A parallel frontal solver for finite element applications

In finite element simulations, the overall computing time is dominated by the time needed to solve large sparse linear systems of equations. We report on the design and development of a parallel frontal code that can significantly reduce the wallclock time needed for the solution of these systems. The algorithm used is based on dividing the finite element domain into subdomains and applying the frontal method to each subdomain in parallel. The so-called multiple front approach is shown to reduce the amount of work and memory required compared with the frontal method and, when run on a small number of processes, achieves good speedups. The code, HSL_MP42, has been developed for the Harwell Subroutine Library (http://www.numerical.rl.ac.uk/hsl). It is written in Fortran 90 and, by using MPI for message passing, achieves portability across a wide range of modern computer architectures. Copyright © 2001 John Wiley & Sons, Ltd.

[1]  Jennifer A. Scott.  On ordering elements for a frontal solver , 1999 .

[2]  I. Duff,et al.  The Use of multiple fronts in Gaussian elimination , 1994 .

[3]  Jack J. Dongarra,et al.  A set of level 3 basic linear algebra subprograms , 1990, TOMS.

[4]  Jennifer A. Scott.  Exploiting zeros in frontal solvers , 1997 .

[5]  Jennifer A. Scott,et al.  The design of a new frontal code for solving sparse, unsymmetric systems , 1996, TOMS.

[6]  Iain S. Duff,et al.  Concurrent Multifrontal Methods: Shared Memory, Cache, and Frontwidth Issues , 1987 .

[7]  Iain S. Duff,et al.  Design features of a frontal code for solving sparse unsymmetric linear systems out-of-core , 1984 .

[8]  Jennifer A. Scott.  The design of a parallel frontal solver , 1999 .

[9]  Jennifer A. Scott,et al.  MA42 - A new frontal code for solving sparse unsymmetric systems , 1993 .

[10]  Mark A. Stadtherr,et al.  Parallel frontal solver for large-scale process simulation and optimization , 1997 .

[11]  Patrick Amestoy,et al.  Vectorization of a Multiprocessor Multifrontal Code , 1989, Int. J. High Perform. Comput. Appl..

[12]  Mark A. Stadtherr,et al.  A parallel block frontal solver for large scale process simulation : Reordering effects , 1997 .

[13]  E. Lui,et al.  A parallel frontal solver on the alliant FX/80 , 1991 .

[14]  Bruce Hendrickson,et al.  The Chaco user`s guide. Version 1.0 , 1993 .

[15]  I. Duff,et al.  THE USE OF PROFILE REDUCTION ALGORITHMS WITH A FRONTAL CODE , 1989 .

[16]  Bruce M. Irons,et al.  A frontal solution program for finite element analysis , 1970 .

[17]  Jennifer A. Scott,et al.  PERFORMANCE ISSUES FOR FRONTAL SCHEMES ON A CACHE-BASED HIGH-PERFORMANCE COMPUTER , 1997 .