Application of the Crout version of the incomplete LU factorization (ILUC) to the Boundary Element Analysis for Wave Diffraction Problems

Abstract

Incomplete LU factorizations (ILU), combined with the generalized minimal residual method (GMRES), are often regarded as the best ‘general purpose’ iterative solvers. The dual threshold incomplete LU factorization (ILUT) is a well-known ILU preconditioner. It is effective for general sparse linear systems. However, for dense matrices, the cost for the construction of this preconditioner is high. We thus consider the Crout version of the ILU preconditioner (ILUC) in this study. It is known that ILUC can compute much faster than ILUT for sparse matrices. We apply the ILUC preconditioner for the analysis of the boundary value problem related to the diffraction wave field around a Very Large Floating Structure (VLFS) and show that this preconditioner is, in some cases, effective for dense linear systems.