GRMES Iterative Solution of Matrix Systems Derived from Boundary Element Techniques
MICHIGAN UNIV ANN ARBOR DEPT OF MECHANICAL ENGINEERING AND APPLIED MECHANICS
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We apply the Generalized Minimal Residual GMRES iterative equation solution technique to a set of full, unsymmetric matrix systems generated by a standard boundary element method. The test problems chosen produced well conditioned matrices. The GMRES technique, when used without preconditioning and with a sufficient number of trial vectors, solved the matrix system using as few as 23 of the operations required by a direct Gauss reduction. The class of partial LU decomposition preconditioners tested degraded the condition number of the matrices, and consequently did not reduce the GMRES solution time. In general, the GMRES technique does not appear to be of practical interest compared to the direct reduction unless other factors availability of a good approximation to the final solution, etc. intervene.
- Numerical Mathematics