation of lithium-ion batteries in electric vehicles

NASA Astrophysics Data System (ADS)

Farmann, Alexander; Waag, Wladislaw; Sauer, Dirk Uwe

2015-12-01

Robust algorithms using reduced order equivalent circuit model (ECM) for an accurate and reliable estimation of battery states in various applications become more popular. In this study, a novel adaptive, self-learning heuristic algorithm for on-board impedance parameters and voltage estimation of lithium-ion batteries (LIBs) in electric vehicles is introduced. The presented approach is verified using LIBs with different composition of chemistries (NMC/C, NMC/LTO, LFP/C) at different aging states. An impedance-based reduced order ECM incorporating ohmic resistance and a combination of a constant phase element and a resistance (so-called ZARC-element) is employed. Existing algorithms in vehicles are much more limited in the complexity of the ECMs. The algorithm is validated using seven day real vehicle data with high temperature variation including very low temperatures (from -20 °C to +30 °C) at different Depth-of-Discharges (DoDs). Two possibilities to approximate both ZARC-elements with finite number of RC-elements on-board are shown and the results of the voltage estimation are compared. Moreover, the current dependence of the charge-transfer resistance is considered by employing Butler-Volmer equation. Achieved results indicate that both models yield almost the same grade of accuracy.

Nyx: Adaptive mesh, massively-parallel, cosmological simulation code

NASA Astrophysics Data System (ADS)

Almgren, Ann; Beckner, Vince; Friesen, Brian; Lukic, Zarija; Zhang, Weiqun

2017-12-01

Nyx code solves equations of compressible hydrodynamics on an adaptive grid hierarchy coupled with an N-body treatment of dark matter. The gas dynamics in Nyx use a finite volume methodology on an adaptive set of 3-D Eulerian grids; dark matter is represented as discrete particles moving under the influence of gravity. Particles are evolved via a particle-mesh method, using Cloud-in-Cell deposition/interpolation scheme. Both baryonic and dark matter contribute to the gravitational field. In addition, Nyx includes physics for accurately modeling the intergalactic medium; in optically thin limits and assuming ionization equilibrium, the code calculates heating and cooling processes of the primordial-composition gas in an ionizing ultraviolet background radiation field.

A User's Guide to AMR1D: An Instructional Adaptive Mesh Refinement Code for Unstructured Grids

NASA Technical Reports Server (NTRS)

deFainchtein, Rosalinda

1996-01-01

This report documents the code AMR1D, which is currently posted on the World Wide Web (http://sdcd.gsfc.nasa.gov/ESS/exchange/contrib/de-fainchtein/adaptive _mesh_refinement.html). AMR1D is a one-dimensional finite element fluid-dynamics solver, capable of adaptive mesh refinement (AMR). It was written as an instructional tool for AMR on unstructured mesh codes. It is meant to illustrate the minimum requirements for AMR on more than one dimension. For that purpose, it uses the same type of data structure that would be necessary on a two-dimensional AMR code (loosely following the algorithm described by Lohner).

COMET-AR User's Manual: COmputational MEchanics Testbed with Adaptive Refinement

NASA Technical Reports Server (NTRS)

Moas, E. (Editor)

1997-01-01

The COMET-AR User's Manual provides a reference manual for the Computational Structural Mechanics Testbed with Adaptive Refinement (COMET-AR), a software system developed jointly by Lockheed Palo Alto Research Laboratory and NASA Langley Research Center under contract NAS1-18444. The COMET-AR system is an extended version of an earlier finite element based structural analysis system called COMET, also developed by Lockheed and NASA. The primary extensions are the adaptive mesh refinement capabilities and a new "object-like" database interface that makes COMET-AR easier to extend further. This User's Manual provides a detailed description of the user interface to COMET-AR from the viewpoint of a structural analyst.

Thermal comfort analysis: A case study of LIG housing in Chhattisgarh

NASA Astrophysics Data System (ADS)

Netam, Nisha; Sanyal, Shubhashis; Bhowmick, Shubhankar

2016-07-01

The present work reports the evaluation of temperature distribution inside a Low Income Group (LIG) house located in the city of Raipur, Chhattisgarh, using a Agros2D which is multi-platform C++ application capable of higher-order finite element formulation with h, p and hp adaptivity for the solution of differential equations based on the Hermes library. Variation of room air temperature along the length (x) of the house is calculated at different altitudes viz. 0.5m, 1m, 1.5m, 2m, 2.5m, and 3m. 2D model is generated for all the respective altitudes which show the temperature distribution inside the building.

A numerical study of the axisymmetric Couette-Taylor problem using a fast high-resolution second-order central scheme

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

Kupferman, R.

The author presents a numerical study of the axisymmetric Couette-Taylor problem using a finite difference scheme. The scheme is based on a staggered version of a second-order central-differencing method combined with a discrete Hodge projection. The use of central-differencing operators obviates the need to trace the characteristic flow associated with the hyperbolic terms. The result is a simple and efficient scheme which is readily adaptable to other geometries and to more complicated flows. The scheme exhibits competitive performance in terms of accuracy, resolution, and robustness. The numerical results agree accurately with linear stability theory and with previous numerical studies.

Dendritic Growth with Fluid Flow for Pure Materials

NASA Technical Reports Server (NTRS)

Jeong, Jun-Ho; Dantzig, Jonathan A.; Goldenfeld, Nigel

2003-01-01

We have developed a three-dimensional, adaptive, parallel finite element code to examine solidification of pure materials under conditions of forced flow. We have examined the effect of undercooling, surface tension anisotropy and imposed flow velocity on the growth. The flow significantly alters the growth process, producing dendrites that grow faster, and with greater tip curvature, into the flow. The selection constant decreases slightly with flow velocity in our calculations. The results of the calculations agree well with the transport solution of Saville and Beaghton at high undercooling and high anisotropy. At low undercooling, significant deviations are found. We attribute this difference to the influence of other parts of the dendrite, removed from the tip, on the flow field.

Finite-error metrological bounds on multiparameter Hamiltonian estimation

NASA Astrophysics Data System (ADS)

Kura, Naoto; Ueda, Masahito

2018-01-01

Estimation of multiple parameters in an unknown Hamiltonian is investigated. We present upper and lower bounds on the time required to complete the estimation within a prescribed error tolerance δ . The lower bound is given on the basis of the Cramér-Rao inequality, where the quantum Fisher information is bounded by the squared evolution time. The upper bound is obtained by an explicit construction of estimation procedures. By comparing the cases with different numbers of Hamiltonian channels, we also find that the few-channel procedure with adaptive feedback and the many-channel procedure with entanglement are equivalent in the sense that they require the same amount of time resource up to a constant factor.

A visco-poroelastic model of functional adaptation in bones reconstructed with bio-resorbable materials.

PubMed

Giorgio, Ivan; Andreaus, Ugo; Scerrato, Daria; dell'Isola, Francesco

2016-10-01

In this paper, the phenomena of resorption and growth of bone tissue and resorption of the biomaterial inside a bicomponent system are studied by means of a numerical method based on finite elements. The material behavior is described by a poro-viscoelastic model with infiltrated voids. The mechanical stimulus that drives these processes is a linear combination of density of strain energy and viscous dissipation. The external excitation is represented by a bending load slowly variable with sinusoidal law characterized by different frequencies. Investigated aspects are the influence of the load frequency, of type of the stimulus and of the effective porosity on the time evolution of the mass densities of considered system.

Initial performance results for high-aspect ratio gold MEMS deformable mirrors

NASA Astrophysics Data System (ADS)

Fernández, Bautista; Kubby, Joel

2009-02-01

The fabrication and initial performance results of high-aspect ratio 3-dimensional Micro-Electro-Mechanical System (MEMS) Deformable Mirrors (DM) for Adaptive Optics (AO) will be discussed. The DM systems were fabricated out of gold, and consist of actuators bonded to a continuous face sheet, with different boundary conditions. DM mirror displacements vs. voltage have been measured with a white light interferometer and the corresponding results compared to Finite Element Analysis (FEA) simulations. Interferometer scans of a DM have shown that ~9.4um of stroke can be achieved with low voltage, thus showing that this fabrication process holds promise in the manufacturing of future MEMS DM's for the next generation of extremely large telescopes.

Computer Based Porosity Design by Multi Phase Topology Optimization

NASA Astrophysics Data System (ADS)

Burblies, Andreas; Busse, Matthias

2008-02-01

A numerical simulation technique called Multi Phase Topology Optimization (MPTO) based on finite element method has been developed and refined by Fraunhofer IFAM during the last five years. MPTO is able to determine the optimum distribution of two or more different materials in components under thermal and mechanical loads. The objective of optimization is to minimize the component's elastic energy. Conventional topology optimization methods which simulate adaptive bone mineralization have got the disadvantage that there is a continuous change of mass by growth processes. MPTO keeps all initial material concentrations and uses methods adapted from molecular dynamics to find energy minimum. Applying MPTO to mechanically loaded components with a high number of different material densities, the optimization results show graded and sometimes anisotropic porosity distributions which are very similar to natural bone structures. Now it is possible to design the macro- and microstructure of a mechanical component in one step. Computer based porosity design structures can be manufactured by new Rapid Prototyping technologies. Fraunhofer IFAM has applied successfully 3D-Printing and Selective Laser Sintering methods in order to produce very stiff light weight components with graded porosities calculated by MPTO.

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.

Recent Developments in Computational Techniques for Applied Hydrodynamics.

DTIC Science & Technology

1979-12-07

by block number) Numerical Method Fluids Incompressible Flow Finite Difference Methods Poisson Equation Convective Equations -MABSTRACT (Continue on...weaknesses of the different approaches are analyzed. Finite - difference techniques have particularly attractive properties in this framework. Hence it will...be worthwhile to correct, at least partially, the difficulties from which Eulerian and Lagrangian finite - difference techniques suffer, discussed in

ADAPTIVE FINITE-ELEMENT SIMULATION OF STOKES FLOW IN POROUS MEDIA. (R825689C068)

EPA Science Inventory

Abstract

The Stokes problem describes flow of an incompressible constant-viscosity fluid when the Reynolds number is small so that inertial and transient-time effects are negligible. The numerical solution of the Stokes problem requires special care, since classical fi...

Mixed finite-difference scheme for free vibration analysis of noncircular cylinders

NASA Technical Reports Server (NTRS)

Noor, A. K.; Stephens, W. B.

1973-01-01

A mixed finite-difference scheme is presented for the free-vibration analysis of simply supported closed noncircular cylindrical shells. The problem is formulated in terms of eight first-order differential equations in the circumferential coordinate which possess a symmetric coefficient matrix and are free of the derivatives of the elastic and geometric characteristics of the shell. In the finite-difference discretization, two interlacing grids are used for the different fundamental unknowns in such a way as to avoid averaging in the difference-quotient expressions used for the first derivative. The resulting finite-difference equations are symmetric. The inverse-power method is used for obtaining the eigenvalues and eigenvectors.

Understanding human dynamics in microblog posting activities

NASA Astrophysics Data System (ADS)

Jiang, Zhihong; Zhang, Yubao; Wang, Hui; Li, Pei

2013-02-01

Human activity patterns are an important issue in behavior dynamics research. Empirical evidence indicates that human activity patterns can be characterized by a heavy-tailed inter-event time distribution. However, most researchers give an understanding by only modeling the power-law feature of the inter-event time distribution, and those overlooked non-power-law features are likely to be nontrivial. In this work, we propose a behavior dynamics model, called the finite memory model, in which humans adaptively change their activity rates based on a finite memory of recent activities, which is driven by inherent individual interest. Theoretical analysis shows a finite memory model can properly explain various heavy-tailed inter-event time distributions, including a regular power law and some non-power-law deviations. To validate the model, we carry out an empirical study based on microblogging activity from thousands of microbloggers in the Celebrity Hall of the Sina microblog. The results show further that the model is reasonably effective. We conclude that finite memory is an effective dynamics element to describe the heavy-tailed human activity pattern.

Dual-quaternion based fault-tolerant control for spacecraft formation flying with finite-time convergence.

PubMed

Dong, Hongyang; Hu, Qinglei; Ma, Guangfu

2016-03-01

Study results of developing control system for spacecraft formation proximity operations between a target and a chaser are presented. In particular, a coupled model using dual quaternion is employed to describe the proximity problem of spacecraft formation, and a nonlinear adaptive fault-tolerant feedback control law is developed to enable the chaser spacecraft to track the position and attitude of the target even though its actuator occurs fault. Multiple-task capability of the proposed control system is further demonstrated in the presence of disturbances and parametric uncertainties as well. In addition, the practical finite-time stability feature of the closed-loop system is guaranteed theoretically under the designed control law. Numerical simulation of the proposed method is presented to demonstrate the advantages with respect to interference suppression, fast tracking, fault tolerant and practical finite-time stability. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Stochastic control approaches for sensor management in search and exploitation

NASA Astrophysics Data System (ADS)

Hitchings, Darin Chester

Recent improvements in the capabilities of autonomous vehicles have motivated their increased use in such applications as defense, homeland security, environmental monitoring, and surveillance. To enhance performance in these applications, new algorithms are required to control teams of robots autonomously and through limited interactions with human operators. In this dissertation we develop new algorithms for control of robots performing information-seeking missions in unknown environments. These missions require robots to control their sensors in order to discover the presence of objects, keep track of the objects, and learn what these objects are, given a fixed sensing budget. Initially, we investigate control of multiple sensors, with a finite set of sensing options and finite-valued measurements, to locate and classify objects given a limited resource budget. The control problem is formulated as a Partially Observed Markov Decision Problem (POMDP), but its exact solution requires excessive computation. Under the assumption that sensor error statistics are independent and time-invariant, we develop a class of algorithms using Lagrangian Relaxation techniques to obtain optimal mixed strategies using performance bounds developed in previous research. We investigate alternative Receding Horizon (RH) controllers to convert the mixed strategies to feasible adaptive-sensing strategies and evaluate the relative performance of these controllers in simulation. The resulting controllers provide superior performance to alternative algorithms proposed in the literature and obtain solutions to large-scale POMDP problems several orders of magnitude faster than optimal Dynamic Programming (DP) approaches with comparable performance quality. We extend our results for finite action, finite measurement sensor control to scenarios with moving objects. We use Hidden Markov Models (HMMs) for the evolution of objects, according to the dynamics of a birth-death process. We develop a new lower bound on the performance of adaptive controllers in these scenarios, develop algorithms for computing solutions to this lower bound, and use these algorithms as part of a RH controller for sensor allocation in the presence of moving objects We also consider an adaptive Search problem where sensing actions are continuous and the underlying measurement space is also continuous. We extend our previous hierarchical decomposition approach based on performance bounds to this problem and develop novel implementations of Stochastic Dynamic Programming (SDP) techniques to solve this problem. Our algorithms are nearly two orders of magnitude faster than previously proposed approaches and yield solutions of comparable quality. For supervisory control, we discuss how human operators can work with and augment robotic teams performing these tasks. Our focus is on how tasks are partitioned among teams of robots and how a human operator can make intelligent decisions for task partitioning. We explore these questions through the design of a game that involves robot automata controlled by our algorithms and a human supervisor that partitions tasks based on different levels of support information. This game can be used with human subject experiments to explore the effect of information on quality of supervisory control.

A finite element boundary integral formulation for radiation and scattering by cavity antennas using tetrahedral elements

NASA Technical Reports Server (NTRS)

Gong, J.; Volakis, J. L.; Chatterjee, A.; Jin, J. M.

1992-01-01

A hybrid finite element boundary integral formulation is developed using tetrahedral and/or triangular elements for discretizing the cavity and/or aperture of microstrip antenna arrays. The tetrahedral elements with edge based linear expansion functions are chosen for modeling the volume region and triangular elements are used for discretizing the aperture. The edge based expansion functions are divergenceless thus removing the requirement to introduce a penalty term and the tetrahedral elements permit greater geometrical adaptability than the rectangular bricks. The underlying theory and resulting expressions are discussed in detail together with some numerical scattering examples for comparison and demonstration.

A-posteriori error estimation for the finite point method with applications to compressible flow

NASA Astrophysics Data System (ADS)

Ortega, Enrique; Flores, Roberto; Oñate, Eugenio; Idelsohn, Sergio

2017-08-01

An a-posteriori error estimate with application to inviscid compressible flow problems is presented. The estimate is a surrogate measure of the discretization error, obtained from an approximation to the truncation terms of the governing equations. This approximation is calculated from the discrete nodal differential residuals using a reconstructed solution field on a modified stencil of points. Both the error estimation methodology and the flow solution scheme are implemented using the Finite Point Method, a meshless technique enabling higher-order approximations and reconstruction procedures on general unstructured discretizations. The performance of the proposed error indicator is studied and applications to adaptive grid refinement are presented.

Finite difference and Runge-Kutta methods for solving vibration problems

NASA Astrophysics Data System (ADS)

Lintang Renganis Radityani, Scolastika; Mungkasi, Sudi

2017-11-01

The vibration of a storey building can be modelled into a system of second order ordinary differential equations. If the number of floors of a building is large, then the result is a large scale system of second order ordinary differential equations. The large scale system is difficult to solve, and if it can be solved, the solution may not be accurate. Therefore, in this paper, we seek for accurate methods for solving vibration problems. We compare the performance of numerical finite difference and Runge-Kutta methods for solving large scale systems of second order ordinary differential equations. The finite difference methods include the forward and central differences. The Runge-Kutta methods include the Euler and Heun methods. Our research results show that the central finite difference and the Heun methods produce more accurate solutions than the forward finite difference and the Euler methods do.

