線形分散と浅海長波の非線形性を合わせ持つモデル方程式（第４報）－非対称疎行列系へのBi-CGSTAB法の適用－

概要

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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.
琉球大学工学部の論文