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Nonlinear Multiplicative Schwarz Preconditioning in Natural Convection Cavity Flow 23rd

Nonlinear Multiplicative Schwarz Preconditioning in Natural ...

引用

23rd International Conference on Domain Decomposition Methods

作者： Liu, Lulu Zhang, Wei Keyes, David E. USI Inst Computat Sci CH-6900 Lugano Switzerland KAUST Program Mech Engn Thuwal 239556900 Saudi Arabia KAUST Program Appl Math & Computat Sci Thuwal 239556900 Saudi Arabia KAUST Extreme Comp Res Ctr Thuwal 239556900 Saudi Arabia

ISBN: (纸本)9783319523897;9783319523880

A natural convection cavity flow problem is solved using nonlinear multiplicative Schwarz preconditioners, as a Gauss-Seidel-like variant of additive Schwarz preconditioned inexact Newton (ASPIN). The nonlinear preconditioning extends the domain of convergence of Newton’s method to high Rayleigh numbers. Convergence performance varies widely with respect to different groupings of the fields of this multicomponent problem, and with respect to different orderings of the groupings. © Springer International Publishing AG 2017.

关键词： Natural convection

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Development of Nonlinear Structural Analysis Using Co-rotational Finite Elements with Improved Domain Decomposition Method 23rd

Development of Nonlinear Structural Analysis Using Co-rotati...

引用

23rd International Conference on Domain Decomposition Methods

作者： Cho, Haeseong Kwak, JunYoung Joo, Hyunshig Shin, SangJoon Seoul Natl Univ Dept Mech & Aerosp Engn Seoul South Korea Korea Aerosp Res Inst Rocket Engine Team Daejeon South Korea Seoul Natl Univ Inst Adv Aerosp Technol Dept Mech & Aerosp Engn Seoul South Korea

ISBN: (纸本)9783319523897;9783319523880

Recent advances in computational science and technologies induce increasing size of the engineering problems, and impact the fields of computational fluids and structural dynamics as well as multi-physics problems, such as fluid-structure interactions. At the same time, structural components used in many engineering applications show geometrically nonlinear characteristics. Therefore, development of effective solution methodologies for large-size nonlinear structural problems is required seriously in the fields of the mechanical and aerospace engineering. Especially, general finite element methods require a large number of elements in order to predict precise stress or deformation, resulting in increased computational costs due to enlarged computational time and memory requirement. Therefore, careful selection of grid size and solution methodology becomes important. © Springer International Publishing AG 2017.

关键词： Domain decomposition methods

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New Nonlinear FETI-DP Methods Based on a Partial Nonlinear Elimination of Variables 23rd

New Nonlinear FETI-DP Methods Based on a Partial Nonlinear E...

引用

23rd International Conference on Domain Decomposition Methods

作者： Klawonn, Axel Lanser, Martin Rheinbach, Oliver Uran, Matthias Univ Cologne Math Inst Weyertal 86-90 D-50931 Cologne Germany Tech Univ Bergakad Freiberg Inst Numer Math & Optimierung Fak Math & Informat Akad Str 6 D-09596 Freiberg Germany

ISBN: (纸本)9783319523897;9783319523880

We introduce two new nonlinear FETI-DP (Finite Element Tearing and Interconnecting-Dual-Primal) methods based on a partial nonlinear elimination of variables and provide a comparison to Newton-Krylov-FETI-DP, Nonlinear-FETI-DP-1, and Nonlinear-FETI-DP-2, which have already been described earlier. In contrast to classical Newton-Krylov-FETI-DP methods, where a geometrical decomposition after a Newton linearization is performed, in nonlinear FETI-DP methods, the discretized nonlinear problem is decomposed before linearization. The approaches helps to localize work and reduce communication and thus are better suited for modern computer architectures. © Springer International Publishing AG 2017.

