Domain-Based Parallelism and Problem Decomposition Methods in Computational Science and Engineering最新文献

8. A Parallel Multi-Level Solution Method for Large Markov Chains 8. 大马尔可夫链的并行多级解方法

Domain-Based Parallelism and Problem Decomposition Methods in Computational Science and Engineering Pub Date : 1900-01-01 DOI: 10.1137/1.9781611971507.ch8

G. Horton

引用次数: 2

13. Linear Scaling Algorithms for Large Scale Electronic Structure Calculations 13. 大规模电子结构计算的线性标度算法

Domain-Based Parallelism and Problem Decomposition Methods in Computational Science and Engineering Pub Date : 1900-01-01 DOI: 10.1137/1.9781611971507.ch13

E. Stechel

引用次数: 0

14. Problem Decomposition in Quantum Chemistry 14. 量子化学中的问题分解

Domain-Based Parallelism and Problem Decomposition Methods in Computational Science and Engineering Pub Date : 1900-01-01 DOI: 10.1137/1.9781611971507.ch14

Hans-Joachim Werner

引用次数: 3

1. A Family of Overlapping Schwarz Algorithms for Nonsymmetric and Indefinite Elliptic Problems 1. 非对称和不定椭圆问题的重叠Schwarz算法族

Domain-Based Parallelism and Problem Decomposition Methods in Computational Science and Engineering Pub Date : 1900-01-01 DOI: 10.1137/1.9781611971507.ch1

X. Cai

{"title":"1. A Family of Overlapping Schwarz Algorithms for Nonsymmetric and Indefinite Elliptic Problems","authors":"X. Cai","doi":"10.1137/1.9781611971507.ch1","DOIUrl":"https://doi.org/10.1137/1.9781611971507.ch1","url":null,"abstract":"The classical Schwarz alternating method has recently been generalized in several directions This e ort has resulted in a number of new powerful domain decomposition methods for solving general elliptic problems including the nonsymmetric and inde nite cases In this paper we present several overlapping Schwarz preconditioned Krylov space iterative methods for solving elliptic boundary value problems with operators that are dominated by the self adjoint second order terms but need not be either self adjoint or de nite All algorithms discussed in this paper involve two levels of preconditioning and one of the critical components is a global coarse grid problem We show that under certain assumptions the algorithms are optimal in the sense that the convergence rates of the preconditioned Krylov iterative methods are independent of the number of unknowns of the linear system and also the number of subdomains The optimal convergence theory holds for problems in both two and three dimensional spaces and for both structured and unstructured grids Some numerical results are presented also Introduction In this paper we present a family of overlapping domain de composition methods for the solution of large sparse nonsymmetric and or indef inite linear systems of equations obtained by discretizing elliptic partial di erential equations This family of methods originates from the classical Schwarz alternating algorithm introduced in by H A Schwarz in an existence proof for elliptic boundary value problems de ned in certain irregular regions This method has at tracted much attention as a convenient computational method for the solution of a large class of elliptic or parabolic equations see e g especially on parallel machines There are essentially two ways to use the algorithm as a computational tool The rst approach is to use it directly on the continuous partial di erential equa tion de ned on a physical domain The mesh partitioning and the PDE discretization are then carried out subdomain by subdomain which may sometimes result in non matching grids between overlapping subdomains The second approach is to use it on the already discretized PDE i e a linear system of algebraic equations In this ap proach a global grid is assumed to have been introduced before the domain or mesh is partitioned into subdomains We shall consider only the second approach Some of the material presented in this paper can also be found the references This family of overlapping Schwarz algorithms has been shown to be e cient and robust for solving di erential equations of many di erent types under a wide range of circumstances In this paper we shall focus only on the class of nonsymmetric and or inde nite second order elliptic nite element or nite di erence equations The solution of such problems is an important computational kernel in implicit methods for example the Jacobian problems that need to be solved in any Newton like method used in the solution of nonlinear partial di erenti","PeriodicalId":267437,"journal":{"name":"Domain-Based Parallelism and Problem Decomposition Methods in Computational Science and Engineering","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114802231","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 8

11. Fictitious Domain/Domain Decomposition Methods for Partial Differential Equations 11. 偏微分方程的虚域/域分解方法

Domain-Based Parallelism and Problem Decomposition Methods in Computational Science and Engineering Pub Date : 1900-01-01 DOI: 10.1137/1.9781611971507.ch11

R. Glowinski, T. Pan, J. Périaux

引用次数: 4

7. Decomposition of Space-Time Domains: Accelerated Waveform Methods, with Application to Semiconductor Device Simulation 7. 时空域分解:加速波形方法及其在半导体器件仿真中的应用

Domain-Based Parallelism and Problem Decomposition Methods in Computational Science and Engineering Pub Date : 1900-01-01 DOI: 10.1137/1.9781611971507.ch7

A. Lumsdaine, M. Reichelt

引用次数: 1

9. Optimizing Substructuring Methods for Repeated Right Hand Sides, Scalable Parallel Coarse Solvers, and Global/Local Analysis 9. 优化子结构方法的重复右手边，可扩展的并行粗解，和全局/局部分析

Domain-Based Parallelism and Problem Decomposition Methods in Computational Science and Engineering Pub Date : 1900-01-01 DOI: 10.1137/1.9781611971507.ch9

C. Farhat

引用次数: 9

12. Multipole and Precorrected-FFT Accelerated Iterative Methods for Solving Surface Integral Formulations of Three-dimensional Laplace Problems 12. 求解三维拉普拉斯问题表面积分公式的多极和预校正fft加速迭代方法

Domain-Based Parallelism and Problem Decomposition Methods in Computational Science and Engineering Pub Date : 1900-01-01 DOI: 10.1137/1.9781611971507.ch12

K. Nabors, J. Phillips, F. T. Korsmeyer, Jacob K. White

引用次数: 5

10. Parallel Implementation of a Domain Decomposition Method for Non-Linear Elasticity Problems 10. 非线性弹性问题的区域分解方法并行实现

Domain-Based Parallelism and Problem Decomposition Methods in Computational Science and Engineering Pub Date : 1900-01-01 DOI: 10.1137/1.9781611971507.ch10

F. Roux

引用次数: 10

4. Parallel Implicit Methods for Aerodynamic Applications on Unstructured Grids 4. 非结构网格气动应用的并行隐式方法

Domain-Based Parallelism and Problem Decomposition Methods in Computational Science and Engineering Pub Date : 1900-01-01 DOI: 10.1137/1.9781611971507.ch4

V. Venkatakrishnan

引用次数: 9