Extending PSBLAS to Build Parallel Schwarz Preconditioners

We describe some extensions to Parallel Sparse BLAS (PSBLAS), a library of routines providing basic Linear Algebra operations needed to build iterative sparse linear system solvers on distributed-memory parallel computers. We focus on the implementation of parallel Additive Schwarz preconditioners, widely used in the solution of linear systems arising from a variety of applications. We report a performance analysis of these PSBLAS-based preconditioners on test cases arising from automotive engine simulations. We also make a comparison with equivalent software from the well-known PETSc library.

[1]  Daniel B. Szyld,et al.  An Algebraic Convergence Theory for Restricted Additive Schwarz Methods Using Weighted Max Norms , 2001, SIAM J. Numer. Anal..

[2]  Xiao-Chuan Cai,et al.  A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems , 1999, SIAM J. Sci. Comput..

[3]  Iain S. Duff,et al.  Level 3 basic linear algebra subprograms for sparse matrices: a user-level interface , 1997, TOMS.

[4]  Michele Colajanni,et al.  Using a Parallel Library of Sparse Linear Algebra in a Fluid Dynamics Application Code on Linux Clusters , 2002 .

[5]  Yousef Saad,et al.  Overlapping Domain Decomposition Algorithms for General Sparse Matrices , 1996, Numer. Linear Algebra Appl..

[6]  O. Widlund Domain Decomposition Algorithms , 1993 .

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

[8]  C. W. Hirt,et al.  An Arbitrary Lagrangian-Eulerian Computing Method for All Flow Speeds , 1997 .

[9]  S DuffIain,et al.  An overview of the sparse basic linear algebra subprograms , 2002 .

[10]  Iain S. Duff,et al.  An overview of the sparse basic linear algebra subprograms: The new standard from the BLAS technical forum , 2002, TOMS.

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

[12]  Barry F. Smith,et al.  Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations , 1996 .

[13]  Olof B. Widlund,et al.  Domain Decomposition Algorithms for Indefinite Elliptic Problems , 2017, SIAM J. Sci. Comput..

[14]  Michele Colajanni,et al.  PSBLAS: a library for parallel linear algebra computation on sparse matrices , 2000, TOMS.

[15]  M. Gander,et al.  Why Restricted Additive Schwarz Converges Faster than Additive Schwarz , 2003 .