Deformation of two-phase aggregates using standard numerical methods

NASA Astrophysics Data System (ADS)

Duretz, Thibault; Yamato, Philippe; Schmalholz, Stefan M.

2013-04-01

Geodynamic problems often involve the large deformation of material encompassing material boundaries. In geophysical fluids, such boundaries often coincide with a discontinuity in the viscosity (or effective viscosity) field and subsequently in the pressure field. Here, we employ popular implementations of the finite difference and finite element methods for solving viscous flow problems. On one hand, we implemented finite difference method coupled with a Lagrangian marker-in-cell technique to represent the deforming fluid. Thanks to it Eulerian nature, this method has a limited geometric flexibility but is characterized by a light and stable discretization. On the other hand, we employ the Lagrangian finite element method which offers full geometric flexibility at the cost of relatively heavier discretization. In order to test the accuracy of the finite difference scheme, we ran large strain simple shear deformation of aggregates containing either weak of strong circular inclusion (1e6 viscosity ratio). The results, obtained for different grid resolutions, are compared to Lagrangian finite element results which are considered as reference solution. The comparison is then used to establish up to which strain can finite difference simulations be run given the nature of the inclusions (dimensions, viscosity) and the resolution of the Eulerian mesh.

Numerical solution of the Saint-Venant equations by an efficient hybrid finite-volume/finite-difference method

NASA Astrophysics Data System (ADS)

Lai, Wencong; Khan, Abdul A.

2018-04-01

A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of Saint-Venant equations in one-dimensional open channel flows. The method adopts a mass-conservative finite volume discretization for the continuity equation and a semi-implicit finite difference discretization for the dynamic-wave momentum equation. The spatial discretization of the convective flux term in the momentum equation employs an upwind scheme and the water-surface gradient term is discretized using three different schemes. The performance of the numerical method is investigated in terms of efficiency and accuracy using various examples, including steady flow over a bump, dam-break flow over wet and dry downstream channels, wetting and drying in a parabolic bowl, and dam-break floods in laboratory physical models. Numerical solutions from the hybrid method are compared with solutions from a finite volume method along with analytic solutions or experimental measurements. Comparisons demonstrates that the hybrid method is efficient, accurate, and robust in modeling various flow scenarios, including subcritical, supercritical, and transcritical flows. In this method, the QUICK scheme for the surface slope discretization is more accurate and less diffusive than the center difference and the weighted average schemes.

The CRONOS Code for Astrophysical Magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Kissmann, R.; Kleimann, J.; Krebl, B.; Wiengarten, T.

2018-06-01

We describe the magnetohydrodynamics (MHD) code CRONOS, which has been used in astrophysics and space-physics studies in recent years. CRONOS has been designed to be easily adaptable to the problem in hand, where the user can expand or exchange core modules or add new functionality to the code. This modularity comes about through its implementation using a C++ class structure. The core components of the code include solvers for both hydrodynamical (HD) and MHD problems. These problems are solved on different rectangular grids, which currently support Cartesian, spherical, and cylindrical coordinates. CRONOS uses a finite-volume description with different approximate Riemann solvers that can be chosen at runtime. Here, we describe the implementation of the code with a view toward its ongoing development. We illustrate the code’s potential through several (M)HD test problems and some astrophysical applications.

Adaptive Mesh Refinement for Microelectronic Device Design

NASA Technical Reports Server (NTRS)

Cwik, Tom; Lou, John; Norton, Charles

1999-01-01

Finite element and finite volume methods are used in a variety of design simulations when it is necessary to compute fields throughout regions that contain varying materials or geometry. Convergence of the simulation can be assessed by uniformly increasing the mesh density until an observable quantity stabilizes. Depending on the electrical size of the problem, uniform refinement of the mesh may be computationally infeasible due to memory limitations. Similarly, depending on the geometric complexity of the object being modeled, uniform refinement can be inefficient since regions that do not need refinement add to the computational expense. In either case, convergence to the correct (measured) solution is not guaranteed. Adaptive mesh refinement methods attempt to selectively refine the region of the mesh that is estimated to contain proportionally higher solution errors. The refinement may be obtained by decreasing the element size (h-refinement), by increasing the order of the element (p-refinement) or by a combination of the two (h-p refinement). A successful adaptive strategy refines the mesh to produce an accurate solution measured against the correct fields without undue computational expense. This is accomplished by the use of a) reliable a posteriori error estimates, b) hierarchal elements, and c) automatic adaptive mesh generation. Adaptive methods are also useful when problems with multi-scale field variations are encountered. These occur in active electronic devices that have thin doped layers and also when mixed physics is used in the calculation. The mesh needs to be fine at and near the thin layer to capture rapid field or charge variations, but can coarsen away from these layers where field variations smoothen and charge densities are uniform. This poster will present an adaptive mesh refinement package that runs on parallel computers and is applied to specific microelectronic device simulations. Passive sensors that operate in the infrared portion of the spectrum as well as active device simulations that model charge transport and Maxwell's equations will be presented.

Finite-key security analyses on passive decoy-state QKD protocols with different unstable sources.

PubMed

Song, Ting-Ting; Qin, Su-Juan; Wen, Qiao-Yan; Wang, Yu-Kun; Jia, Heng-Yue

2015-10-16

In quantum communication, passive decoy-state QKD protocols can eliminate many side channels, but the protocols without any finite-key analyses are not suitable for in practice. The finite-key securities of passive decoy-state (PDS) QKD protocols with two different unstable sources, type-II parametric down-convention (PDC) and phase randomized weak coherent pulses (WCPs), are analyzed in our paper. According to the PDS QKD protocols, we establish an optimizing programming respectively and obtain the lower bounds of finite-key rates. Under some reasonable values of quantum setup parameters, the lower bounds of finite-key rates are simulated. The simulation results show that at different transmission distances, the affections of different fluctuations on key rates are different. Moreover, the PDS QKD protocol with an unstable PDC source can resist more intensity fluctuations and more statistical fluctuation.

Adaptive beamlet-based finite-size pencil beam dose calculation for independent verification of IMRT and VMAT.

PubMed

Park, Justin C; Li, Jonathan G; Arhjoul, Lahcen; Yan, Guanghua; Lu, Bo; Fan, Qiyong; Liu, Chihray

2015-04-01

The use of sophisticated dose calculation procedure in modern radiation therapy treatment planning is inevitable in order to account for complex treatment fields created by multileaf collimators (MLCs). As a consequence, independent volumetric dose verification is time consuming, which affects the efficiency of clinical workflow. In this study, the authors present an efficient adaptive beamlet-based finite-size pencil beam (AB-FSPB) dose calculation algorithm that minimizes the computational procedure while preserving the accuracy. The computational time of finite-size pencil beam (FSPB) algorithm is proportional to the number of infinitesimal and identical beamlets that constitute an arbitrary field shape. In AB-FSPB, dose distribution from each beamlet is mathematically modeled such that the sizes of beamlets to represent an arbitrary field shape no longer need to be infinitesimal nor identical. As a result, it is possible to represent an arbitrary field shape with combinations of different sized and minimal number of beamlets. In addition, the authors included the model parameters to consider MLC for its rounded edge and transmission. Root mean square error (RMSE) between treatment planning system and conventional FSPB on a 10 × 10 cm(2) square field using 10 × 10, 2.5 × 2.5, and 0.5 × 0.5 cm(2) beamlet sizes were 4.90%, 3.19%, and 2.87%, respectively, compared with RMSE of 1.10%, 1.11%, and 1.14% for AB-FSPB. This finding holds true for a larger square field size of 25 × 25 cm(2), where RMSE for 25 × 25, 2.5 × 2.5, and 0.5 × 0.5 cm(2) beamlet sizes were 5.41%, 4.76%, and 3.54% in FSPB, respectively, compared with RMSE of 0.86%, 0.83%, and 0.88% for AB-FSPB. It was found that AB-FSPB could successfully account for the MLC transmissions without major discrepancy. The algorithm was also graphical processing unit (GPU) compatible to maximize its computational speed. For an intensity modulated radiation therapy (∼12 segments) and a volumetric modulated arc therapy fields (∼90 control points) with a 3D grid size of 2.0 × 2.0 × 2.0 mm(3), dose was computed within 3-5 and 10-15 s timeframe, respectively. The authors have developed an efficient adaptive beamlet-based pencil beam dose calculation algorithm. The fast computation nature along with GPU compatibility has shown better performance than conventional FSPB. This enables the implementation of AB-FSPB in the clinical environment for independent volumetric dose verification.

Adaptive MPC based on MIMO ARX-Laguerre model.

PubMed

Ben Abdelwahed, Imen; Mbarek, Abdelkader; Bouzrara, Kais

2017-03-01

This paper proposes a method for synthesizing an adaptive predictive controller using a reduced complexity model. This latter is given by the projection of the ARX model on Laguerre bases. The resulting model is entitled MIMO ARX-Laguerre and it is characterized by an easy recursive representation. The adaptive predictive control law is computed based on multi-step-ahead finite-element predictors, identified directly from experimental input/output data. The model is tuned in each iteration by an online identification algorithms of both model parameters and Laguerre poles. The proposed approach avoids time consuming numerical optimization algorithms associated with most common linear predictive control strategies, which makes it suitable for real-time implementation. The method is used to synthesize and test in numerical simulations adaptive predictive controllers for the CSTR process benchmark. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

COMPARISONS OF THE FINITE-ELEMENT-WITH-DISCONTIGUOUS-SUPPORT METHOD TO CONTINUOUS-ENERGY MONTE CARLO FOR PIN-CELL PROBLEMS

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

A. T. Till; M. Hanuš; J. Lou

The standard multigroup (MG) method for energy discretization of the transport equation can be sensitive to approximations in the weighting spectrum chosen for cross-section averaging. As a result, MG often inaccurately treats important phenomena such as self-shielding variations across a material. From a finite-element viewpoint, MG uses a single fixed basis function (the pre-selected spectrum) within each group, with no mechanism to adapt to local solution behavior. In this work, we introduce the Finite-Element-with-Discontiguous-Support (FEDS) method, whose only approximation with respect to energy is that the angular flux is a linear combination of unknowns multiplied by basis functions. A basismore » function is non-zero only in the discontiguous set of energy intervals associated with its energy element. Discontiguous energy elements are generalizations of bands and are determined by minimizing a norm of the difference between snapshot spectra and their averages over the energy elements. We begin by presenting the theory of the FEDS method. We then compare to continuous-energy Monte Carlo for one-dimensional slab and two-dimensional pin-cell problem. We find FEDS to be accurate and efficient at producing quantities of interest such as reaction rates and eigenvalues. Results show that FEDS converges at a rate that is approximately first-order in the number of energy elements and that FEDS is less sensitive to weighting spectrum than standard MG.« less

Life assessment of structural components using inelastic finite element analyses

NASA Technical Reports Server (NTRS)

Arya, Vinod K.; Halford, Gary R.

1993-01-01

The need for enhanced and improved performance of structural components subject to severe cyclic thermal/mechanical loadings, such as in the aerospace industry, requires development of appropriate solution technologies involving time-dependent inelastic analyses. Such analyses are mandatory to predict local stress-strain response and to assess more accurately the cyclic life time of structural components. The NASA-Lewis Research Center is cognizant of this need. As a result of concerted efforts at Lewis during the last few years, several such finite element solution technologies (in conjunction with the finite element program MARC) were developed and successfully applied to numerous uniaxial and multiaxial problems. These solution technologies, although developed for use with MARC program, are general in nature and can easily be extended for adaptation with other finite element programs such as ABAQUS, ANSYS, etc. The description and results obtained from two such inelastic finite element solution technologies are presented. The first employs a classical (non-unified) creep-plasticity model. An application of this technology is presented for a hypersonic inlet cowl-lip problem. The second of these technologies uses a unified creep-plasticity model put forth by Freed. The structural component for which this finite element solution technology is illustrated, is a cylindrical rocket engine thrust chamber. The advantages of employing a viscoplastic model for nonlinear time-dependent structural analyses are demonstrated. The life analyses for cowl-lip and cylindrical thrust chambers are presented. These analyses are conducted by using the stress-strain response of these components obtained from the corresponding finite element analyses.

An object-oriented, coprocessor-accelerated model for ice sheet simulations

NASA Astrophysics Data System (ADS)

Seddik, H.; Greve, R.

2013-12-01

Recently, numerous models capable of modeling the thermo-dynamics of ice sheets have been developed within the ice sheet modeling community. Their capabilities have been characterized by a wide range of features with different numerical methods (finite difference or finite element), different implementations of the ice flow mechanics (shallow-ice, higher-order, full Stokes) and different treatments for the basal and coastal areas (basal hydrology, basal sliding, ice shelves). Shallow-ice models (SICOPOLIS, IcIES, PISM, etc) have been widely used for modeling whole ice sheets (Greenland and Antarctica) due to the relatively low computational cost of the shallow-ice approximation but higher order (ISSM, AIF) and full Stokes (Elmer/Ice) models have been recently used to model the Greenland ice sheet. The advance in processor speed and the decrease in cost for accessing large amount of memory and storage have undoubtedly been the driving force in the commoditization of models with higher capabilities, and the popularity of Elmer/Ice (http://elmerice.elmerfem.com) with an active user base is a notable representation of this trend. Elmer/Ice is a full Stokes model built on top of the multi-physics package Elmer (http://www.csc.fi/english/pages/elmer) which provides the full machinery for the complex finite element procedure and is fully parallel (mesh partitioning with OpenMPI communication). Elmer is mainly written in Fortran 90 and targets essentially traditional processors as the code base was not initially written to run on modern coprocessors (yet adding support for the recently introduced x86 based coprocessors is possible). Furthermore, a truly modular and object-oriented implementation is required for quick adaptation to fast evolving capabilities in hardware (Fortran 2003 provides an object-oriented programming model while not being clean and requiring a tricky refactoring of Elmer code). In this work, the object-oriented, coprocessor-accelerated finite element code Sainou is introduced. Sainou is an Elmer fork which is reimplemented in Objective C and used for experimenting with ice sheet models running on coprocessors, essentially GPU devices. GPUs are highly parallel processors that provide opportunities for fine-grained parallelization of the full Stokes problem using the standard OpenCL language (http://www.khronos.org/opencl/) to access the device. Sainou is built upon a collection of Objective C base classes that service a modular kernel (itself a base class) which provides the core methods to solve the finite element problem. An early implementation of Sainou will be presented with emphasis on the object architecture and the strategies of parallelizations. The computation of a simple heat conduction problem is used to test the implementation which also provides experimental support for running the global matrix assembly on GPU.

Technical Feasibility of Centrifugal Techniques for Evaluating Hazardous Waste Migration

DTIC Science & Technology

1987-12-01

direct evaluation of the -influence of acceleration on soil moisture movement. A fully implicit finite difference solution scheme was used. The...using the finite difference scheme mentioned earlier. 2. The soil test apparatus for the centrifuge tests was designed and constructed. 110 3...npcr3 f~nJPX 115 S.. 0i U 4 I3 u cc/ U) C~j tC LL~~*- Lý u ’ uiu ’ 4-’ Uju x~j~r3np~~r~tj~jpU W3= 116 Finite Difference Model The finite difference

A study of the response of nonlinear springs

NASA Technical Reports Server (NTRS)

Hyer, M. W.; Knott, T. W.; Johnson, E. R.

1991-01-01

The various phases to developing a methodology for studying the response of a spring-reinforced arch subjected to a point load are discussed. The arch is simply supported at its ends with both the spring and the point load assumed to be at midspan. The spring is present to off-set the typical snap through behavior normally associated with arches, and to provide a structure that responds with constant resistance over a finite displacement. The various phases discussed consist of the following: (1) development of the closed-form solution for the shallow arch case; (2) development of a finite difference analysis to study (shallow) arches; and (3) development of a finite element analysis for studying more general shallow and nonshallow arches. The two numerical analyses rely on a continuation scheme to move the solution past limit points, and to move onto bifurcated paths, both characteristics being common to the arch problem. An eigenvalue method is used for a continuation scheme. The finite difference analysis is based on a mixed formulation (force and displacement variables) of the governing equations. The governing equations for the mixed formulation are in first order form, making the finite difference implementation convenient. However, the mixed formulation is not well-suited for the eigenvalue continuation scheme. This provided the motivation for the displacement based finite element analysis. Both the finite difference and the finite element analyses are compared with the closed form shallow arch solution. Agreement is excellent, except for the potential problems with the finite difference analysis and the continuation scheme. Agreement between the finite element analysis and another investigator's numerical analysis for deep arches is also good.

Optimization of finite difference forward modeling for elastic waves based on optimum combined window functions

NASA Astrophysics Data System (ADS)

Jian, Wang; Xiaohong, Meng; Hong, Liu; Wanqiu, Zheng; Yaning, Liu; Sheng, Gui; Zhiyang, Wang

2017-03-01

Full waveform inversion and reverse time migration are active research areas for seismic exploration. Forward modeling in the time domain determines the precision of the results, and numerical solutions of finite difference have been widely adopted as an important mathematical tool for forward modeling. In this article, the optimum combined of window functions was designed based on the finite difference operator using a truncated approximation of the spatial convolution series in pseudo-spectrum space, to normalize the outcomes of existing window functions for different orders. The proposed combined window functions not only inherit the characteristics of the various window functions, to provide better truncation results, but also control the truncation error of the finite difference operator manually and visually by adjusting the combinations and analyzing the characteristics of the main and side lobes of the amplitude response. Error level and elastic forward modeling under the proposed combined system were compared with outcomes from conventional window functions and modified binomial windows. Numerical dispersion is significantly suppressed, which is compared with modified binomial window function finite-difference and conventional finite-difference. Numerical simulation verifies the reliability of the proposed method.

