New Evaluation Index of Incomplete Cholesky Preconditioning Effect

In Incomplete LU (ILU) preconditioning, orderings often affect the effect of preconditioning. The authors recently proposed a simple evaluation way for orderings in the ILU preconditioning technique. The present paper introduces the evaluation method in unstructured analyses in which the effect of preconditioning is not easily estimated. The evaluation index, which has a simple relationship with the matrix norm of the remainder matrix, is easily computed without additional memory requirement. The computational cost of the index is trivial in the total iterative solution process. The effectiveness of the method is examined by numerical tests using coefficient matrix data from the Matrix Market, a finite-difference analysis of Poisson equation, and a 3-d electromagnetic field analysis.