A Multi-Level Preconditioner with Applicationsto the Numerical Simulation of Coating ProblemsYousef

A multi-level preconditioned iterative method based on a multi-level block ILU factoriza-tion preconditioning technique is introduced and is applied to the solution of unstructured sparse linear systems arising from the numerical simulation of coating problems. The coef-cient matrices usually have several rows with zero diagonal values that may cause stability diiculty in standard ILU factorization techniques. The new preconditioning strategy employs a diagonal threshold tolerance and a local reordering of individual blocks to increase robustness of the multi-level block ILU factorization process.

[1]  Fred Wubs,et al.  A fast linear-system solver for large unstructured problems on a shared-memory computer , 1996 .

[2]  H. Elman.  A stability analysis of incomplete LU factorizations , 1986 .

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

[4]  A. H. Sherman,et al.  Comparative Analysis of the Cuthill–McKee and the Reverse Cuthill–McKee Ordering Algorithms for Sparse Matrices , 1976 .

[5]  Victor Eijkhout,et al.  Design of a Library of Parallel Preconditioners , 2000, Int. J. High Perform. Comput. Appl..

[6]  Jun Zhang,et al.  Domain Decomposition and MultiLevel Type Techniques for General Sparse Linear Systems , 1997 .

[7]  Jun Zhang,et al.  BILUTM: A Domain-Based Multilevel Block ILUT Preconditioner for General Sparse Matrices , 1999, SIAM J. Matrix Anal. Appl..

[8]  J. Pasciak,et al.  Computer solution of large sparse positive definite systems , 1982 .

[9]  I. Gustafsson.  A class of first order factorization methods , 1978 .

[10]  Randolph E. Bank,et al.  The Incomplete Factorization Multigraph Algorithm , 1999, SIAM J. Sci. Comput..

[11]  Yousef Saad,et al.  A Flexible Inner-Outer Preconditioned GMRES Algorithm , 1993, SIAM J. Sci. Comput..

[12]  Jun Zhang,et al.  Diagonal threshold techniques in robust multi-level ILU preconditioners for general sparse linear systems , 1999, Numer. Linear Algebra Appl..

[13]  R. P. Kendall,et al.  An Approximate Factorization Procedure for Solving Self-Adjoint Elliptic Difference Equations , 1968 .

[14]  I. Duff,et al.  The effect of ordering on preconditioned conjugate gradients , 1989 .

[15]  Jun Zhang,et al.  BILUM: Block Versions of Multielimination and Multilevel ILU Preconditioner for General Sparse Linear Systems , 1999, SIAM J. Sci. Comput..

[16]  Y. Saad,et al.  Experimental study of ILU preconditioners for indefinite matrices , 1997 .

[17]  Masha Sosonkina,et al.  Distributed Schur Complement Techniques for General Sparse Linear Systems , 1999, SIAM J. Sci. Comput..

[18]  Jun Zhang,et al.  Preconditioned Krylov subspace methods for solving nonsymmetric matrices from CFD applications , 2000 .