Interface Relaxation Methods for Elliptic Differential Equations

A population of seven non-overlapping domain decomposition methods for solving elliptic differential equations are viewed and formulated as iterated interface relaxation procedures. A comprehensive review of the underlying mathematical ideas and the computational characteristics is given. The existing theoretical results are also reviewed and high level descriptions of the various algorithms are presented. The effectiveness of these methods on various differential problems is investigated by presenting and discussing preliminary performance evaluation data.

[1]  T. Chan,et al.  A Survey of Preconditioners for Domain Decomposition. , 1985 .

[2]  P. Tallec,et al.  Domain decomposition methods for large linearly elliptic three-dimensional problems , 1991 .

[3]  John R. Rice,et al.  Solving elliptic problems using ELLPACK , 1985, Springer series in computational mathematics.

[4]  T. Chan,et al.  Domain decomposition algorithms , 1994, Acta Numerica.

[5]  Tony F. Chan,et al.  On the Relationship between Overlapping and Nonoverlapping Domain Decomposition Methods , 1992, SIAM J. Matrix Anal. Appl..

[6]  Jinchao Xu,et al.  Some Nonoverlapping Domain Decomposition Methods , 1998, SIAM Rev..

[7]  Olof B. Widlund,et al.  To overlap or not to overlap: a note on a domain decomposition method for elliptic problems , 1989 .

[8]  Ramesh Natarajan.  Domain Decomposition Using Spectral Expansions of Steklov-Poincaré Operators , 1995, SIAM J. Sci. Comput..

[9]  S. Jaffard.  Wavelet methods for fast resolution of elliptic problems , 1992 .

[10]  Tony F. Chan,et al.  Geometry related convergence results for domain decomposition algorithms , 1991 .

[11]  Wilhelm Heinrichs.  Domain decomposition for fourth-order problems , 1993 .

[12]  Qingping Deng.  Timely Communicaton: An Analysis for a Nonoverlapping Domain Decomposition Iterative Procedure , 1997, SIAM J. Sci. Comput..

[13]  Tony F. Chan,et al.  Eigendecomposition of Domain Decomposition Interface Operators for Constant Coefficient Elliptic Problems , 1991, SIAM J. Sci. Comput..

[14]  John R. Rice,et al.  Analysis of a nonoverlapping domain decomposition method for elliptic partial differential equations , 1997 .

[15]  Alfio Quarteroni,et al.  An Iterative Procedure with Interface Relaxation for Domain Decomposition Methods , 1988 .

[16]  William Gropp,et al.  A comparison of domain decomposition techniques for elliptic partial differential equations and their parallel implementation , 1985, PP.

[17]  John R. Rice,et al.  An agent-based approach to building multidisciplinary problem-solving environments , 1996 .

[18]  Junping Wang,et al.  A parallel iterative procedure applicable to the approximate solution of second order partial differential equations by mixed finite element methods , 1993 .

[19]  Ramesh Natarajan.  Domain Decomposition using Spectral Expansions of Steklov-Poincaré Operators II: A Matrix Formulation , 1997, SIAM J. Sci. Comput..

[20]  Roland Glowinski,et al.  A Domain Decomposition Method for the Acoustic Wave Equation with Discontinuous Coefficients and Grid Change , 1997 .

[21]  Mo Mu,et al.  Solving Composite Problems with Interface Relaxation , 1999, SIAM J. Sci. Comput..

[22]  John R. Rice,et al.  Modeling with collaborating PDE solvers—Theory and practice , 1995 .

[23]  Seongjai Kim,et al.  A parallelizable iterative procedure for the Helmholtz problem , 1994 .