Efficient Iterative Solvers for Modified Mild Slope Equation

J. Ocean Eng. Technol. 2006;20(6):61-66.

Yoon, Jong-Tae;Park, Seung-Min;

Department of Civil Engineering, Kyungsung University;Department of Civil Engineering, Kyungsung University;

수정완경사방정식을 위한 반복기법의 효율성 비교

윤종태;박승민;

경성대학교 토목공학과;경성대학교 토목공학과;

Keywords: Modified mild slope equation, Generalized conjugate gradient method, Bi-conjugate gradient method, Preconditoning, Wave transformation

핵심용어: 수정완경사방정식, 일반공액경사법, 약공액경사안정법, 전처리, 파랑변형

Abstract

Two iterative solvers are applied to solve the modified mild slope equation. The elliptic formulation of the governing equation is selected for numerical treatment because it is partly suited for complex wave fields, like those encountered inside harbors. The requirement that the computational model should be capable of dealing with a large problem domain is addressed by implementing and testing two iterative solvers, which are based on the Stabilized Bi-Conjugate Gradient Method (BiCGSTAB) and Generalized Conjugate Gradient Method (GCGM). The characteristics of the solvers are compared, using the results for Berkhoff's shoal test, used widely as a benchmark in coastal modeling. It is shown that the GCGM algorithm has a better convergence rate than BiCGSTAB, and preconditioning of these algorithms gives more than half a reduction of computational cost.