A SOR iterative algorithm for the finite difference and the finite element methods that is efficient and parallelizable

Abstract An efficient and simple parallel SOR iterative algorithm is presented for the finite difference and finite element methods. Based on domain subdividing and computing sequence reordering, this algorithm has been proven to be efficient and simple to implement. No coloring scheme and no overlapping blocks are required. With this parallel algorithm, not only computations for the mesh points in the subdomain but also computations for the mesh points on the inferace are carried out parallely. In addition, programming efforts to implement the parallel algorithm are simplified. When compared with the results using the conventional sequential algorithm, excellent efficiencies are obtained using the parallel algorithm.

[1]  Charbel Farhat,et al.  A parallel active column equation solver , 1988 .

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

[3]  Charbel Farhat,et al.  Modal superposition dynamic analysis on concurrent multiprocessors , 1986 .

[4]  Graham F. Carey,et al.  Parallel supercomputing: methods, algorithms and applications , 1989 .

[5]  Charbel Farhat,et al.  Implicit parallel processing in structural mechanics , 1994 .

[6]  J. C. Bruch,et al.  A HIGHLY EFFICIENT ITERATIVE PARALLEL COMPUTATIONAL METHOD FOR FINITE ELEMENT SYSTEMS , 1993 .

[7]  R. White.  Multisplitting and parallel iterative methods , 1987 .

[8]  David J. Evans,et al.  Parallel S.O.R. iterative methods , 1984, Parallel Comput..

[9]  J. Bruch,et al.  Studies of an interface relaxation domain decomposition technique using finite elements on a parallel computer , 1993 .

[10]  Loyce Adams,et al.  Reordering computations for parallel execution , 1986 .

[11]  J. C. Bruch.  Multisplitting and domain decomposition , 1993 .

[12]  Charbel Farhat.  Which parallel finite element algorithm for which architecture and which problem , 1990 .

[13]  Alfio Quarteroni,et al.  A relaxation procedure for domain decomposition methods using finite elements , 1989 .

[14]  Charbel Farhat,et al.  Concurrent iterative solution of large finite element systems , 1987 .

[15]  Charbel Farhat,et al.  Towards parallel I/O in finite element simulations , 1989 .

[16]  Carlos Alberto Brebbia,et al.  Domain Decomposition for Free Boundary Seepage , 1991 .

[17]  Charbel Farhat,et al.  A consistency analysis of a class of concurrent transient implicit/explicit algorithms , 1990 .

[18]  J. G. Malone.  Automated mesh decomposition and concurrent finite element analysis for hypercube multiprocessor computers , 1988 .

[19]  J. Bruch,et al.  A Domain Decomposition Technique Applied to a Free Surface Seepage Problem , 1991 .

[20]  Charbel Farhat,et al.  A new finite element concurrent computer program architecture , 1987 .

[21]  Charbel Farhat,et al.  A simple and efficient automatic fem domain decomposer , 1988 .