关键词： Linearization

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Improved Coefficients for Polynomial Filtering in ESSEX 1

引用

2nd International Workshop on Eigenvalue Problems - Algorithms, Software and Applications in Petascale Computing (EPASA)

作者： Galgon, Martin Kraemer, Lukas Lang, Bruno Alvermann, Andreas Fehske, Holger Pieper, Andreas Hager, Georg Kreutzer, Moritz Shahzad, Faisal Wellein, Gerhard Basermann, Achim Roehrig-Zoellner, Melven Thies, Jonas Univ Wuppertal Sch Math & Nat Sci Wuppertal Germany Univ Greifswald Inst Phys Greifswald Germany Erlangen Reg Comp Ctr Erlangen Germany German Aerosp Ctr DLR Simulat & Software Technol Cologne Germany

ISBN: (数字)9783319624266

ISBN: (纸本)9783319624266;9783319624242

The ESSEX project is an ongoing effort to provide exascale-enabled sparse eigensolvers, especially for quantum physics and related application areas. In this paper we first briefly summarize some key achievements that have been made within this project. Then we focus on a projection-based eigensolver with polynomial approximation of the projector. This eigensolver can be used for computing hundreds of interior eigenvalues of large sparse matrices. We describe techniques that allow using lower-degree polynomials than possible with standard Chebyshev expansion of the window function and kernel smoothing. With these polynomials, the degree, and thus the number of matrix-vector multiplications, typically can be reduced by roughly one half, resulting in comparable savings in runtime.

关键词： Polynomial approximation

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A Two-Level Additive Schwarz Domain Decomposition Preconditioner for a Flat-Top Partition of Unity Method 1

引用

8th International Workshop on Meshfree Methods for Partial Differential Equations

作者： Brenner, Susanne C. Davis, Christopher B. Sung, Li-yeng Louisiana State Univ Dept Math Ctr Computat & Technol Baton Rouge LA 70803 USA Tennessee Technol Univ Dept Math Cookeville TN 38505 USA

We investigate a two-level additive Schwarz domain decomposition preconditioner for a flat-top partition of unity method. We establish condition number estimates for the biharmonic problem and present numerical result... 详细信息

ISBN: (数字)9783319519548

ISBN: (纸本)9783319519548;9783319519531

关键词： Domain decomposition methods

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A Direct Elliptic Solver Based on Hierarchically Low-Rank Schur Complements 23rd

A Direct Elliptic Solver Based on Hierarchically Low-Rank Sc...

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23rd International Conference on Domain Decomposition Methods

作者： Chavez, Gustavo Turkiyyah, George Keyes, David E. King Abdullah Univ Sci & Technol Extreme Comp Res Ctr Thuwal 23955 Saudi Arabia

ISBN: (纸本)9783319523897;9783319523880

A parallel fast direct solver for rank-compressible block tridiagonal linear systems is presented. Algorithmic synergies between Cyclic Reduction and Hierarchical matrix arithmetic operations result in a solver with arithmetic complexity and memory footprint. We provide a baseline for performance and applicability by comparing with well-known implementations of the -LU factorization and algebraic multigrid within a shared-memory parallel environment that leverages the concurrency features of the method. Numerical experiments reveal that this method is comparable with other fast direct solvers based on Hierarchical Matrices such as -LU and that it can tackle problems where algebraic multigrid fails to converge. © Springer International Publishing AG 2017.

关键词： Linear systems

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Recent Progress in Linear Response Eigenvalue Problems 1

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2nd International Workshop on Eigenvalue Problems - Algorithms, Software and Applications in Petascale Computing (EPASA)

作者： Bai, Zhaojun Li, Ren-Cang Univ Calif Davis Dept Comp Sci Davis CA 95616 USA Univ Calif Davis Dept Math Davis CA 95616 USA Univ Texas Arlington Dept Math POB 19408 Arlington TX 76019 USA

ISBN: (数字)9783319624266

ISBN: (纸本)9783319624266;9783319624242

Linear response eigenvalue problems arise from the calculation of excitation states of many-particle systems in computational materials science. In this paper, from the point of view of numerical linear algebra and matrix computations, we review the progress of linear response eigenvalue problems in theory and algorithms since 2012.

