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MODELLING OF WAVE PROPAGATION IN THE NEARSHORE REGION USING THE MILD SLOPE EQUATION WITH GMRES‐BASED ITERATIVE SOLVERS
Author(s) -
ZHAO Y.,
ANASTASIOU K.
Publication year - 1996
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/(sici)1097-0363(19960830)23:4<397::aid-fld428>3.0.co;2-7
Subject(s) - generalized minimal residual method , solver , mathematics , iterative method , convergence (economics) , linear system , system of linear equations , coefficient matrix , mathematical optimization , mathematical analysis , eigenvalues and eigenvectors , physics , economics , economic growth , quantum mechanics
The mild slope equation in its linear and non‐linear forms is used for the modelling of nearshore wave propagation. The finite difference method is used to descretize the governing elliptic equations and the resulting system of equations is solved using GMRES‐based iterative method. The original GMRES solution technique of Saad and Schultz is not directly applicable to the present case owing to the complex coefficient matrix. The simpler GMRES algorithm of Walker and Zhou is used as the core solver, making the upper Hessenberg factorization unneccessary when solving the least squares problem. Several preconditioning‐based acceleration strategies are tested and the results show that the GMRES‐based iteration scheme performs very well and leads to monotonic convergence for all the test‐cases considered.