Full Wave Analysis of Passive Microwave Monolithic Integrated Circuit Devices Using a Generalized Finite Difference Time Domain (GFDTD) Algorithm

NASA Technical Reports Server (NTRS)

Lansing, Faiza S.; Rascoe, Daniel L.

1993-01-01

This paper presents a modified Finite-Difference Time-Domain (FDTD) technique using a generalized conformed orthogonal grid. The use of the Conformed Orthogonal Grid, Finite Difference Time Domain (GFDTD) enables the designer to match all the circuit dimensions, hence eliminating a major source o error in the analysis.

Puncture-and-Pull Biomechanics in the Teeth of Predatory Coelurosaurian Dinosaurs.

PubMed

Torices, Angelica; Wilkinson, Ryan; Arbour, Victoria M; Ruiz-Omeñaca, Jose Ignacio; Currie, Philip J

2018-05-07

The teeth of putatively carnivorous dinosaurs are often blade-shaped with well-defined serrated cutting edges (Figure 1). These ziphodont teeth are often easily differentiated based on the morphology and density of the denticles [1, 2]. A tearing function has been proposed for theropod denticles in general [3], but the functional significance of denticle phenotypic variation has received less attention. In particular, the unusual hooked denticles found in troodontids suggest a different feeding strategy or diet compared to other small theropods. We used a two-pronged approach to investigate the function of denticle shape variation across theropods with both congruent body shapes and sizes (e.g., dromaeosaurids versus troodontids) and highly disparate body shapes and sizes (e.g., troodontids versus tyrannosaurids), using microwear and finite element analyses (Figure 1). We found that many toothed coelurosaurian theropods employed a puncture-and-pull feeding movement, in which parallel scratches form while biting down into prey and oblique scratches form as the head is pulled backward with the jaws closed. In finite element simulations, theropod teeth had the lowest stresses when bite forces were aligned with the oblique family of microwear scratches. Different denticle morphologies performed differently under a variety of simulated biting angles: Dromaeosaurus and Saurornitholestes were well-adapted for handling struggling prey, whereas troodontid teeth were more likely to fail at non-optimal bite angles. Troodontids may have favored softer, smaller, or immobile prey. Copyright © 2018 Elsevier Ltd. All rights reserved.

78 FR 1206 - Notice of Availability of Government-Owned Inventions; Available for Licensing

Federal Register 2010, 2011, 2012, 2013, 2014

2013-01-08

.... Patent No. 8,238,924: Real-Time Optimization of Allocation of Resources//U.S. Patent No. 7,685,207: Adaptive Web-Based Asset Control System. ADDRESSES: Requests for copies of the patents cited should be...: Patent application 12/650,413: Finite State Machine Architecture for Software Development (a system for...

Cantorian Set Theory and Teaching Prospective Teachers

ERIC Educational Resources Information Center

Narli, Serkan; Baser, Nes'e

2008-01-01

Infinity has contradictions arising from its nature. Since mind is actually adapted to finite realities attained by behaviors in space and time, when one starts to deal with real infinity, contradictions will arise. In particular, Cantorian Set Theory for it involves the notion of "equivalence of a set to one of its proper subsets,"…

Cantorian Set Theory and Teaching Prospective Teachers

ERIC Educational Resources Information Center

Narli, Serkan; Baser, Nes'e

2008-01-01

Infinity has contradictions arising from its nature. Since mind is actually adapted to finite realities attained by behaviors in space and time, when one starts to deal with real infinity, contradictions will arise. In particular, Cantorian Set Theory, for it involves the notion of "equivalence of a set to one of its proper subsets," causes…

Self-adaptive Solution Strategies

NASA Technical Reports Server (NTRS)

Padovan, J.

1984-01-01

The development of enhancements to current generation nonlinear finite element algorithms of the incremental Newton-Raphson type was overviewed. Work was introduced on alternative formulations which lead to improve algorithms that avoid the need for global level updating and inversion. To quantify the enhanced Newton-Raphson scheme and the new alternative algorithm, the results of several benchmarks are presented.

Retrieving infinite numbers of patterns in a spin-glass model of immune networks

NASA Astrophysics Data System (ADS)

Agliari, E.; Annibale, A.; Barra, A.; Coolen, A. C. C.; Tantari, D.

2017-01-01

The similarity between neural and (adaptive) immune networks has been known for decades, but so far we did not understand the mechanism that allows the immune system, unlike associative neural networks, to recall and execute a large number of memorized defense strategies in parallel. The explanation turns out to lie in the network topology. Neurons interact typically with a large number of other neurons, whereas interactions among lymphocytes in immune networks are very specific, and described by graphs with finite connectivity. In this paper we use replica techniques to solve a statistical mechanical immune network model with “coordinator branches” (T-cells) and “effector branches” (B-cells), and show how the finite connectivity enables the coordinators to manage an extensive number of effectors simultaneously, even above the percolation threshold (where clonal cross-talk is not negligible). A consequence of its underlying topological sparsity is that the adaptive immune system exhibits only weak ergodicity breaking, so that also spontaneous switch-like effects as bi-stabilities are present: the latter may play a significant role in the maintenance of immune homeostasis.

Efficient robust doubly adaptive regularized regression with applications.

PubMed

Karunamuni, Rohana J; Kong, Linglong; Tu, Wei

2018-01-01

We consider the problem of estimation and variable selection for general linear regression models. Regularized regression procedures have been widely used for variable selection, but most existing methods perform poorly in the presence of outliers. We construct a new penalized procedure that simultaneously attains full efficiency and maximum robustness. Furthermore, the proposed procedure satisfies the oracle properties. The new procedure is designed to achieve sparse and robust solutions by imposing adaptive weights on both the decision loss and the penalty function. The proposed method of estimation and variable selection attains full efficiency when the model is correct and, at the same time, achieves maximum robustness when outliers are present. We examine the robustness properties using the finite-sample breakdown point and an influence function. We show that the proposed estimator attains the maximum breakdown point. Furthermore, there is no loss in efficiency when there are no outliers or the error distribution is normal. For practical implementation of the proposed method, we present a computational algorithm. We examine the finite-sample and robustness properties using Monte Carlo studies. Two datasets are also analyzed.

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

NASA Astrophysics Data System (ADS)

Liu, Y.; Li, Y.

2016-12-01

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

Finite-horizon differential games for missile-target interception system using adaptive dynamic programming with input constraints

NASA Astrophysics Data System (ADS)

Sun, Jingliang; Liu, Chunsheng

2018-01-01

In this paper, the problem of intercepting a manoeuvring target within a fixed final time is posed in a non-linear constrained zero-sum differential game framework. The Nash equilibrium solution is found by solving the finite-horizon constrained differential game problem via adaptive dynamic programming technique. Besides, a suitable non-quadratic functional is utilised to encode the control constraints into a differential game problem. The single critic network with constant weights and time-varying activation functions is constructed to approximate the solution of associated time-varying Hamilton-Jacobi-Isaacs equation online. To properly satisfy the terminal constraint, an additional error term is incorporated in a novel weight-updating law such that the terminal constraint error is also minimised over time. By utilising Lyapunov's direct method, the closed-loop differential game system and the estimation weight error of the critic network are proved to be uniformly ultimately bounded. Finally, the effectiveness of the proposed method is demonstrated by using a simple non-linear system and a non-linear missile-target interception system, assuming first-order dynamics for the interceptor and target.

Finite-element-based matching of pre- and intraoperative data for image-guided endovascular aneurysm repair

PubMed Central

Dumenil, Aurélien; Kaladji, Adrien; Castro, Miguel; Esneault, Simon; Lucas, Antoine; Rochette, Michel; Goksu, Cemil; Haigron, Pascal

2013-01-01

Endovascular repair of abdominal aortic aneurysms is a well-established technique throughout the medical and surgical communities. Although increasingly indicated, this technique does have some limitations. Because intervention is commonly performed under fluoroscopic control, two-dimensional (2D) visualization of the aneurysm requires the injection of a contrast agent. The projective nature of this imaging modality inevitably leads to topographic errors, and does not give information on arterial wall quality at the time of deployment. A specially-adapted intraoperative navigation interface could increase deployment accuracy and reveal such information, which preoperative three-dimensional (3D) imaging might otherwise provide. One difficulty is the precise matching of preoperative data (images and models) and intraoperative observations affected by anatomical deformations due to tool-tissue interactions. Our proposed solution involves a finite element-based preoperative simulation of tool/tissue interactions, its adaptive tuning regarding patient specific data, and the matching with intra-operative data. The biomechanical model was first tuned on a group of 10 patients and assessed on a second group of 8 patients. PMID:23269745

The self adapting washer for lag screw fixation of mandibular fractures: finite element analysis and preclinical evaluation.

PubMed

Terheyden, H; Mühlendyck, C; Feldmann, H; Ludwig, K; Härle, F

1999-02-01

Besides rigid fixation, lag screws have distinct advantages compared with plates in appropriate indications in mandibular fractures. However, in current lag screw systems, the relatively small area of the screw head has to transfer the tensile force which can exceed 1000 N in the symphysis, to the thin cortical bone plate. Countersinking, which is obligatory in most systems, will weaken the cortical plate. Finite element analysis (FEA) revealed that load in this situation can exceed the normal tensile strength of metal and bone. Consequently, a new washer was constructed which both increased the supporting surface and did not require countersinking. The washer is self adapting (SAW) to the cortical plate in a defined position, forming a ball and socket joint with the screw head. Using the FEA model, a ten-fold reduction in load on bone and metal was observed with the new washer. In a miniature pig mandibular symphysis fracture model, the clinical applicability and a favourable histological reaction were demonstrated, compared with conventional lag screw designs.

Local mesh adaptation technique for front tracking problems

NASA Astrophysics Data System (ADS)

Lock, N.; Jaeger, M.; Medale, M.; Occelli, R.

1998-09-01

A numerical model is developed for the simulation of moving interfaces in viscous incompressible flows. The model is based on the finite element method with a pseudo-concentration technique to track the front. Since a Eulerian approach is chosen, the interface is advected by the flow through a fixed mesh. Therefore, material discontinuity across the interface cannot be described accurately. To remedy this problem, the model has been supplemented with a local mesh adaptation technique. This latter consists in updating the mesh at each time step to the interface position, such that element boundaries lie along the front. It has been implemented for unstructured triangular finite element meshes. The outcome of this technique is that it allows an accurate treatment of material discontinuity across the interface and, if necessary, a modelling of interface phenomena such as surface tension by using specific boundary elements. For illustration, two examples are computed and presented in this paper: the broken dam problem and the Rayleigh-Taylor instability. Good agreement has been obtained in the comparison of the numerical results with theory or available experimental data.

Combination of the discontinuous Galerkin method with finite differences for simulation of seismic wave propagation

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

Lisitsa, Vadim, E-mail: lisitsavv@ipgg.sbras.ru; Novosibirsk State University, Novosibirsk; Tcheverda, Vladimir

We present an algorithm for the numerical simulation of seismic wave propagation in models with a complex near surface part and free surface topography. The approach is based on the combination of finite differences with the discontinuous Galerkin method. The discontinuous Galerkin method can be used on polyhedral meshes; thus, it is easy to handle the complex surfaces in the models. However, this approach is computationally intense in comparison with finite differences. Finite differences are computationally efficient, but in general, they require rectangular grids, leading to the stair-step approximation of the interfaces, which causes strong diffraction of the wavefield. Inmore » this research we present a hybrid algorithm where the discontinuous Galerkin method is used in a relatively small upper part of the model and finite differences are applied to the main part of the model.« less

Finite-key security analyses on passive decoy-state QKD protocols with different unstable sources

PubMed Central

Song, Ting-Ting; Qin, Su-Juan; Wen, Qiao-Yan; Wang, Yu-Kun; Jia, Heng-Yue

2015-01-01

In quantum communication, passive decoy-state QKD protocols can eliminate many side channels, but the protocols without any finite-key analyses are not suitable for in practice. The finite-key securities of passive decoy-state (PDS) QKD protocols with two different unstable sources, type-II parametric down-convention (PDC) and phase randomized weak coherent pulses (WCPs), are analyzed in our paper. According to the PDS QKD protocols, we establish an optimizing programming respectively and obtain the lower bounds of finite-key rates. Under some reasonable values of quantum setup parameters, the lower bounds of finite-key rates are simulated. The simulation results show that at different transmission distances, the affections of different fluctuations on key rates are different. Moreover, the PDS QKD protocol with an unstable PDC source can resist more intensity fluctuations and more statistical fluctuation. PMID:26471947

Sliding mode disturbance observer-enhanced adaptive control for the air-breathing hypersonic flight vehicle

NASA Astrophysics Data System (ADS)

An, Hao; Wang, Changhong; Fidan, Baris

2017-10-01

This paper presents a backstepping procedure to design an adaptive controller for the air-breathing hypersonic flight vehicle (AHFV) subject to external disturbances and actuator saturations. In each step, a sliding mode exact disturbance observer (SMEDO) is exploited to exactly estimate the lumped disturbance in finite time. Specific dynamics are introduced to handle the possible actuator saturations. Based on SMEDO and introduced dynamics, an adaptive control law is designed, along with the consideration on ;explosion of complexity; in backstepping design. The developed controller is equipped with fast disturbance rejection and great capability to accommodate the saturated actuators, which also lead to a wider application scope. A simulation study is provided to show the effectiveness and superiority of the proposed controller.

Adaptive Crack Modeling with Interface Solid Elements for Plain and Fiber Reinforced Concrete Structures.

PubMed

Zhan, Yijian; Meschke, Günther

2017-07-08

The effective analysis of the nonlinear behavior of cement-based engineering structures not only demands physically-reliable models, but also computationally-efficient algorithms. Based on a continuum interface element formulation that is suitable to capture complex cracking phenomena in concrete materials and structures, an adaptive mesh processing technique is proposed for computational simulations of plain and fiber-reinforced concrete structures to progressively disintegrate the initial finite element mesh and to add degenerated solid elements into the interfacial gaps. In comparison with the implementation where the entire mesh is processed prior to the computation, the proposed adaptive cracking model allows simulating the failure behavior of plain and fiber-reinforced concrete structures with remarkably reduced computational expense.

Adaptive frequency-domain equalization in digital coherent optical receivers.

PubMed

Faruk, Md Saifuddin; Kikuchi, Kazuro

2011-06-20

We propose a novel frequency-domain adaptive equalizer in digital coherent optical receivers, which can reduce computational complexity of the conventional time-domain adaptive equalizer based on finite-impulse-response (FIR) filters. The proposed equalizer can operate on the input sequence sampled by free-running analog-to-digital converters (ADCs) at the rate of two samples per symbol; therefore, the arbitrary initial sampling phase of ADCs can be adjusted so that the best symbol-spaced sequence is produced. The equalizer can also be configured in the butterfly structure, which enables demultiplexing of polarization tributaries apart from equalization of linear transmission impairments. The performance of the proposed equalization scheme is verified by 40-Gbits/s dual-polarization quadrature phase-shift keying (QPSK) transmission experiments.

Adaptive Crack Modeling with Interface Solid Elements for Plain and Fiber Reinforced Concrete Structures

PubMed Central

Zhan, Yijian

2017-01-01

The effective analysis of the nonlinear behavior of cement-based engineering structures not only demands physically-reliable models, but also computationally-efficient algorithms. Based on a continuum interface element formulation that is suitable to capture complex cracking phenomena in concrete materials and structures, an adaptive mesh processing technique is proposed for computational simulations of plain and fiber-reinforced concrete structures to progressively disintegrate the initial finite element mesh and to add degenerated solid elements into the interfacial gaps. In comparison with the implementation where the entire mesh is processed prior to the computation, the proposed adaptive cracking model allows simulating the failure behavior of plain and fiber-reinforced concrete structures with remarkably reduced computational expense. PMID:28773130

Coordinate Families for the Schwarzschild Geometry Based on Radial Timelike Geodesics

NASA Technical Reports Server (NTRS)

Finch, Tehani K.

2015-01-01

We explore the connections between various coordinate systems associated with observersmoving inwardly along radial geodesics in the Schwarzschild geometry. Painleve-Gullstrand (PG) time is adapted to freely falling observers dropped from rest from infinity; Lake-Martel-Poisson (LMP) time coordinates are adapted to observers who start at infinity with non-zero initial inward velocity; Gautreau-Hoffmann time coordinates are adapted to observers dropped from rest from a finite distance from the black hole horizon.We construct from these an LMP family and a proper-time family of time coordinates, the intersection of which is PG time. We demonstrate that these coordinate families are distinct, but related, one-parameter generalizations of PG time, and show linkage to Lemaître coordinates as well.

Fast online generalized multiscale finite element method using constraint energy minimization

NASA Astrophysics Data System (ADS)

Chung, Eric T.; Efendiev, Yalchin; Leung, Wing Tat

2018-02-01

Local multiscale methods often construct multiscale basis functions in the offline stage without taking into account input parameters, such as source terms, boundary conditions, and so on. These basis functions are then used in the online stage with a specific input parameter to solve the global problem at a reduced computational cost. Recently, online approaches have been introduced, where multiscale basis functions are adaptively constructed in some regions to reduce the error significantly. In multiscale methods, it is desired to have only 1-2 iterations to reduce the error to a desired threshold. Using Generalized Multiscale Finite Element Framework [10], it was shown that by choosing sufficient number of offline basis functions, the error reduction can be made independent of physical parameters, such as scales and contrast. In this paper, our goal is to improve this. Using our recently proposed approach [4] and special online basis construction in oversampled regions, we show that the error reduction can be made sufficiently large by appropriately selecting oversampling regions. Our numerical results show that one can achieve a three order of magnitude error reduction, which is better than our previous methods. We also develop an adaptive algorithm and enrich in selected regions with large residuals. In our adaptive method, we show that the convergence rate can be determined by a user-defined parameter and we confirm this by numerical simulations. The analysis of the method is presented.

