On modified block SSOR iteration methods for linear systems from steady incompressible viscous flow problems
In order to solve the large sparse systems of linear equations arising from numerical solutions of two-dimensional steady incompressible viscous flow problems in primitive variable formulation, we present block SSOR and modified block SSOR iteration methods based on the special structures of the coe...
Saved in:
Published in | Applied mathematics and computation Vol. 217; no. 7; pp. 3050 - 3068 |
---|---|
Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Amsterdam
Elsevier Inc
01.12.2010
Elsevier |
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | In order to solve the large sparse systems of linear equations arising from numerical solutions of two-dimensional steady incompressible viscous flow problems in primitive variable formulation, we present block SSOR and modified block SSOR iteration methods based on the special structures of the coefficient matrices. In each step of the block SSOR iteration, we employ the block LU factorization to solve the sub-systems of linear equations. We show that the block LU factorization is existent and stable when the coefficient matrices are block diagonally dominant of type-II by columns. Under suitable conditions, we establish convergence theorems for both block SSOR and modified block SSOR iteration methods. In addition, the block SSOR iteration and AF-ADI method are considered as preconditioners for the nonsymmetric systems of linear equations. Numerical experiments show that both block SSOR and modified block SSOR iterations are feasible iterative solvers and they are also effective for preconditioning Krylov subspace methods such as GMRES and BiCGSTAB when used to solve this class of systems of linear equations. |
---|---|
Bibliography: | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
ISSN: | 0096-3003 1873-5649 |
DOI: | 10.1016/j.amc.2010.08.039 |