Model Equations Combining Full Linear Dispersion With Long Wave Nonlinearity, Part4 - Application of Bi-CGSTAB to sparse nonsymmetric systems -

摘要

A skillful iterative solver is needed for handling the large, sparse nonlinear system with a nonsymmetric matrix that arises from the discretization of the model equation for nonlinear wave evolution. Recently, with favorable stability properties in iteration process, the Bi-CGSTAB method as a variant of the Bi-Conjugate Gradient method has been proposed for solving nonsymmetric linear systems. The iterative method is examined in nonlinear wave analyses on the step-type reef in two-dimensions. Numerical experiments indicate efficiency of Bi-CGSTAB, preconditioned with incomplete Choleski decomposition. For the algorithm to converge by iterative computation it is important to make the diagonal blocks of the coefficient matrix be M-matrix. Because of the linear degree of convergence of the nonlinear system, however, a successful acceleration scheme is required for further development.