Finite Adaptation and Multistep Moves in the Metropolis-Hastings Algorithm for Variable Selection in Genome-Wide Association Analysis

PubMed Central

Peltola, Tomi; Marttinen, Pekka; Vehtari, Aki

2012-01-01

High-dimensional datasets with large amounts of redundant information are nowadays available for hypothesis-free exploration of scientific questions. A particular case is genome-wide association analysis, where variations in the genome are searched for effects on disease or other traits. Bayesian variable selection has been demonstrated as a possible analysis approach, which can account for the multifactorial nature of the genetic effects in a linear regression model. Yet, the computation presents a challenge and application to large-scale data is not routine. Here, we study aspects of the computation using the Metropolis-Hastings algorithm for the variable selection: finite adaptation of the proposal distributions, multistep moves for changing the inclusion state of multiple variables in a single proposal and multistep move size adaptation. We also experiment with a delayed rejection step for the multistep moves. Results on simulated and real data show increase in the sampling efficiency. We also demonstrate that with application specific proposals, the approach can overcome a specific mixing problem in real data with 3822 individuals and 1,051,811 single nucleotide polymorphisms and uncover a variant pair with synergistic effect on the studied trait. Moreover, we illustrate multimodality in the real dataset related to a restrictive prior distribution on the genetic effect sizes and advocate a more flexible alternative. PMID:23166669

Computer simulations show that Neanderthal facial morphology represents adaptation to cold and high energy demands, but not heavy biting.

PubMed

Wroe, Stephen; Parr, William C H; Ledogar, Justin A; Bourke, Jason; Evans, Samuel P; Fiorenza, Luca; Benazzi, Stefano; Hublin, Jean-Jacques; Stringer, Chris; Kullmer, Ottmar; Curry, Michael; Rae, Todd C; Yokley, Todd R

2018-04-11

Three adaptive hypotheses have been forwarded to explain the distinctive Neanderthal face: (i) an improved ability to accommodate high anterior bite forces, (ii) more effective conditioning of cold and/or dry air and, (iii) adaptation to facilitate greater ventilatory demands. We test these hypotheses using three-dimensional models of Neanderthals, modern humans, and a close outgroup ( Homo heidelbergensis ), applying finite-element analysis (FEA) and computational fluid dynamics (CFD). This is the most comprehensive application of either approach applied to date and the first to include both. FEA reveals few differences between H. heidelbergensis , modern humans, and Neanderthals in their capacities to sustain high anterior tooth loadings. CFD shows that the nasal cavities of Neanderthals and especially modern humans condition air more efficiently than does that of H. heidelbergensis , suggesting that both evolved to better withstand cold and/or dry climates than less derived Homo We further find that Neanderthals could move considerably more air through the nasal pathway than could H. heidelbergensis or modern humans, consistent with the propositions that, relative to our outgroup Homo , Neanderthal facial morphology evolved to reflect improved capacities to better condition cold, dry air, and, to move greater air volumes in response to higher energetic requirements. © 2018 The Author(s).

Multi-dimensional Upwind Fluctuation Splitting Scheme with Mesh Adaption for Hypersonic Viscous Flow. Degree awarded by Virginia Polytechnic Inst. and State Univ., 9 Nov. 2001

NASA Technical Reports Server (NTRS)

Wood, William A., III

2002-01-01

A multi-dimensional upwind fluctuation splitting scheme is developed and implemented for two-dimensional and axisymmetric formulations of the Navier-Stokes equations on unstructured meshes. Key features of the scheme are the compact stencil, full upwinding, and non-linear discretization which allow for second-order accuracy with enforced positivity. Throughout, the fluctuation splitting scheme is compared to a current state-of-the-art finite volume approach, a second-order, dual mesh upwind flux difference splitting scheme (DMFDSFV), and is shown to produce more accurate results using fewer computer resources for a wide range of test cases. A Blasius flat plate viscous validation case reveals a more accurate upsilon-velocity profile for fluctuation splitting, and the reduced artificial dissipation production is shown relative to DMFDSFV. Remarkably, the fluctuation splitting scheme shows grid converged skin friction coefficients with only five points in the boundary layer for this case. The second half of the report develops a local, compact, anisotropic unstructured mesh adaptation scheme in conjunction with the multi-dimensional upwind solver, exhibiting a characteristic alignment behavior for scalar problems. The adaptation strategy is extended to the two-dimensional and axisymmetric Navier-Stokes equations of motion through the concept of fluctuation minimization.

Full Waveform 2.5D Teleseismic Surface Wave Tomography with Application to the Tien Shan

NASA Astrophysics Data System (ADS)

Roecker, S. W.; Priestley, K. F.; Baker, B. I.

2011-12-01

We adapt the 2.5D spectral domain finite difference waveform tomography algorithm of Roecker et al. (2010) to permit the analysis of teleseismically recorded surface waves. The teleseismic body wave technique of generating synthetic waveforms by specifying an analytic solution for a background wavefield in a 1D model and solving for a scattered field excited by this background is equally applicable to surface waves. We use the locked mode approach of Gomberg and Masters (1988) to calculate the background Greens functions at each point of the finite difference (FD) grid. Because of the much greater concentration of energy at the surface, we adopt the cell-based FD operators of Min et al. (2004) to calculate the free surface boundary conditions, and the generalized stretching function of Komatitch and Martin (2007) to improve the absorption in the PML. We use this algorithm to analyze broad band seismograms of events in Sumatra recorded by the MANAS array in the Tien Shan. Our results show that the upper mantle beneath much of the central Tien Shan has shear wavespeeds at least 10% lower than the lithosphere beneath the Tarim basin to the south or the Kazach shield to the north. At the same time, there appears to be a remnant lithospheric lid beneath the Kyrgyz range in the north, an observation consistent with previous receiver function studies in this area.

Finite-difference computations of rotor loads

NASA Technical Reports Server (NTRS)

Caradonna, F. X.; Tung, C.

1985-01-01

This paper demonstrates the current and future potential of finite-difference methods for solving real rotor problems which now rely largely on empiricism. The demonstration consists of a simple means of combining existing finite-difference, integral, and comprehensive loads codes to predict real transonic rotor flows. These computations are performed for hover and high-advance-ratio flight. Comparisons are made with experimental pressure data.

Finite-difference computations of rotor loads

NASA Technical Reports Server (NTRS)

Caradonna, F. X.; Tung, C.

1985-01-01

The current and future potential of finite difference methods for solving real rotor problems which now rely largely on empiricism are demonstrated. The demonstration consists of a simple means of combining existing finite-difference, integral, and comprehensive loads codes to predict real transonic rotor flows. These computations are performed for hover and high-advanced-ratio flight. Comparisons are made with experimental pressure data.

Stochastic Least-Squares Petrov--Galerkin Method for Parameterized Linear Systems

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

Lee, Kookjin; Carlberg, Kevin; Elman, Howard C.

Here, we consider the numerical solution of parameterized linear systems where the system matrix, the solution, and the right-hand side are parameterized by a set of uncertain input parameters. We explore spectral methods in which the solutions are approximated in a chosen finite-dimensional subspace. It has been shown that the stochastic Galerkin projection technique fails to minimize any measure of the solution error. As a remedy for this, we propose a novel stochatic least-squares Petrov--Galerkin (LSPG) method. The proposed method is optimal in the sense that it produces the solution that minimizes a weightedmore » $$\\ell^2$$-norm of the residual over all solutions in a given finite-dimensional subspace. Moreover, the method can be adapted to minimize the solution error in different weighted $$\\ell^2$$-norms by simply applying a weighting function within the least-squares formulation. In addition, a goal-oriented seminorm induced by an output quantity of interest can be minimized by defining a weighting function as a linear functional of the solution. We establish optimality and error bounds for the proposed method, and extensive numerical experiments show that the weighted LSPG method outperforms other spectral methods in minimizing corresponding target weighted norms.« less

A WENO-solver combined with adaptive momentum discretization for the Wigner transport equation and its application to resonant tunneling diodes

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

Dorda, Antonius, E-mail: dorda@tugraz.at; Schürrer, Ferdinand, E-mail: ferdinand.schuerrer@tugraz.at

2015-03-01

We present a novel numerical scheme for the deterministic solution of the Wigner transport equation, especially suited to deal with situations in which strong quantum effects are present. The unique feature of the algorithm is the expansion of the Wigner function in local basis functions, similar to finite element or finite volume methods. This procedure yields a discretization of the pseudo-differential operator that conserves the particle density on arbitrarily chosen grids. The high flexibility in refining the grid spacing together with the weighted essentially non-oscillatory (WENO) scheme for the advection term allows for an accurate and well-resolved simulation of themore » phase space dynamics. A resonant tunneling diode is considered as test case and a detailed convergence study is given by comparing the results to a non-equilibrium Green's functions calculation. The impact of the considered domain size and of the grid spacing is analyzed. The obtained convergence of the results towards a quasi-exact agreement of the steady state Wigner and Green's functions computations demonstrates the accuracy of the scheme, as well as the high flexibility to adjust to different physical situations.« less

Seismic wave propagation modeling

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

Jones, E.M.; Olsen, K.B.

1998-12-31

This is the final report of a one-year, Laboratory Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). A hybrid, finite-difference technique was developed for modeling nonlinear soil amplification from three-dimensional, finite-fault radiation patters for earthquakes in arbitrary earth models. The method was applied to the 17 January 1994 Northridge earthquake. Particle velocities were computed on a plane at 5-km depth, immediately above the causative fault. Time-series of the strike-perpendicular, lateral velocities then were propagated vertically in a soil column typical of the San Fernando Valley. Suitable material models were adapted from a suite used tomore » model ground motions at the US Nevada Test Site. The effects of nonlinearity reduced relative spectral amplitudes by about 40% at frequencies above 1.5 Hz but only by 10% at lower frequencies. Runs made with source-depth amplitudes increased by a factor of two showed relative amplitudes above 1.5 Hz reduced by a total of 70% above 1.5 Hz and 20% at lower frequencies. Runs made with elastic-plastic material models showed similar behavior to runs made with Masing-Rule models.« less

A finite element approach to self-consistent field theory calculations of multiblock polymers

NASA Astrophysics Data System (ADS)

Ackerman, David M.; Delaney, Kris; Fredrickson, Glenn H.; Ganapathysubramanian, Baskar

2017-02-01

Self-consistent field theory (SCFT) has proven to be a powerful tool for modeling equilibrium microstructures of soft materials, particularly for multiblock polymers. A very successful approach to numerically solving the SCFT set of equations is based on using a spectral approach. While widely successful, this approach has limitations especially in the context of current technologically relevant applications. These limitations include non-trivial approaches for modeling complex geometries, difficulties in extending to non-periodic domains, as well as non-trivial extensions for spatial adaptivity. As a viable alternative to spectral schemes, we develop a finite element formulation of the SCFT paradigm for calculating equilibrium polymer morphologies. We discuss the formulation and address implementation challenges that ensure accuracy and efficiency. We explore higher order chain contour steppers that are efficiently implemented with Richardson Extrapolation. This approach is highly scalable and suitable for systems with arbitrary shapes. We show spatial and temporal convergence and illustrate scaling on up to 2048 cores. Finally, we illustrate confinement effects for selected complex geometries. This has implications for materials design for nanoscale applications where dimensions are such that equilibrium morphologies dramatically differ from the bulk phases.

Random element method for numerical modeling of diffusional processes

NASA Technical Reports Server (NTRS)

Ghoniem, A. F.; Oppenheim, A. K.

1982-01-01

The random element method is a generalization of the random vortex method that was developed for the numerical modeling of momentum transport processes as expressed in terms of the Navier-Stokes equations. The method is based on the concept that random walk, as exemplified by Brownian motion, is the stochastic manifestation of diffusional processes. The algorithm based on this method is grid-free and does not require the diffusion equation to be discritized over a mesh, it is thus devoid of numerical diffusion associated with finite difference methods. Moreover, the algorithm is self-adaptive in space and explicit in time, resulting in an improved numerical resolution of gradients as well as a simple and efficient computational procedure. The method is applied here to an assortment of problems of diffusion of momentum and energy in one-dimension as well as heat conduction in two-dimensions in order to assess its validity and accuracy. The numerical solutions obtained are found to be in good agreement with exact solution except for a statistical error introduced by using a finite number of elements, the error can be reduced by increasing the number of elements or by using ensemble averaging over a number of solutions.

Scaling in two-fluid pinch-off

NASA Astrophysics Data System (ADS)

Pommer, Chris; Suryo, Ronald; Subramani, Hariprasad; Harris, Michael; Basaran, Osman

2009-11-01

Two-fluid pinch-off is encountered when drops or bubbles of one fluid are ejected from a nozzle into another fluid or when a compound jet breaks. While the breakup of a drop in a passive environment and that of a passive bubble in a liquid are well understood, the physics of pinch-off when both the inner and outer fluids are dynamically active is inadequately understood. In this talk, the breakup of a compound jet whose core and shell are both incompressible Newtonian fluids is analyzed computationally by a method of lines ALE algorithm which uses finite elements with elliptic mesh generation for spatial discretization and adaptive finite differences for time integration. Pinch-off dynamics are investigated well beyond the limit of experiments set by the wavelength of visible light and that of various algorithms used in the literature. Simulations show that the minimum neck radius r initially scales with time τ before breakup as &αcirc; where α varies over a certain range. However, depending on the values of the governing dimensionless groups, this initial scaling regime may be transitory and, closer to pinch-off, the dynamics may transition to a final asymptotic regime for which r ˜&βcirc;, where β!=α.

A WENO-solver combined with adaptive momentum discretization for the Wigner transport equation and its application to resonant tunneling diodes

PubMed Central

Dorda, Antonius; Schürrer, Ferdinand

2015-01-01

We present a novel numerical scheme for the deterministic solution of the Wigner transport equation, especially suited to deal with situations in which strong quantum effects are present. The unique feature of the algorithm is the expansion of the Wigner function in local basis functions, similar to finite element or finite volume methods. This procedure yields a discretization of the pseudo-differential operator that conserves the particle density on arbitrarily chosen grids. The high flexibility in refining the grid spacing together with the weighted essentially non-oscillatory (WENO) scheme for the advection term allows for an accurate and well-resolved simulation of the phase space dynamics. A resonant tunneling diode is considered as test case and a detailed convergence study is given by comparing the results to a non-equilibrium Green's functions calculation. The impact of the considered domain size and of the grid spacing is analyzed. The obtained convergence of the results towards a quasi-exact agreement of the steady state Wigner and Green's functions computations demonstrates the accuracy of the scheme, as well as the high flexibility to adjust to different physical situations. PMID:25892748

A WENO-solver combined with adaptive momentum discretization for the Wigner transport equation and its application to resonant tunneling diodes.

PubMed

Dorda, Antonius; Schürrer, Ferdinand

2015-03-01

We present a novel numerical scheme for the deterministic solution of the Wigner transport equation, especially suited to deal with situations in which strong quantum effects are present. The unique feature of the algorithm is the expansion of the Wigner function in local basis functions, similar to finite element or finite volume methods. This procedure yields a discretization of the pseudo-differential operator that conserves the particle density on arbitrarily chosen grids. The high flexibility in refining the grid spacing together with the weighted essentially non-oscillatory (WENO) scheme for the advection term allows for an accurate and well-resolved simulation of the phase space dynamics. A resonant tunneling diode is considered as test case and a detailed convergence study is given by comparing the results to a non-equilibrium Green's functions calculation. The impact of the considered domain size and of the grid spacing is analyzed. The obtained convergence of the results towards a quasi-exact agreement of the steady state Wigner and Green's functions computations demonstrates the accuracy of the scheme, as well as the high flexibility to adjust to different physical situations.

A finite element approach to self-consistent field theory calculations of multiblock polymers

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

Ackerman, David M.; Delaney, Kris; Fredrickson, Glenn H.

