Abstract
To solve iteratively linear system $Au=b$ with large sparse strongly non-symmetric matrix $A$ we propose preconditioning $\hat A \hat u = \hat b$, $\hat A=(I+\tau L_1)^{-1} A (I+\tau U_1)^{-1},\; \tau>0$ where respectively lower and upper triangular matrices $L_1$ and $U_1$ are so that $L_1+U_1=1/2(A-A^*)$. Such preconditioning technique may be treated as a variant of ILU-factorization, and we call it MSSILU --- Modified Skew-Symmetric ILU.
We investigate and optimize (with respect to $\tau$) convergence of preconditioned Richardson method (RM) of the following special form: ${\hat x}^{m+1}=(I-\tau \hat A){\hat x}^m+\tau {\hat b},\; m\geq 0$, where $\tau $ is the same as in $\hat A$. For this method we give an estimate for rate of convergence in relevant Euclidean norm for the case of positivereal matrix $A$.
Numerical experiments have included solving linear systems arising from 5-point FD approximation of convection--diffusion equation with dominated convection by MSSILU+RM, MSSILU+GMRES(2) and MSSILU+GMRES(10).
Original language | Undefined |
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Pages (from-to) | 483-484 |
Number of pages | 2 |
Journal | Zeitschrift für angewandte Mathematik und Mechanik |
Volume | 76 |
Issue number | Suppl. |
DOIs | |
Publication status | Published - 1996 |
Keywords
- EWI-2757
- IR-65614