Incomplete block factorization preconditioning for indefinite elliptic problems | Zendy

ChunHua Guo | Zendy

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Incomplete block factorization preconditioning for indefinite elliptic problems

Author(s) -

ChunHua Guo

Publication year - 1999

Publication title -

numerische mathematik

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.214

H-Index - 90

eISSN - 0945-3245

pISSN - 0029-599X

DOI - 10.1007/s002119900076

Subject(s) - mathematics , preconditioner , incomplete lu factorization , tridiagonal matrix , incomplete cholesky factorization , eigenvalues and eigenvectors , factorization , linear system , coefficient matrix , block (permutation group theory) , conjugate gradient method , matrix (chemical analysis) , numerical analysis , matrix decomposition , mathematical analysis , mathematical optimization , algorithm , combinatorics , physics , materials science , quantum mechanics , composite material

Summary. The application of the finite difference method to approximate the solution of an indefinite elliptic problem produces a linear system whose coefficient matrix is block tridiagonal and symmetric indefinite. Such a linear system can be solved efficiently by a conjugate residual method, particularly when combined with a good preconditioner. We show that specific incomplete block factorization exists for the indefinite matrix if the mesh size is reasonably small, and that this factorization can serve as an efficient preconditioner. Some efforts are made to estimate the eigenvalues of the preconditioned matrix. Numerical results are also given.

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