Self-consistent field theory (SCFT) has proven to be a powerful tool for modeling equilibrium microstructures of soft materials, particularly for multiblock polymers. A very successful approach to numerically solving the SCFT set of equations is based on using a spectral approach. While widely successful, this approach has limitations especially in the context of current technologically relevant applications. These limitations include non-trivial approaches for modeling complex geometries, difficulties in extending to non-periodic domains, as well as non-trivial extensions for spatial adaptivity. As a viable alternative to spectral schemes, we develop a finite element formulation of the SCFT paradigm for calculating equilibriummore » polymer morphologies. We discuss the formulation and address implementation challenges that ensure accuracy and efficiency. We explore higher order chain contour steppers that are efficiently implemented with Richardson Extrapolation. This approach is highly scalable and suitable for systems with arbitrary shapes. We show spatial and temporal convergence and illustrate scaling on up to 2048 cores. Finally, we illustrate confinement effects for selected complex geometries. This has implications for materials design for nanoscale applications where dimensions are such that equilibrium morphologies dramatically differ from the bulk phases.« less

Deterministic and reliability based optimization of integrated thermal protection system composite panel using adaptive sampling techniques

NASA Astrophysics Data System (ADS)

Ravishankar, Bharani

Conventional space vehicles have thermal protection systems (TPS) that provide protection to an underlying structure that carries the flight loads. In an attempt to save weight, there is interest in an integrated TPS (ITPS) that combines the structural function and the TPS function. This has weight saving potential, but complicates the design of the ITPS that now has both thermal and structural failure modes. The main objectives of this dissertation was to optimally design the ITPS subjected to thermal and mechanical loads through deterministic and reliability based optimization. The optimization of the ITPS structure requires computationally expensive finite element analyses of 3D ITPS (solid) model. To reduce the computational expenses involved in the structural analysis, finite element based homogenization method was employed, homogenizing the 3D ITPS model to a 2D orthotropic plate. However it was found that homogenization was applicable only for panels that are much larger than the characteristic dimensions of the repeating unit cell in the ITPS panel. Hence a single unit cell was used for the optimization process to reduce the computational cost. Deterministic and probabilistic optimization of the ITPS panel required evaluation of failure constraints at various design points. This further demands computationally expensive finite element analyses which was replaced by efficient, low fidelity surrogate models. In an optimization process, it is important to represent the constraints accurately to find the optimum design. Instead of building global surrogate models using large number of designs, the computational resources were directed towards target regions near constraint boundaries for accurate representation of constraints using adaptive sampling strategies. Efficient Global Reliability Analyses (EGRA) facilitates sequentially sampling of design points around the region of interest in the design space. EGRA was applied to the response surface construction of the failure constraints in the deterministic and reliability based optimization of the ITPS panel. It was shown that using adaptive sampling, the number of designs required to find the optimum were reduced drastically, while improving the accuracy. System reliability of ITPS was estimated using Monte Carlo Simulation (MCS) based method. Separable Monte Carlo method was employed that allowed separable sampling of the random variables to predict the probability of failure accurately. The reliability analysis considered uncertainties in the geometry, material properties, loading conditions of the panel and error in finite element modeling. These uncertainties further increased the computational cost of MCS techniques which was also reduced by employing surrogate models. In order to estimate the error in the probability of failure estimate, bootstrapping method was applied. This research work thus demonstrates optimization of the ITPS composite panel with multiple failure modes and large number of uncertainties using adaptive sampling techniques.

International Symposium on Numerical Methods in Engineering, 5th, Ecole Polytechnique Federale de Lausanne, Switzerland, Sept. 11-15, 1989, Proceedings. Volumes 1 & 2

NASA Astrophysics Data System (ADS)

Gruber, Ralph; Periaux, Jaques; Shaw, Richard Paul

Recent advances in computational mechanics are discussed in reviews and reports. Topics addressed include spectral superpositions on finite elements for shear banding problems, strain-based finite plasticity, numerical simulation of hypersonic viscous continuum flow, constitutive laws in solid mechanics, dynamics problems, fracture mechanics and damage tolerance, composite plates and shells, contact and friction, metal forming and solidification, coupling problems, and adaptive FEMs. Consideration is given to chemical flows, convection problems, free boundaries and artificial boundary conditions, domain-decomposition and multigrid methods, combustion and thermal analysis, wave propagation, mixed and hybrid FEMs, integral-equation methods, optimization, software engineering, and vector and parallel computing.

Finite element analysis of Al 2024/Cu-Al-Ni shape memory alloy composites with defects/cracks

NASA Astrophysics Data System (ADS)

Kotresh, M.; Benal, M. M., Dr; Siddalinga Swamy, N. H., Dr

2018-02-01

In this work, a numerical approach to predict the stress field behaviour of defect/crack in shape memory alloy (SMA) particles reinforced composite known as the adaptive composite is presented. Simulation is based on the finite element method. The critical stress field approach was used to determine the stresses around defect/crack. Thereby stress amplification issue is being resolved. In this paper, the effect volume % of shape memory alloy and shape memory effect of reinforcement for as-cast and SME trained composites are examined and discussed. Shape memory effect known as training is achieved by pre-straining of reinforcement particles by equivalent changes in their expansion coefficients.

Multiple types of synchronization analysis for discontinuous Cohen-Grossberg neural networks with time-varying delays.

PubMed

Li, Jiarong; Jiang, Haijun; Hu, Cheng; Yu, Zhiyong

2018-03-01

This paper is devoted to the exponential synchronization, finite time synchronization, and fixed-time synchronization of Cohen-Grossberg neural networks (CGNNs) with discontinuous activations and time-varying delays. Discontinuous feedback controller and Novel adaptive feedback controller are designed to realize global exponential synchronization, finite time synchronization and fixed-time synchronization by adjusting the values of the parameters ω in the controller. Furthermore, the settling time of the fixed-time synchronization derived in this paper is less conservative and more accurate. Finally, some numerical examples are provided to show the effectiveness and flexibility of the results derived in this paper. Copyright © 2018 Elsevier Ltd. All rights reserved.

Computational optical palpation: a finite-element approach to micro-scale tactile imaging using a compliant sensor

PubMed Central

Sampson, David D.; Kennedy, Brendan F.

2017-01-01

High-resolution tactile imaging, superior to the sense of touch, has potential for future biomedical applications such as robotic surgery. In this paper, we propose a tactile imaging method, termed computational optical palpation, based on measuring the change in thickness of a thin, compliant layer with optical coherence tomography and calculating tactile stress using finite-element analysis. We demonstrate our method on test targets and on freshly excised human breast fibroadenoma, demonstrating a resolution of up to 15–25 µm and a field of view of up to 7 mm. Our method is open source and readily adaptable to other imaging modalities, such as ultrasonography and confocal microscopy. PMID:28250098

Improving Stiffness-to-weight Ratio of Spot-welded Structures based upon Nonlinear Finite Element Modelling

NASA Astrophysics Data System (ADS)

Zhang, Shengyong

2017-07-01

Spot welding has been widely used for vehicle body construction due to its advantages of high speed and adaptability for automation. An effort to increase the stiffness-to-weight ratio of spot-welded structures is investigated based upon nonlinear finite element analysis. Topology optimization is conducted for reducing weight in the overlapping regions by choosing an appropriate topology. Three spot-welded models (lap, doubt-hat and T-shape) that approximate “typical” vehicle body components are studied for validating and illustrating the proposed method. It is concluded that removing underutilized material from overlapping regions can result in a significant increase in structural stiffness-to-weight ratio.

Adaptation of a program for nonlinear finite element analysis to the CDC STAR 100 computer

NASA Technical Reports Server (NTRS)

Pifko, A. B.; Ogilvie, P. L.

1978-01-01

The conversion of a nonlinear finite element program to the CDC STAR 100 pipeline computer is discussed. The program called DYCAST was developed for the crash simulation of structures. Initial results with the STAR 100 computer indicated that significant gains in computation time are possible for operations on gloval arrays. However, for element level computations that do not lend themselves easily to long vector processing, the STAR 100 was slower than comparable scalar computers. On this basis it is concluded that in order for pipeline computers to impact the economic feasibility of large nonlinear analyses it is absolutely essential that algorithms be devised to improve the efficiency of element level computations.

Importance of the cutoff value in the quadratic adaptive integrate-and-fire model.

PubMed

Touboul, Jonathan

2009-08-01

The quadratic adaptive integrate-and-fire model (Izhikevich, 2003 , 2007 ) is able to reproduce various firing patterns of cortical neurons and is widely used in large-scale simulations of neural networks. This model describes the dynamics of the membrane potential by a differential equation that is quadratic in the voltage, coupled to a second equation for adaptation. Integration is stopped during the rise phase of a spike at a voltage cutoff value V(c) or when it blows up. Subsequently the membrane potential is reset, and the adaptation variable is increased by a fixed amount. We show in this note that in the absence of a cutoff value, not only the voltage but also the adaptation variable diverges in finite time during spike generation in the quadratic model. The divergence of the adaptation variable makes the system very sensitive to the cutoff: changing V(c) can dramatically alter the spike patterns. Furthermore, from a computational viewpoint, the divergence of the adaptation variable implies that the time steps for numerical simulation need to be small and adaptive. However, divergence of the adaptation variable does not occur for the quartic model (Touboul, 2008 ) and the adaptive exponential integrate-and-fire model (Brette & Gerstner, 2005 ). Hence, these models are robust to changes in the cutoff value.

Computer-Oriented Calculus Courses Using Finite Differences.

ERIC Educational Resources Information Center

Gordon, Sheldon P.

The so-called discrete approach in calculus instruction involves introducing topics from the calculus of finite differences and finite sums, both for motivation and as useful tools for applications of the calculus. In particular, it provides an ideal setting in which to incorporate computers into calculus courses. This approach has been…

Interpolation methods and the accuracy of lattice-Boltzmann mesh refinement

DOE PAGES

Guzik, Stephen M.; Weisgraber, Todd H.; Colella, Phillip; ...

2013-12-10

A lattice-Boltzmann model to solve the equivalent of the Navier-Stokes equations on adap- tively refined grids is presented. A method for transferring information across interfaces between different grid resolutions was developed following established techniques for finite- volume representations. This new approach relies on a space-time interpolation and solving constrained least-squares problems to ensure conservation. The effectiveness of this method at maintaining the second order accuracy of lattice-Boltzmann is demonstrated through a series of benchmark simulations and detailed mesh refinement studies. These results exhibit smaller solution errors and improved convergence when compared with similar approaches relying only on spatial interpolation. Examplesmore » highlighting the mesh adaptivity of this method are also provided.« less

Low-rank approximation in the numerical modeling of the Farley-Buneman instability in ionospheric plasma

NASA Astrophysics Data System (ADS)

Dolgov, S. V.; Smirnov, A. P.; Tyrtyshnikov, E. E.

2014-04-01

We consider numerical modeling of the Farley-Buneman instability in the Earth's ionosphere plasma. The ion behavior is governed by the kinetic Vlasov equation with the BGK collisional term in the four-dimensional phase space, and since the finite difference discretization on a tensor product grid is used, this equation becomes the most computationally challenging part of the scheme. To relax the complexity and memory consumption, an adaptive model reduction using the low-rank separation of variables, namely the Tensor Train format, is employed. The approach was verified via a prototype MATLAB implementation. Numerical experiments demonstrate the possibility of efficient separation of space and velocity variables, resulting in the solution storage reduction by a factor of order tens.

Compact cell-centered discretization stencils at fine-coarse block structured grid interfaces

NASA Astrophysics Data System (ADS)

Pletzer, Alexander; Jamroz, Ben; Crockett, Robert; Sides, Scott

2014-03-01

Different strategies for coupling fine-coarse grid patches are explored in the context of the adaptive mesh refinement (AMR) method. We show that applying linear interpolation to fill in the fine grid ghost values can produce a finite volume stencil of comparable accuracy to quadratic interpolation provided the cell volumes are adjusted. The volume of fine cells expands whereas the volume of neighboring coarse cells contracts. The amount by which the cells contract/expand depends on whether the interface is a face, an edge, or a corner. It is shown that quadratic or better interpolation is required when the conductivity is spatially varying, anisotropic, the refinement ratio is other than two, or when the fine-coarse interface is concave.

Nonlinear analysis of composite thin-walled helicopter blades

NASA Astrophysics Data System (ADS)

Kalfon, J. P.; Rand, O.

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

Discrete-time switching periodic adaptive control for time-varying parameters with unknown periodicity

NASA Astrophysics Data System (ADS)

Yu, Miao; Huang, Deqing; Yang, Wanqiu

2018-06-01

In this paper, we address the problem of unknown periodicity for a class of discrete-time nonlinear parametric systems without assuming any growth conditions on the nonlinearities. The unknown periodicity hides in the parametric uncertainties, which is difficult to estimate with existing techniques. By incorporating a logic-based switching mechanism, we identify the period and bound of unknown parameter simultaneously. Lyapunov-based analysis is given to demonstrate that a finite number of switchings can guarantee the asymptotic tracking for the nonlinear parametric systems. The simulation result also shows the efficacy of the proposed switching periodic adaptive control approach.

Prediction and control of chaotic processes using nonlinear adaptive networks

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

Jones, R.D.; Barnes, C.W.; Flake, G.W.

1990-01-01

We present the theory of nonlinear adaptive networks and discuss a few applications. In particular, we review the theory of feedforward backpropagation networks. We then present the theory of the Connectionist Normalized Linear Spline network in both its feedforward and iterated modes. Also, we briefly discuss the theory of stochastic cellular automata. We then discuss applications to chaotic time series, tidal prediction in Venice lagoon, finite differencing, sonar transient detection, control of nonlinear processes, control of a negative ion source, balancing a double inverted pendulum and design advice for free electron lasers and laser fusion targets.

On the role of dimensionality and sample size for unstructured and structured covariance matrix estimation

NASA Technical Reports Server (NTRS)

Morgera, S. D.; Cooper, D. B.

1976-01-01

The experimental observation that a surprisingly small sample size vis-a-vis dimension is needed to achieve good signal-to-interference ratio (SIR) performance with an adaptive predetection filter is explained. The adaptive filter requires estimates as obtained by a recursive stochastic algorithm of the inverse of the filter input data covariance matrix. The SIR performance with sample size is compared for the situations where the covariance matrix estimates are of unstructured (generalized) form and of structured (finite Toeplitz) form; the latter case is consistent with weak stationarity of the input data stochastic process.

Motion planning for an adaptive wing structure with macro-fiber composite actuators

NASA Astrophysics Data System (ADS)

Schröck, J.; Meurer, T.; Kugi, A.

2009-05-01

A systematic approach for flatness-based motion planning and feedforward control is presented for the transient shaping of a piezo-actuated rectangular cantilevered plate modeling an adaptive wing. In the first step the consideration of an idealized infinite-dimensional input allows to determine the state and input parametrization in terms of a flat or basic output, which is used for a systematic motion planning approach. Subsequently, the obtained idealized input function is projected onto a finite number of suitably placed Macro-fiber Composite (MFC) patch actuators. The tracking performance of the proposed approach is evaluated in a simulation scenario.

Optimizing the passenger air bag of an adaptive restraint system for multiple size occupants.

PubMed

Bai, Zhonghao; Jiang, Binhui; Zhu, Feng; Cao, Libo

2014-01-01

The development of the adaptive occupant restraint system (AORS) has led to an innovative way to optimize such systems for multiple size occupants. An AORS consists of multiple units such as adaptive air bags, seat belts, etc. During a collision, as a supplemental protective device, air bags can provide constraint force and play a role in dissipating the crash energy of the occupants' head and thorax. This article presents an investigation into an adaptive passenger air bag (PAB). The purpose of this study is to develop a base shape of a PAB for different size occupants using an optimization method. Four typical base shapes of a PAB were designed based on geometric data on the passenger side. Then 4 PAB finite element (FE) models and a validated sled with different size dummy models were developed in MADYMO (TNO, Rijswijk, The Netherlands) to conduct the optimization to obtain the best baseline PAB that would be used in the AORS. The objective functions-that is, the minimum total probability of injuries (∑Pcomb) of the 5th percentile female and 50th and 95th percentile male dummies-were adopted to evaluate the optimal configurations. The injury probability (Pcomb) for each dummy was adopted from the U.S. New Car Assessment Program (US-NCAP). The parameters of the AORS were first optimized for different types of PAB base shapes in a frontal impact. Then, contact time duration and force between the PAB and dummy head/chest were optimized by adjusting the parameters of the PAB, such as the number and position of tethers, lower the Pcomb of the 95th percentile male dummy. According to the optimization results, 4 typical PABs could provide effective protection to 5th and 50th percentile dummies. However, due to the heavy and large torsos of the 95th percentile occupants, the current occupant restraint system does not demonstrate satisfactory protective function, particularly for the thorax.

Extinction Dynamics and Control in Adaptive Networks

NASA Astrophysics Data System (ADS)

Schwartz, Ira; Shaw, Leah; Hindes, Jason

Disease control is of paramount importance in public health. Moreover, models of disease spread are an important component in implementing effective vaccination and treatment campaigns. However, human behavior in response to an outbreak has only recently been included in epidemic models on networks. Here we develop the mathematical machinery to describe the dynamics of extinction in finite populations that include human adaptive behavior. The formalism enables us to compute the optimal, fluctuation-induced path to extinction, and predict the average extinction time in adaptive networks as a function of the adaptation rate. We find that both observables have several unique scalings depending on the relative speed of infection and adaptivity. Finally, we discuss how the theory can be used to design optimal control programs in general networks, by coupling the effective force of noise with treatment and human behavior. Research supported by U.S. Naval Research Laboratory funding (Grant No. N0001414WX00023) and the Office of Naval Research (Grant No. N0001414WX20610).

Fast digital zooming system using directionally adaptive image interpolation and restoration.

PubMed

Kang, Wonseok; Jeon, Jaehwan; Yu, Soohwan; Paik, Joonki

2014-01-01

This paper presents a fast digital zooming system for mobile consumer cameras using directionally adaptive image interpolation and restoration methods. The proposed interpolation algorithm performs edge refinement along the initially estimated edge orientation using directionally steerable filters. Either the directionally weighted linear or adaptive cubic-spline interpolation filter is then selectively used according to the refined edge orientation for removing jagged artifacts in the slanted edge region. A novel image restoration algorithm is also presented for removing blurring artifacts caused by the linear or cubic-spline interpolation using the directionally adaptive truncated constrained least squares (TCLS) filter. Both proposed steerable filter-based interpolation and the TCLS-based restoration filters have a finite impulse response (FIR) structure for real time processing in an image signal processing (ISP) chain. Experimental results show that the proposed digital zooming system provides high-quality magnified images with FIR filter-based fast computational structure.