关键词： Computation theory

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An Error Resilience Strategy of a Complex Moment-Based Eigensolver 1

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2nd International Workshop on Eigenvalue Problems - Algorithms, Software and Applications in Petascale Computing (EPASA)

作者： Imakura, Akira Futamura, Yasunori Sakurai, Tetsuya Univ Tsukuba 1-1-1 Tennodai Tsukuba Ibaraki 3058573 Japan

ISBN: (数字)9783319624266

ISBN: (纸本)9783319624266;9783319624242

Recently, complex moment-based eigensolvers have been actively developed in highly parallel environments to solve large and sparse eigenvalue problems. In this paper, we provide an error resilience strategy of a Rayleigh-Ritz type complex moment-based parallel eigensolver for solving generalized eigenvalue problems. Our strategy is based on an error bound of the eigensolver in the case that soft-errors like bit-flip occur. Using the error bound, we achieve an inherent error resilience of the eigensolver that does not require standard checkpointing and replication techniques in the most time-consuming part.

关键词： Eigenvalues and eigenfunctions

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Simulation of Blood Flow in Patient-specific Cerebral Arteries with a Domain Decomposition Method 23rd

Simulation of Blood Flow in Patient-specific Cerebral Arteri...

引用

23rd International Conference on Domain Decomposition Methods

作者： Shiu, Wen-Shin Yan, Zhengzheng Liu, Jia Chen, Rongliang Hwang, Feng-Nan Cai, Xiao-Chuan Chinese Acad Sci Shenzhen Inst Adv Technol Shenzhen 518055 Guangdong Peoples R China Natl Cent Univ Dept Math Taoyuan 32001 Taiwan Univ Colorado Dept Comp Sci Boulder CO 80309 USA

ISBN: (纸本)9783319523897;9783319523880

We simulate blood flow in patient-specific cerebral arteries. The complicated geometry in the human brain makes the problem challenging. We use a fully unstructured three dimensional mesh to cover the artery, and Galerkin/least-squares finite element method to discretize the incompressible Navier-Stokes equations, that are employed to model the blood flow, and the resulting large sparse nonlinear system of equations is solved by a Newton-Krylov-Schwarz algorithm. From the computed flow fields, we are able to understand certain behavior of the blood flow of this particular patient before and after a stenosis is surgically removed. We also report the robustness and parallel performance of the domain decomposition based algorithm. © Springer International Publishing AG 2017.

关键词： Domain decomposition methods

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Parallel Overlapping Schwarz with an Energy-Minimizing Coarse Space 23rd

Parallel Overlapping Schwarz with an Energy-Minimizing Coars...

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23rd International Conference on Domain Decomposition Methods

作者： Heinlein, Alexander Klawonn, Axel Rheinbach, Oliver Univ Cologne Math Inst Weyertal 86-90 D-50931 Cologne Germany Tech Univ Bergakad Freiberg Fak Math & Informat Inst Numer Math & Optimierung Akad Str 6 D-09596 Freiberg Germany

ISBN: (纸本)9783319523897;9783319523880

Parallel results obtained with a new implementation of an overlapping Schwarz method using an energy minimizing coarse space are presented. We consider structured and unstructured domain decompositions for scalar elliptic and linear elasticity model problems in two dimensions. In particular, strong and weak parallel scalability studies for up to 1024 processor cores are presented for both types of problems. Additionally, weak scalability results for a three-dimensional linear elasticity model problem using up to 4096 processor cores are discussed. Finally, an application from fully-coupled fluid-structure interaction using a nonlinear hyperelastic material model for the structure is shown. © Springer International Publishing AG 2017.

关键词： Fluid structure interaction

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