PARDISO: a high-performance serial and parallel sparse linear solver in semiconductor device simulation

Abstract The package PARDISO is a high-performance, robust and easy to use software for solving large sparse symmetric or structurally symmetric linear systems of equations on shared memory multiprocessors. PARDISO uses a combination of left- and right-looking Level-3 BLAS supernode techniques to exploit pipelining parallelism. It delivers up to 960 Mflop/s on COMPAQ Alpha ES40 (667 MHz) for irregular problems and sparse matrix factorization has been clocked up at a speedup of 7 on an 8-node SGI Origin 2000. The paper gives an overview of the algorithm, performance results and the integration of the solver into complex industrial simulation tools. Finally, an example is discussed inherently (due to the design goal) producing linear systems close to singularity.

[1]  Iain S. Duff.  Multiprocessing a sparse matrix code on the Alliant FX/8 , 1989 .

[2]  J. Bunch,et al.  Some stable methods for calculating inertia and solving symmetric linear systems , 1977 .

[3]  Joseph W. H. Liu.  The role of elimination trees in sparse factorization , 1990 .

[4]  Wolfgang Fichtner,et al.  Efficient Sparse LU Factorization with Left-Right Looking Strategy on Shared Memory Multiprocessors , 2000 .

[5]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[6]  Wolfgang Fichtner,et al.  Scalable Parallel Sparse Factorization with Left-Right Looking Strategy on Shared Memory Multoprocessors , 1999, HPCN Europe.

[7]  George Karypis,et al.  PSPASES: Building a High Performance Scalable Parallel Direct Solver for Sparse Linear Systems , 1999 .

[8]  Patrick R. Amestoy,et al.  Multifrontal parallel distributed symmetric and unsymmetric solvers , 2000 .

[9]  Patrick Amestoy,et al.  Memory Management Issues in Sparse Multifrontal Methods On Multiprocessors , 1993, Int. J. High Perform. Comput. Appl..

[10]  Barry W. Peyton,et al.  A Supernodal Cholesky Factorization Algorithm for Shared-Memory Multiprocessors , 1991, SIAM J. Sci. Comput..

[11]  Arno Liegmann.  Efficient solution of large sparse linear systems , 1995 .

[12]  Olaf Schenk,et al.  Scalable parallel sparse LU factorization methods on shared memory multiprocessors , 2000 .

[13]  James Demmel,et al.  An Asynchronous Parallel Supernodal Algorithm for Sparse Gaussian Elimination , 1997, SIAM J. Matrix Anal. Appl..

[14]  Vipin Kumar,et al.  A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs , 1998, SIAM J. Sci. Comput..