A new anisotropic mesh adaptation method based upon hierarchical a posteriori error estimates

NASA Astrophysics Data System (ADS)

Huang, Weizhang; Kamenski, Lennard; Lang, Jens

2010-03-01

A new anisotropic mesh adaptation strategy for finite element solution of elliptic differential equations is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in some metric space, with the metric tensor being computed based on hierarchical a posteriori error estimates. A global hierarchical error estimate is employed in this study to obtain reliable directional information of the solution. Instead of solving the global error problem exactly, which is costly in general, we solve it iteratively using the symmetric Gauß-Seidel method. Numerical results show that a few GS iterations are sufficient for obtaining a reasonably good approximation to the error for use in anisotropic mesh adaptation. The new method is compared with several strategies using local error estimators or recovered Hessians. Numerical results are presented for a selection of test examples and a mathematical model for heat conduction in a thermal battery with large orthotropic jumps in the material coefficients.

ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Fambri, F.; Dumbser, M.; Köppel, S.; Rezzolla, L.; Zanotti, O.

2018-07-01

We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved space-times. In this paper, we assume the background space-time to be given and static, i.e. we make use of the Cowling approximation. The governing partial differential equations are solved via a new family of fully discrete and arbitrary high-order accurate path-conservative discontinuous Galerkin (DG) finite-element methods combined with adaptive mesh refinement and time accurate local time-stepping. In order to deal with shock waves and other discontinuities, the high-order DG schemes are supplemented with a novel a posteriori subcell finite-volume limiter, which makes the new algorithms as robust as classical second-order total-variation diminishing finite-volume methods at shocks and discontinuities, but also as accurate as unlimited high-order DG schemes in smooth regions of the flow. We show the advantages of this new approach by means of various classical two- and three-dimensional benchmark problems on fixed space-times. Finally, we present a performance and accuracy comparisons between Runge-Kutta DG schemes and ADER high-order finite-volume schemes, showing the higher efficiency of DG schemes.

ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Fambri, F.; Dumbser, M.; Köppel, S.; Rezzolla, L.; Zanotti, O.

2018-03-01

We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved spacetimes. In this paper we assume the background spacetime to be given and static, i.e. we make use of the Cowling approximation. The governing partial differential equations are solved via a new family of fully-discrete and arbitrary high-order accurate path-conservative discontinuous Galerkin (DG) finite-element methods combined with adaptive mesh refinement and time accurate local timestepping. In order to deal with shock waves and other discontinuities, the high-order DG schemes are supplemented with a novel a-posteriori subcell finite-volume limiter, which makes the new algorithms as robust as classical second-order total-variation diminishing finite-volume methods at shocks and discontinuities, but also as accurate as unlimited high-order DG schemes in smooth regions of the flow. We show the advantages of this new approach by means of various classical two- and three-dimensional benchmark problems on fixed spacetimes. Finally, we present a performance and accuracy comparisons between Runge-Kutta DG schemes and ADER high-order finite-volume schemes, showing the higher efficiency of DG schemes.

Long-life physical property preservation and postendodontic rehabilitation with the Composipost.

PubMed

Duret, B; Duret, F; Reynaud, M

1996-01-01

Most coronal radicular reconstructions are made of cast inlay core metals or prefabricated posts covered in composite. The differences in the mechanical properties of these elements create a heterogeneous mass with inconsistent mechanical behavior. Studies using the Finite Element Method have shown the biomechanical disturbances caused by the inclusion of materials with a modulus of elasticity that is superior to that of dentine (i.e., nickel, chrome, zircon, etc). The use of materials with a modulus of elasticity close to that of dentine does not disturb the flow of stress inside the root. To our knowledge, only a composite material structured with programmable mechanical properties would be capable of producing both high mechanical performance and a modulus of elasticity adapted to dentine values. The C-POST, made of carbon epoxy, accommodates the demands of the dentine, as well as the in vitro stress linked to the prosthesis. The internal structure, consisting of long high-performance carbon fibers, unidirectionally and equally stretched, confers a totally original behavior that is adapted to clinical objectives. In addition, the C-POST has a fracture resistance superior to most metals.

NASCRIN - NUMERICAL ANALYSIS OF SCRAMJET INLET

NASA Technical Reports Server (NTRS)

Kumar, A.

1994-01-01

The NASCRIN program was developed for analyzing two-dimensional flow fields in supersonic combustion ramjet (scramjet) inlets. NASCRIN solves the two-dimensional Euler or Navier-Stokes equations in conservative form by an unsplit, explicit, two-step finite-difference method. A more recent explicit-implicit, two-step scheme has also been incorporated in the code for viscous flow analysis. An algebraic, two-layer eddy-viscosity model is used for the turbulent flow calculations. NASCRIN can analyze both inviscid and viscous flows with no struts, one strut, or multiple struts embedded in the flow field. NASCRIN can be used in a quasi-three-dimensional sense for some scramjet inlets under certain simplifying assumptions. Although developed for supersonic internal flow, NASCRIN may be adapted to a variety of other flow problems. In particular, it should be readily adaptable to subsonic inflow with supersonic outflow, supersonic inflow with subsonic outflow, or fully subsonic flow. The NASCRIN program is available for batch execution on the CDC CYBER 203. The vectorized FORTRAN version was developed in 1983. NASCRIN has a central memory requirement of approximately 300K words for a grid size of about 3,000 points.

A Analysis of the Low Frequency Sound Field in Non-Rectangular Enclosures Using the Finite Element Method.

NASA Astrophysics Data System (ADS)

Geddes, Earl Russell

The details of the low frequency sound field for a rectangular room can be studied by the use of an established analytic technique--separation of variables. The solution is straightforward and the results are well-known. A non -rectangular room has boundary conditions which are not separable and therefore other solution techniques must be used. This study shows that the finite element method can be adapted for use in the study of sound fields in arbitrary shaped enclosures. The finite element acoustics problem is formulated and the modification of a standard program, which is necessary for solving acoustic field problems, is examined. The solution of the semi-non-rectangular room problem (one where the floor and ceiling remain parallel) is carried out by a combined finite element/separation of variables approach. The solution results are used to construct the Green's function for the low frequency sound field in five rooms (or data cases): (1) a rectangular (Louden) room; (2) The smallest wall of the Louden room canted 20 degrees from normal; (3) The largest wall of the Louden room canted 20 degrees from normal; (4) both the largest and the smallest walls are canted 20 degrees; and (5) a five-sided room variation of Case 4. Case 1, the rectangular room was calculated using both the finite element method and the separation of variables technique. The results for the two methods are compared in order to access the accuracy of the finite element method models. The modal damping coefficient are calculated and the results examined. The statistics of the source and receiver average normalized RMS P('2) responses in the 80 Hz, 100 Hz, and 125 Hz one-third octave bands are developed. The receiver averaged pressure response is developed to determine the effect of the source locations on the response. Twelve source locations are examined and the results tabulated for comparison. The effect of a finite sized source is looked at briefly. Finally, the standard deviation of the spatial pressure response is studied. The results for this characteristic show that it not significantly different in any of the rooms. The conclusions of the study are that only the frequency variations of the pressure response are affected by a room's shape. Further, in general, the simplest modification of a rectangular room (i.e., changing the angle of only one of the smallest walls), produces the most pronounced decrease of the pressure response variations in the low frequency region.

Computing resonant frequency of C-shaped compact microstrip antennas by using ANFIS

NASA Astrophysics Data System (ADS)

Akdagli, Ali; Kayabasi, Ahmet; Develi, Ibrahim

2015-03-01

In this work, the resonant frequency of C-shaped compact microstrip antennas (CCMAs) operating at UHF band is computed by using the adaptive neuro-fuzzy inference system (ANFIS). For this purpose, 144 CCMAs with various relative dielectric constants and different physical dimensions were simulated by the XFDTD software package based on the finite-difference time domain (FDTD) method. One hundred and twenty-nine CCMAs were employed for training, while the remaining 15 CCMAs were used for testing of the ANFIS model. Average percentage error (APE) values were obtained as 0.8413% and 1.259% for training and testing, respectively. In order to demonstrate its validity and accuracy, the proposed ANFIS model was also tested over the simulation data given in the literature, and APE was obtained as 0.916%. These results show that ANFIS can be successfully used to compute the resonant frequency of CCMAs.

Resource Optimization and World Peace. Occasional Paper 30.

ERIC Educational Resources Information Center

Purcell, Arthur H.

A comprehensive, international program is proposed to help nations optimize and conserve natural resources. The aim of the program is to increase the overall supply of natural resources available to improve the chances for world peace. The energy and material resources of the world are finite. We must live with and adapt to the concept of finite…

Modelisation de materiaux composites adaptatifs munis d'actionneurs en alliage a memoire de forme

NASA Astrophysics Data System (ADS)

Simoneau, Charles

Technological development of structures having the capabilities to adapt themselves to different operating conditions is increasing in many areas of research such as aerospace. In fact, numerous works are now oriented toward the design of adaptive aircraft wings where the goal is to enhance the aerodynamic properties of the wing. Following this approach, the work realised in the framework of this master thesis presents the steps leading to the creation of a numerical model that can be used to predict the behavior of an adaptive panel, and therefore, eventually of an adaptive aircraft wing. Foremost, the adaptive panel of this project has been designed from a carbon-epoxy composite, acting as host structure, where shape memory alloy (SMA) wires, acting as actuators, have been inserted in it. SMA actuators have also been embedded asymmetrically along the direction of the panel thickness in order to generate a bending moment when the SMA wires are activated. To achieve the modeling of such structure it has been firstly shown that a numerical model composed of only solid finite elements could be used to represent the panel. However, a second numerical model composed of shell, beam and link finite elements showed that identical results can be obtained with much less nodes (the first model was composed of more than 300 000 nodes compared with 1 000 nodes for the second). The combination of shell-beam-link elements has then been chosen. Secondly, a constitutive relation had to be used for modeling the particular behavior of SMA. For the present work, a uniaxial version of the Likhachev's model is used. Due to its fairly straightforward mathematical formulation, this material law is able to model the main functional properties of SMA including the two-way shape memory effect (TWSME) at zero stress obtained after a thermomechanical education treatment. The last step was to compare the results of the numerical simulations with those obtained with a prototype where 19 actuators were embedded in a composite panel of 425 mm x 425 mm. Various load cases were performed. However, during experimental tests, it has been found that the measured actuator temperature was systematically underestimated. Therefore, by comparing the radius of curvature (rho) of the panel as a function of the activation temperature (T) of the actuators, an offset (in temperature) between the curves numerically and experimentally obtained is observable. Aside from this technological difficulty, the experimental and numerical results are very similar and therefore, this numerical model can be used for predicting the behavior of an adaptive panel. In addition, one the main advantages of this numerical model resides in its versatility where it has been shown that a "warping" of the panel could be realized by controlling independently each actuator. Future works should now obviously focus on the temperature measurement while considering the improvement of the numerical model and the possibility to model an initially curved adaptive panel whose form could resemble an aircraft wing.

Navier-Stokes Solutions for Spin-Up from Rest in a Cylindrical Container

DTIC Science & Technology

1979-09-01

CONDITIONS The calculations employ a finite - difference analog of the unsteady axisyimetric Navier-Stokes equations formulated in cylindrical coordinates...derivatives are approximated by second- order accurate one-sided difference formulae involving three time levels. * The following finite - difference ...equation are identical in form to Equations (13). The finite - difference representations for the ?-equation are: "(i)[aJ~lk " /i’,J-l2k] T (14a) •g I

Advanced composites structural concepts and materials technologies for primary aircraft structures: Structural response and failure analysis

NASA Technical Reports Server (NTRS)

Dorris, William J.; Hairr, John W.; Huang, Jui-Tien; Ingram, J. Edward; Shah, Bharat M.

1992-01-01

Non-linear analysis methods were adapted and incorporated in a finite element based DIAL code. These methods are necessary to evaluate the global response of a stiffened structure under combined in-plane and out-of-plane loading. These methods include the Arc Length method and target point analysis procedure. A new interface material model was implemented that can model elastic-plastic behavior of the bond adhesive. Direct application of this method is in skin/stiffener interface failure assessment. Addition of the AML (angle minus longitudinal or load) failure procedure and Hasin's failure criteria provides added capability in the failure predictions. Interactive Stiffened Panel Analysis modules were developed as interactive pre-and post-processors. Each module provides the means of performing self-initiated finite elements based analysis of primary structures such as a flat or curved stiffened panel; a corrugated flat sandwich panel; and a curved geodesic fuselage panel. This module brings finite element analysis into the design of composite structures without the requirement for the user to know much about the techniques and procedures needed to actually perform a finite element analysis from scratch. An interactive finite element code was developed to predict bolted joint strength considering material and geometrical non-linearity. The developed method conducts an ultimate strength failure analysis using a set of material degradation models.

An Exponential Finite Difference Technique for Solving Partial Differential Equations. M.S. Thesis - Toledo Univ., Ohio

NASA Technical Reports Server (NTRS)

Handschuh, Robert F.

1987-01-01

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that were more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.

exponential finite difference technique for solving partial differential equations

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

Handschuh, R.F.

1987-01-01

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that weremore » more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.« less

Parallel Adaptive Mesh Refinement for High-Order Finite-Volume Schemes in Computational Fluid Dynamics

NASA Astrophysics Data System (ADS)

Schwing, Alan Michael

For computational fluid dynamics, the governing equations are solved on a discretized domain of nodes, faces, and cells. The quality of the grid or mesh can be a driving source for error in the results. While refinement studies can help guide the creation of a mesh, grid quality is largely determined by user expertise and understanding of the flow physics. Adaptive mesh refinement is a technique for enriching the mesh during a simulation based on metrics for error, impact on important parameters, or location of important flow features. This can offload from the user some of the difficult and ambiguous decisions necessary when discretizing the domain. This work explores the implementation of adaptive mesh refinement in an implicit, unstructured, finite-volume solver. Consideration is made for applying modern computational techniques in the presence of hanging nodes and refined cells. The approach is developed to be independent of the flow solver in order to provide a path for augmenting existing codes. It is designed to be applicable for unsteady simulations and refinement and coarsening of the grid does not impact the conservatism of the underlying numerics. The effect on high-order numerical fluxes of fourth- and sixth-order are explored. Provided the criteria for refinement is appropriately selected, solutions obtained using adapted meshes have no additional error when compared to results obtained on traditional, unadapted meshes. In order to leverage large-scale computational resources common today, the methods are parallelized using MPI. Parallel performance is considered for several test problems in order to assess scalability of both adapted and unadapted grids. Dynamic repartitioning of the mesh during refinement is crucial for load balancing an evolving grid. Development of the methods outlined here depend on a dual-memory approach that is described in detail. Validation of the solver developed here against a number of motivating problems shows favorable comparisons across a range of regimes. Unsteady and steady applications are considered in both subsonic and supersonic flows. Inviscid and viscous simulations achieve similar results at a much reduced cost when employing dynamic mesh adaptation. Several techniques for guiding adaptation are compared. Detailed analysis of statistics from the instrumented solver enable understanding of the costs associated with adaptation. Adaptive mesh refinement shows promise for the test cases presented here. It can be considerably faster than using conventional grids and provides accurate results. The procedures for adapting the grid are light-weight enough to not require significant computational time and yield significant reductions in grid size.

3D Gaussian Beam Modeling

DTIC Science & Technology

2011-09-01

optimized building blocks such as a parallelized tri-diagonal linear solver (used in the “implicit finite differences ” and split-step Pade PE models...and Ding Lee. “A finite - difference treatment of interface conditions for the parabolic wave equation: The horizontal interface.” The Journal of the...Acoustical Society of America, 71(4):855, 1982. 3. Ding Lee and Suzanne T. McDaniel. “A finite - difference treatment of interface conditions for

SOME NEW FINITE DIFFERENCE METHODS FOR HELMHOLTZ EQUATIONS ON IRREGULAR DOMAINS OR WITH INTERFACES

PubMed Central

Wan, Xiaohai; Li, Zhilin

2012-01-01

Solving a Helmholtz equation Δu + λu = f efficiently is a challenge for many applications. For example, the core part of many efficient solvers for the incompressible Navier-Stokes equations is to solve one or several Helmholtz equations. In this paper, two new finite difference methods are proposed for solving Helmholtz equations on irregular domains, or with interfaces. For Helmholtz equations on irregular domains, the accuracy of the numerical solution obtained using the existing augmented immersed interface method (AIIM) may deteriorate when the magnitude of λ is large. In our new method, we use a level set function to extend the source term and the PDE to a larger domain before we apply the AIIM. For Helmholtz equations with interfaces, a new maximum principle preserving finite difference method is developed. The new method still uses the standard five-point stencil with modifications of the finite difference scheme at irregular grid points. The resulting coefficient matrix of the linear system of finite difference equations satisfies the sign property of the discrete maximum principle and can be solved efficiently using a multigrid solver. The finite difference method is also extended to handle temporal discretized equations where the solution coefficient λ is inversely proportional to the mesh size. PMID:22701346

SOME NEW FINITE DIFFERENCE METHODS FOR HELMHOLTZ EQUATIONS ON IRREGULAR DOMAINS OR WITH INTERFACES.

