Effectiveness of GMRES-DR and OSP-ILUC for wave diffraction analysis of a very large floating structure (VLFS)

This paper presents the performance of iterative solvers and preconditioners for the non-Hermitian dense linear systems arising from the boundary value problem related to the diffraction wave field around a very large floating structure (VLFS). These systems can be solved iteratively using the GMRES with deflated restarting (GMRES-DR), which has Krylov subspaces with approximate eigenvectors as starting vectors. The number of iteration needed by GMRES or GMRES-DR can be significantly reduced using preconditioning techniques. Matrix-vector products are approximated by utilizing the fast multipole method (FMM), which need not directly calculate the dense matrix of the far field interactions. The combination of the operator splitting preconditioner (OSP) and the Crout version of the incomplete LU factorization (ILUC) does not require the dense matrix of the far field interactions. Numerical experiments from a hybrid-type VLFS, which is composed of pontoon-part and semi-submersible part, whose length is 3000 m are presented.