PubMed

Wan, Xiaohai; Li, Zhilin

2012-06-01

Solving a Helmholtz equation Δu + λu = f efficiently is a challenge for many applications. For example, the core part of many efficient solvers for the incompressible Navier-Stokes equations is to solve one or several Helmholtz equations. In this paper, two new finite difference methods are proposed for solving Helmholtz equations on irregular domains, or with interfaces. For Helmholtz equations on irregular domains, the accuracy of the numerical solution obtained using the existing augmented immersed interface method (AIIM) may deteriorate when the magnitude of λ is large. In our new method, we use a level set function to extend the source term and the PDE to a larger domain before we apply the AIIM. For Helmholtz equations with interfaces, a new maximum principle preserving finite difference method is developed. The new method still uses the standard five-point stencil with modifications of the finite difference scheme at irregular grid points. The resulting coefficient matrix of the linear system of finite difference equations satisfies the sign property of the discrete maximum principle and can be solved efficiently using a multigrid solver. The finite difference method is also extended to handle temporal discretized equations where the solution coefficient λ is inversely proportional to the mesh size.

A Finite Difference Numerical Model for the Propagation of Finite Amplitude Acoustical Blast Waves Outdoors Over Hard and Porous Surfaces

DTIC Science & Technology

1991-09-01

Difference Numerical Model for the Propagation of Finite Amplitude Acoustical Blast Waves Outdoors Over Hard and Porous Surfaces by Victor W. Sparrow...The nonlinear acoustic propagation effects require a numerical solution in the time domain. To model a porous ground surface, which in the frequency...incident on the hard and porous surfaces were produced. The model predicted that near grazing finite amplitude acoustic blast waves decay with distance

Chemical potential and reaction electronic flux in symmetry controlled reactions.

PubMed

Vogt-Geisse, Stefan; Toro-Labbé, Alejandro

2016-07-15

In symmetry controlled reactions, orbital degeneracies among orbitals of different symmetries can occur along a reaction coordinate. In such case Koopmans' theorem and the finite difference approximation provide a chemical potential profile with nondifferentiable points. This results in an ill-defined reaction electronic flux (REF) profile, since it is defined as the derivative of the chemical potential with respect to the reaction coordinate. To overcome this deficiency, we propose a new way for the calculation of the chemical potential based on a many orbital approach, suitable for reactions in which symmetry is preserved. This new approach gives rise to a new descriptor: symmetry adapted chemical potential (SA-CP), which is the chemical potential corresponding to a given irreducible representation of a symmetry group. A corresponding symmetry adapted reaction electronic flux (SA-REF) is also obtained. Using this approach smooth chemical potential profiles and well defined REFs are achieved. An application of SA-CP and SA-REF is presented by studying the Cs enol-keto tautomerization of thioformic acid. Two SA-REFs are obtained, JA'(ξ) and JA'' (ξ). It is found that the tautomerization proceeds via an in-plane delocalized 3-center 4-electron O-H-S hypervalent bond which is predicted to exist only in the transition state (TS) region. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

A progress report on estuary modeling by the finite-element method

USGS Publications Warehouse

Gray, William G.

1978-01-01

Various schemes are investigated for finite-element modeling of two-dimensional surface-water flows. The first schemes investigated combine finite-element spatial discretization with split-step time stepping schemes that have been found useful in finite-difference computations. Because of the large number of numerical integrations performed in space and the large sparse matrices solved, these finite-element schemes were found to be economically uncompetitive with finite-difference schemes. A very promising leapfrog scheme is proposed which, when combined with a novel very fast spatial integration procedure, eliminates the need to solve any matrices at all. Additional problems attacked included proper propagation of waves and proper specification of the normal flow-boundary condition. This report indicates work in progress and does not come to a definitive conclusion as to the best approach for finite-element modeling of surface-water problems. The results presented represent findings obtained between September 1973 and July 1976. (Woodard-USGS)

An adaptation method to improve secret key rates of time-frequency QKD in atmospheric turbulence channels

NASA Astrophysics Data System (ADS)

Sun, Xiaole; Djordjevic, Ivan B.; Neifeld, Mark A.

2016-03-01

Free-space optical (FSO) channels can be characterized by random power fluctuations due to atmospheric turbulence, which is known as scintillation. Weak coherent source based FSO quantum key distribution (QKD) systems suffer from the scintillation effect because during the deep channel fading the expected detection rate drops, which then gives an eavesdropper opportunity to get additional information about protocol by performing photon number splitting (PNS) attack and blocking single-photon pulses without changing QBER. To overcome this problem, in this paper, we study a large-alphabet QKD protocol, which is achieved by using pulse-position modulation (PPM)-like approach that utilizes the time-frequency uncertainty relation of the weak coherent photon state, called here TF-PPM-QKD protocol. We first complete finite size analysis for TF-PPM-QKD protocol to give practical bounds against non-negligible statistical fluctuation due to finite resources in practical implementations. The impact of scintillation under strong atmospheric turbulence regime is studied then. To overcome the secure key rate performance degradation of TF-PPM-QKD caused by scintillation, we propose an adaptation method for compensating the scintillation impact. By changing source intensity according to the channel state information (CSI), obtained by classical channel, the adaptation method improves the performance of QKD system with respect to the secret key rate. The CSI of a time-varying channel can be predicted using stochastic models, such as autoregressive (AR) models. Based on the channel state predictions, we change the source intensity to the optimal value to achieve a higher secret key rate. We demonstrate that the improvement of the adaptation method is dependent on the prediction accuracy.

Effects of adaptive refinement on the inverse EEG solution

NASA Astrophysics Data System (ADS)

Weinstein, David M.; Johnson, Christopher R.; Schmidt, John A.

1995-10-01

One of the fundamental problems in electroencephalography can be characterized by an inverse problem. Given a subset of electrostatic potentials measured on the surface of the scalp and the geometry and conductivity properties within the head, calculate the current vectors and potential fields within the cerebrum. Mathematically the generalized EEG problem can be stated as solving Poisson's equation of electrical conduction for the primary current sources. The resulting problem is mathematically ill-posed i.e., the solution does not depend continuously on the data, such that small errors in the measurement of the voltages on the scalp can yield unbounded errors in the solution, and, for the general treatment of a solution of Poisson's equation, the solution is non-unique. However, if accurate solutions the general treatment of a solution of Poisson's equation, the solution is non-unique. However, if accurate solutions to such problems could be obtained, neurologists would gain noninvasive accesss to patient-specific cortical activity. Access to such data would ultimately increase the number of patients who could be effectively treated for pathological cortical conditions such as temporal lobe epilepsy. In this paper, we present the effects of spatial adaptive refinement on the inverse EEG problem and show that the use of adaptive methods allow for significantly better estimates of electric and potential fileds within the brain through an inverse procedure. To test these methods, we have constructed several finite element head models from magneteic resonance images of a patient. The finite element meshes ranged in size from 2724 nodes and 12,812 elements to 5224 nodes and 29,135 tetrahedral elements, depending on the level of discretization. We show that an adaptive meshing algorithm minimizes the error in the forward problem due to spatial discretization and thus increases the accuracy of the inverse solution.

Asymptotic analysis of numerical wave propagation in finite difference equations

NASA Technical Reports Server (NTRS)

Giles, M.; Thompkins, W. T., Jr.

1983-01-01

An asymptotic technique is developed for analyzing the propagation and dissipation of wave-like solutions to finite difference equations. It is shown that for each fixed complex frequency there are usually several wave solutions with different wavenumbers and the slowly varying amplitude of each satisfies an asymptotic amplitude equation which includes the effects of smoothly varying coefficients in the finite difference equations. The local group velocity appears in this equation as the velocity of convection of the amplitude. Asymptotic boundary conditions coupling the amplitudes of the different wave solutions are also derived. A wavepacket theory is developed which predicts the motion, and interaction at boundaries, of wavepackets, wave-like disturbances of finite length. Comparison with numerical experiments demonstrates the success and limitations of the theory. Finally an asymptotic global stability analysis is developed.

Connecting mechanics and bone cell activities in the bone remodeling process: an integrated finite element modeling.

PubMed

Hambli, Ridha

2014-01-01

Bone adaptation occurs as a response to external loadings and involves bone resorption by osteoclasts followed by the formation of new bone by osteoblasts. It is directly triggered by the transduction phase by osteocytes embedded within the bone matrix. The bone remodeling process is governed by the interactions between osteoblasts and osteoclasts through the expression of several autocrine and paracrine factors that control bone cell populations and their relative rate of differentiation and proliferation. A review of the literature shows that despite the progress in bone remodeling simulation using the finite element (FE) method, there is still a lack of predictive models that explicitly consider the interaction between osteoblasts and osteoclasts combined with the mechanical response of bone. The current study attempts to develop an FE model to describe the bone remodeling process, taking into consideration the activities of osteoclasts and osteoblasts. The mechanical behavior of bone is described by taking into account the bone material fatigue damage accumulation and mineralization. A coupled strain-damage stimulus function is proposed, which controls the level of autocrine and paracrine factors. The cellular behavior is based on Komarova et al.'s (2003) dynamic law, which describes the autocrine and paracrine interactions between osteoblasts and osteoclasts and computes cell population dynamics and changes in bone mass at a discrete site of bone remodeling. Therefore, when an external mechanical stress is applied, bone formation and resorption is governed by cells dynamic rather than adaptive elasticity approaches. The proposed FE model has been implemented in the FE code Abaqus (UMAT routine). An example of human proximal femur is investigated using the model developed. The model was able to predict final human proximal femur adaptation similar to the patterns observed in a human proximal femur. The results obtained reveal complex spatio-temporal bone adaptation. The proposed FEM model gives insight into how bone cells adapt their architecture to the mechanical and biological environment.

Mixed finite-difference scheme for analysis of simply supported thick plates.

NASA Technical Reports Server (NTRS)

Noor, A. K.

1973-01-01

A mixed finite-difference scheme is presented for the stress and free vibration analysis of simply supported nonhomogeneous and layered orthotropic thick plates. The analytical formulation is based on the linear, three-dimensional theory of orthotropic elasticity and a Fourier approach is used to reduce the governing equations to six first-order ordinary differential equations in the thickness coordinate. The governing equations possess a symmetric coefficient matrix and are free of derivatives of the elastic characteristics of the plate. In the finite difference discretization two interlacing grids are used for the different fundamental unknowns in such a way as to reduce both the local discretization error and the bandwidth of the resulting finite-difference field equations. Numerical studies are presented for the effects of reducing the interior and boundary discretization errors and of mesh refinement on the accuracy and convergence of solutions. It is shown that the proposed scheme, in addition to a number of other advantages, leads to highly accurate results, even when a small number of finite difference intervals is used.

The maintenance of sex: Ronald Fisher meets the Red Queen.

PubMed

Green, David; Mason, Chris

2013-08-21

Sex in higher diploids carries a two-fold cost of males that should reduce its fitness relative to cloning, and result in its extinction. Instead, sex is widespread and clonal species face early obsolescence. One possible reason is that sex is an adaptation that allows organisms to respond more effectively to endless changes in their environment. The purpose of this study was to model mutation and selection in a diploid organism in an evolving environment and ascertain their support for sex. We used a computational approach to model finite populations where a haploid environment subjects a diploid host to endlessly evolving change. Evolution in both populations is primarily through adoption of novel advantageous mutations within a large allele space. Sex outcompetes cloning by two complementary mechanisms. First, sexual diploids adopt advantageous homozygous mutations more rapidly than clonal ones under conditions of lag load (the gap between the actual adaptation of the diploid population and its theoretical optimum). This rate advantage can offset the higher fecundity of cloning. Second, a relative advantage to sex emerges where populations are significantly polymorphic, because clonal polymorphism runs the risk of clonal interference caused by selection on numerous lines of similar adaptation. This interference extends allele lifetime and reduces the rate of adaptation. Sex abolishes the interference, making selection faster and elevating population fitness. Differences in adaptation between sexual and clonal populations increase markedly with the number of loci under selection, the rate of mutation in the host, and a rapidly evolving environment. Clonal interference in these circumstances leads to conditions where the greater fecundity of clones is unable to offset their poor adaptation. Sexual and clonal populations then either co-exist, or sex emerges as the more stable evolutionary strategy. Sex can out-compete clones in a rapidly evolving environment, such as that characterized by pathogens, where clonal interference reduces the adaptation of clonal populations and clones adopt advantageous mutations more slowly. Since all organisms carry parasitic loads, the model is of potentially general applicability.

Hierarchical Strategy for Rapid Analysis Environment

NASA Technical Reports Server (NTRS)

Whitcomb, John

2003-01-01

A new philosophy is developed wherein the hierarchical definition of data is made use of in creating a better environment to conduct analyses of practical problems. This system can be adapted to conduct virtually any type of analysis, since this philosophy is not bound to any specific kind of analysis. It provides a framework to manage different models and its results and more importantly, the interaction between the different models. Thus, it is ideal for many types of finite element analyses like globalAoca1 analysis and those that involve multiple scales and fields. The system developed during the course of this work is just a demonstrator of the basic concepts. A complete implementation of this strategy could potentially make a major impact on the way analyses are conducted. It could considerably reduce the time frame required to conduct the analysis of real-life problems by efficient management of the data involved and reducing the human effort involved. It also helps in better decision making because of more ways to interpret the results. The strategy has been currently implemented for structural analysis, but with more work it could be extended to other fields of science when the finite element method is used to solve the differential equations numerically. This report details the work that has been done during the course of this project and its achievements and results. The following section discusses the meaning of the word hierarchical and the different references to the term in the literature. It talks about the development of the finite element method, its different versions and how hierarchy has been used to improve the methodology. The next section describes the hierarchical philosophy in detail and explains the different concepts and terms associated with it. It goes on to describe the implementation and the features of the demonstrator. A couple of problems are analyzed using the demonstrator program to show the working of the system. The two problems considered are two dimensional plane stress analysis problems. The results are compared with those obtained using conventional analysis. The different challenges faced during the development of this system are discussed. Finally, we conclude with suggestions for future work to add more features and extend it to a wider range of problems.

An artificial neural network model for periodic trajectory generation

NASA Astrophysics Data System (ADS)

Shankar, S.; Gander, R. E.; Wood, H. C.

A neural network model based on biological systems was developed for potential robotic application. The model consists of three interconnected layers of artificial neurons or units: an input layer subdivided into state and plan units, an output layer, and a hidden layer between the two outer layers which serves to implement nonlinear mappings between the input and output activation vectors. Weighted connections are created between the three layers, and learning is effected by modifying these weights. Feedback connections between the output and the input state serve to make the network operate as a finite state machine. The activation vector of the plan units of the input layer emulates the supraspinal commands in biological central pattern generators in that different plan activation vectors correspond to different sequences or trajectories being recalled, even with different frequencies. Three trajectories were chosen for implementation, and learning was accomplished in 10,000 trials. The fault tolerant behavior, adaptiveness, and phase maintenance of the implemented network are discussed.

Adaptively biased sequential importance sampling for rare events in reaction networks with comparison to exact solutions from finite buffer dCME method

PubMed Central

Cao, Youfang; Liang, Jie

2013-01-01

Critical events that occur rarely in biological processes are of great importance, but are challenging to study using Monte Carlo simulation. By introducing biases to reaction selection and reaction rates, weighted stochastic simulation algorithms based on importance sampling allow rare events to be sampled more effectively. However, existing methods do not address the important issue of barrier crossing, which often arises from multistable networks and systems with complex probability landscape. In addition, the proliferation of parameters and the associated computing cost pose significant problems. Here we introduce a general theoretical framework for obtaining optimized biases in sampling individual reactions for estimating probabilities of rare events. We further describe a practical algorithm called adaptively biased sequential importance sampling (ABSIS) method for efficient probability estimation. By adopting a look-ahead strategy and by enumerating short paths from the current state, we estimate the reaction-specific and state-specific forward and backward moving probabilities of the system, which are then used to bias reaction selections. The ABSIS algorithm can automatically detect barrier-crossing regions, and can adjust bias adaptively at different steps of the sampling process, with bias determined by the outcome of exhaustively generated short paths. In addition, there are only two bias parameters to be determined, regardless of the number of the reactions and the complexity of the network. We have applied the ABSIS method to four biochemical networks: the birth-death process, the reversible isomerization, the bistable Schlögl model, and the enzymatic futile cycle model. For comparison, we have also applied the finite buffer discrete chemical master equation (dCME) method recently developed to obtain exact numerical solutions of the underlying discrete chemical master equations of these problems. This allows us to assess sampling results objectively by comparing simulation results with true answers. Overall, ABSIS can accurately and efficiently estimate rare event probabilities for all examples, often with smaller variance than other importance sampling algorithms. The ABSIS method is general and can be applied to study rare events of other stochastic networks with complex probability landscape. PMID:23862966

Adaptively biased sequential importance sampling for rare events in reaction networks with comparison to exact solutions from finite buffer dCME method

NASA Astrophysics Data System (ADS)

Cao, Youfang; Liang, Jie

2013-07-01

Critical events that occur rarely in biological processes are of great importance, but are challenging to study using Monte Carlo simulation. By introducing biases to reaction selection and reaction rates, weighted stochastic simulation algorithms based on importance sampling allow rare events to be sampled more effectively. However, existing methods do not address the important issue of barrier crossing, which often arises from multistable networks and systems with complex probability landscape. In addition, the proliferation of parameters and the associated computing cost pose significant problems. Here we introduce a general theoretical framework for obtaining optimized biases in sampling individual reactions for estimating probabilities of rare events. We further describe a practical algorithm called adaptively biased sequential importance sampling (ABSIS) method for efficient probability estimation. By adopting a look-ahead strategy and by enumerating short paths from the current state, we estimate the reaction-specific and state-specific forward and backward moving probabilities of the system, which are then used to bias reaction selections. The ABSIS algorithm can automatically detect barrier-crossing regions, and can adjust bias adaptively at different steps of the sampling process, with bias determined by the outcome of exhaustively generated short paths. In addition, there are only two bias parameters to be determined, regardless of the number of the reactions and the complexity of the network. We have applied the ABSIS method to four biochemical networks: the birth-death process, the reversible isomerization, the bistable Schlögl model, and the enzymatic futile cycle model. For comparison, we have also applied the finite buffer discrete chemical master equation (dCME) method recently developed to obtain exact numerical solutions of the underlying discrete chemical master equations of these problems. This allows us to assess sampling results objectively by comparing simulation results with true answers. Overall, ABSIS can accurately and efficiently estimate rare event probabilities for all examples, often with smaller variance than other importance sampling algorithms. The ABSIS method is general and can be applied to study rare events of other stochastic networks with complex probability landscape.

Adaptively biased sequential importance sampling for rare events in reaction networks with comparison to exact solutions from finite buffer dCME method.

PubMed

Cao, Youfang; Liang, Jie

2013-07-14

Critical events that occur rarely in biological processes are of great importance, but are challenging to study using Monte Carlo simulation. By introducing biases to reaction selection and reaction rates, weighted stochastic simulation algorithms based on importance sampling allow rare events to be sampled more effectively. However, existing methods do not address the important issue of barrier crossing, which often arises from multistable networks and systems with complex probability landscape. In addition, the proliferation of parameters and the associated computing cost pose significant problems. Here we introduce a general theoretical framework for obtaining optimized biases in sampling individual reactions for estimating probabilities of rare events. We further describe a practical algorithm called adaptively biased sequential importance sampling (ABSIS) method for efficient probability estimation. By adopting a look-ahead strategy and by enumerating short paths from the current state, we estimate the reaction-specific and state-specific forward and backward moving probabilities of the system, which are then used to bias reaction selections. The ABSIS algorithm can automatically detect barrier-crossing regions, and can adjust bias adaptively at different steps of the sampling process, with bias determined by the outcome of exhaustively generated short paths. In addition, there are only two bias parameters to be determined, regardless of the number of the reactions and the complexity of the network. We have applied the ABSIS method to four biochemical networks: the birth-death process, the reversible isomerization, the bistable Schlögl model, and the enzymatic futile cycle model. For comparison, we have also applied the finite buffer discrete chemical master equation (dCME) method recently developed to obtain exact numerical solutions of the underlying discrete chemical master equations of these problems. This allows us to assess sampling results objectively by comparing simulation results with true answers. Overall, ABSIS can accurately and efficiently estimate rare event probabilities for all examples, often with smaller variance than other importance sampling algorithms. The ABSIS method is general and can be applied to study rare events of other stochastic networks with complex probability landscape.

An Adaptive MR-CT Registration Method for MRI-guided Prostate Cancer Radiotherapy

PubMed Central

Zhong, Hualiang; Wen, Ning; Gordon, James; Elshaikh, Mohamed A; Movsas, Benjamin; Chetty, Indrin J.

2015-01-01

Magnetic Resonance images (MRI) have superior soft tissue contrast compared with CT images. Therefore, MRI might be a better imaging modality to differentiate the prostate from surrounding normal organs. Methods to accurately register MRI to simulation CT images are essential, as we transition the use of MRI into the routine clinic setting. In this study, we present a finite element method (FEM) to improve the performance of a commercially available, B-spline-based registration algorithm in the prostate region. Specifically, prostate contours were delineated independently on ten MRI and CT images using the Eclipse treatment planning system. Each pair of MRI and CT images was registered with the B-spline-based algorithm implemented in the VelocityAI system. A bounding box that contains the prostate volume in the CT image was selected and partitioned into a tetrahedral mesh. An adaptive finite element method was then developed to adjust the displacement vector fields (DVFs) of the B-spline-based registrations within the box. The B-spline and FEM-based registrations were evaluated based on the variations of prostate volume and tumor centroid, the unbalanced energy of the generated DVFs, and the clarity of the reconstructed anatomical structures. The results showed that the volumes of the prostate contours warped with the B-spline-based DVFs changed 10.2% on average, relative to the volumes of the prostate contours on the original MR images. This discrepancy was reduced to 1.5% for the FEM-based DVFs. The average unbalanced energy was 2.65 and 0.38 mJ/cm3, and the prostate centroid deviation was 0.37 and 0.28 cm, for the B-spline and FEM-based registrations, respectively. Different from the B-spline-warped MR images, the FEM-warped MR images have clear boundaries between prostates and bladders, and their internal prostatic structures are consistent with those of the original MR images. In summary, the developed adaptive FEM method preserves the prostate volume during the transformation between the MR and CT images and improves the accuracy of the B-spline registrations in the prostate region. The approach will be valuable for development of high-quality MRI-guided radiation therapy. PMID:25775937

An adaptive MR-CT registration method for MRI-guided prostate cancer radiotherapy

NASA Astrophysics Data System (ADS)

Zhong, Hualiang; Wen, Ning; Gordon, James J.; Elshaikh, Mohamed A.; Movsas, Benjamin; Chetty, Indrin J.

2015-04-01

Magnetic Resonance images (MRI) have superior soft tissue contrast compared with CT images. Therefore, MRI might be a better imaging modality to differentiate the prostate from surrounding normal organs. Methods to accurately register MRI to simulation CT images are essential, as we transition the use of MRI into the routine clinic setting. In this study, we present a finite element method (FEM) to improve the performance of a commercially available, B-spline-based registration algorithm in the prostate region. Specifically, prostate contours were delineated independently on ten MRI and CT images using the Eclipse treatment planning system. Each pair of MRI and CT images was registered with the B-spline-based algorithm implemented in the VelocityAI system. A bounding box that contains the prostate volume in the CT image was selected and partitioned into a tetrahedral mesh. An adaptive finite element method was then developed to adjust the displacement vector fields (DVFs) of the B-spline-based registrations within the box. The B-spline and FEM-based registrations were evaluated based on the variations of prostate volume and tumor centroid, the unbalanced energy of the generated DVFs, and the clarity of the reconstructed anatomical structures. The results showed that the volumes of the prostate contours warped with the B-spline-based DVFs changed 10.2% on average, relative to the volumes of the prostate contours on the original MR images. This discrepancy was reduced to 1.5% for the FEM-based DVFs. The average unbalanced energy was 2.65 and 0.38 mJ cm-3, and the prostate centroid deviation was 0.37 and 0.28 cm, for the B-spline and FEM-based registrations, respectively. Different from the B-spline-warped MR images, the FEM-warped MR images have clear boundaries between prostates and bladders, and their internal prostatic structures are consistent with those of the original MR images. In summary, the developed adaptive FEM method preserves the prostate volume during the transformation between the MR and CT images and improves the accuracy of the B-spline registrations in the prostate region. The approach will be valuable for the development of high-quality MRI-guided radiation therapy.

Exact finite difference schemes for the non-linear unidirectional wave equation

NASA Technical Reports Server (NTRS)

Mickens, R. E.

1985-01-01

Attention is given to the construction of exact finite difference schemes for the nonlinear unidirectional wave equation that describes the nonlinear propagation of a wave motion in the positive x-direction. The schemes constructed for these equations are compared with those obtained by using the usual procedures of numerical analysis. It is noted that the order of the exact finite difference models is equal to the order of the differential equation.

Application of finite element approach to transonic flow problems

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Murman, E. M.; Wellford, L. C., Jr.

1976-01-01

A variational finite element model for transonic small disturbance calculations is described. Different strategy is adopted in subsonic and supersonic regions, and blending elements are introduced between different regions. In the supersonic region, no upstream effect is allowed. If rectangular elements with linear shape functions are used, the model is similar to Murman's finite difference operators. Higher order shape functions, nonrectangular elements, and discontinuous approximation of shock waves are also discussed.

A finite element code for modelling tracer transport in a non-isothermal two-phase flow system for CO2 geological storage characterization

NASA Astrophysics Data System (ADS)

Tong, F.; Niemi, A. P.; Yang, Z.; Fagerlund, F.; Licha, T.; Sauter, M.

2011-12-01

This paper presents a new finite element method (FEM) code for modeling tracer transport in a non-isothermal two-phase flow system. The main intended application is simulation of the movement of so-called novel tracers for the purpose of characterization of geologically stored CO2 and its phase partitioning and migration in deep saline formations. The governing equations are based on the conservation of mass and energy. Among the phenomena accounted for are liquid-phase flow, gas flow, heat transport and the movement of the novel tracers. The movement of tracers includes diffusion and the advection associated with the gas and liquid flow. The temperature, gas pressure, suction, concentration of tracer in liquid phase and concentration of tracer in gas phase are chosen as the five primary variables. Parameters such as the density, viscosity, thermal expansion coefficient are expressed in terms of the primary variables. The governing equations are discretized in space using the Galerkin finite element formulation, and are discretized in time by one-dimensional finite difference scheme. This leads to an ill-conditioned FEM equation that has many small entries along the diagonal of the non-symmetric coefficient matrix. In order to deal with the problem of non-symmetric ill-conditioned matrix equation, special techniques are introduced . Firstly, only nonzero elements of the matrix need to be stored. Secondly, it is avoided to directly solve the whole large matrix. Thirdly, a strategy has been used to keep the diversity of solution methods in the calculation process. Additionally, an efficient adaptive mesh technique is included in the code in order to track the wetting front. The code has been validated against several classical analytical solutions, and will be applied for simulating the CO2 injection experiment to be carried out at the Heletz site, Israel, as part of the EU FP7 project MUSTANG.

Prediction of oxygen distribution in aortic valve leaflet considering diffusion and convection.

PubMed

Wang, Ling; Korossis, Sotirios; Fisher, John; Ingham, Eileen; Jin, Zhongmin

2011-07-01

Oxygen supply and transport is an important consideration in the development of tissue engineered constructs. Previous studies from our group have focused on the effect of tissue thickness on the oxygen diffusion within a three-dimensional aortic valve leaflet model, and highlighted the necessity for additional transport mechanisms such as oxygen convection. The aims of this study were to investigate the effect of interstitial fluid flow within the aortic valve leaflet, induced by the cyclic loading of the leaflet, on oxygen transport. Indentation testing and finite element modelings were employed to derive the biphasic properties of the leaflet tissue. The biphasic properties were subsequently used in the computational modeling of oxygen convection in the leaflet, which was based on the effective interstitial fluid velocity and the tissue deformation. Subsequently, the oxygen profile was predicted within the valve leaflet model by solving the diffusion and convection equation simultaneously utilizing the finite difference method. The compression modulus (E) and hydraulic permeability were determined by adapting a finite element model to the experimental indentation test on valvular tissue, E = 0.05MPa, and k =2.0 mm4/Ns. Finite element model of oxygen convection in valvular tissue incorporating the predicted biphasic properties was developed and the interstitial fluid flow rate was calculated falling in range of 0.025-0.25 mm/s depending on the tissue depth. Oxygen distribution within valvular tissue was predicted using one-dimensional oxygen diffusion model taking into consider the interstitial fluid effect. It was found that convection did enhance the oxygen transport in valvular tissue by up to 68% increase in the minimum oxygen tension within the tissue, depending on the strain level of the tissue as reaction of the magnitude and frequencies of the cardiac loading. The effective interstitial fluid velocity was found to play an important role in enhancing the oxygen transport within the valve leaflet. Such an understanding is important in the development of valvular tissue engineered constructs.

Exploring the biomechanics of taurodontism.

PubMed

Benazzi, Stefano; Nguyen, Huynh N; Kullmer, Ottmar; Hublin, Jean-Jacques

2015-02-01

Taurodontism (i.e. enlarged pulp chamber with concomitant apical displacement of the root bi/trifurcation) is considered a dental anomaly with relatively low incidence in contemporary societies, but it represents a typical trait frequently found in Neandertal teeth. Four hypotheses can be envisioned to explain the high frequency in Neandertals: adaptation to a specific occlusal loading regime (biomechanical advantage), adaptation to a high attrition diet, pleiotropic or genetic drift effects. In this contribution we used finite element analysis (FEA) and advanced loading concepts based on macrowear information to evaluate whether taurodontism supplies some dental biomechanical advantages. Loads were applied to the digital model of the lower right first molar (RM1 ) of the Neandertal specimen Le Moustier 1, as well as to the digital models of both a shortened and a hyper-taurodontic version of Le Moustier RM1 . Moreover, we simulated a scenario where an object is held between teeth and pulled in different directions to investigate whether taurodontism might be useful for para-masticatory activities. Our results do not show any meaningful difference among all the simulations, pointing out that taurodontism does not improve the functional biomechanics of the tooth and does not favour para-masticatory pulling activities. Therefore, taurodontism should be considered either an adaptation to a high attrition diet or most likely the result of pleiotropic or genetic drift effects. Finally, our results have important implications for modern dentistry during endodontic treatments, as we observed that filling the pulp chamber with dentine-like material increases tooth stiffness, and ultimately tensile stresses in the crown, thus favouring tooth failure. © 2014 Anatomical Society.

Finite-Size Scaling of a First-Order Dynamical Phase Transition: Adaptive Population Dynamics and an Effective Model

NASA Astrophysics Data System (ADS)

Nemoto, Takahiro; Jack, Robert L.; Lecomte, Vivien

2017-03-01

We analyze large deviations of the time-averaged activity in the one-dimensional Fredrickson-Andersen model, both numerically and analytically. The model exhibits a dynamical phase transition, which appears as a singularity in the large deviation function. We analyze the finite-size scaling of this phase transition numerically, by generalizing an existing cloning algorithm to include a multicanonical feedback control: this significantly improves the computational efficiency. Motivated by these numerical results, we formulate an effective theory for the model in the vicinity of the phase transition, which accounts quantitatively for the observed behavior. We discuss potential applications of the numerical method and the effective theory in a range of more general contexts.

NOTE: Solving the ECG forward problem by means of a meshless finite element method

NASA Astrophysics Data System (ADS)

Li, Z. S.; Zhu, S. A.; He, Bin

2007-07-01

The conventional numerical computational techniques such as the finite element method (FEM) and the boundary element method (BEM) require laborious and time-consuming model meshing. The new meshless FEM only uses the boundary description and the node distribution and no meshing of the model is required. This paper presents the fundamentals and implementation of meshless FEM and the meshless FEM method is adapted to solve the electrocardiography (ECG) forward problem. The method is evaluated on a single-layer torso model, in which the analytical solution exists, and tested in a realistic geometry homogeneous torso model, with satisfactory results being obtained. The present results suggest that the meshless FEM may provide an alternative for ECG forward solutions.

Design of High Field Solenoids made of High Temperature Superconductors

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

Bartalesi, Antonio; /Pisa U.

2010-12-01

This thesis starts from the analytical mechanical analysis of a superconducting solenoid, loaded by self generated Lorentz forces. Also, a finite element model is proposed and verified with the analytical results. To study the anisotropic behavior of a coil made by layers of superconductor and insulation, a finite element meso-mechanic model is proposed and designed. The resulting material properties are then used in the main solenoid analysis. In parallel, design work is performed as well: an existing Insert Test Facility (ITF) is adapted and structurally verified to support a coil made of YBa{sub 2}Cu{sub 3}O{sub 7}, a High Temperature Superconductormore » (HTS). Finally, a technological winding process was proposed and the required tooling is designed.« less

IPS-Empress II inlay-retained fixed partial denture reinforced with zirconia bar: three-dimensional finite element and in-vitro studies.

PubMed

Kermanshah, Hamid; Geramy, Allahyar; Ebrahimi, Shahram Farzin; Bitaraf, Tahereh

2012-12-01

This study evaluated von Mises stress distribution, flexural strength and interface micrographs of IPS-Empress II (IPS) inlay-retained fixed partial dentures (IRFPD) reinforced with Zirconia bars (Zb). In the Finite element analysis, six three-dimensional models of IRFPD were designed using Solid Works 2006. Five models were reinforced with different Zb and a model without Zb was considered as a control. The bridges were loaded by 200 and 500 N forces at the middle of the pontic on the occlusal surface. Subsequently, von Mises stress and displacement of the models were evaluated along a defined path. In the experimental part, 21 bar shape specimens were fabricated from lithium disilicate and zirconia ceramic in three different designs. The zirconia-IPS interfaces and the fractured surfaces of flexural test were observed using SEM. In the connector area, von Mises stress and displacement of the models with Zb under a load of 500 N were decreased compared to the model without the Zb; however, this difference was not considerable at a load of 200 N. In the mesial connector, Von Mises stress and displacement was decreased from 12.5 Mpa for the control model tested at 500 N to 7.0 Mpa for the model with Zb and from 0.0050-0.0041 mm, respectively. SEM analyses showed that, before fracture, interfacial gaps were not observed along the interfaces, but initiated cracks propagated along the interfaces after flexural loading. IPS IRFPD reinforced by Zb can tolerate higher stresses while still functioning effectively and the interfaces may have desirable adaption.

The Malthusian-Darwinian dynamic and the trajectory of civilization

USGS Publications Warehouse

Nekola, Jeffrey C.; Allen, Craig D.; Brown, James H.; Burger, Joseph R.; Davidson, Ana D.; Fristoe, Trevor S.; Hamilton, Marcus J.; Hammond, Sean T.; Kodric-Brown, Astrid; Mercado-Silva, Norman; Okie, Jordan G.

2013-01-01

Two interacting forces influence all populations: the Malthusian dynamic of exponential growth until resource limits are reached, and the Darwinian dynamic of innovation and adaptation to circumvent these limits through biological and/or cultural evolution. The specific manifestations of these forces in modern human society provide an important context for determining how humans can establish a sustainable relationship with the finite Earth.