Tabarek, RysbergenErlangga, YogiTourassis, Vassilios D.2019-08-292019-08-292019-04-19http://nur.nu.edu.kz/handle/123456789/4195Submitted to the Department of Mathematics on Apr 19, 2019, in partial fulfillment of the requirements for the degree of Master of Applied MathematicsIn this thesis we propose and study an efficient iterative multigrid method for the time independent modified mild slope equation with and without energy dissipation term. The algorithm relies on a multigrid method preconditioned with shifted-Laplacian preconditioner and solved by Bi-CGSTAB algorithm. Multigrid analysis results are shown by numerical experiments. Numerical experiments are conducted in depth sloped elliptic shoal introduced by Berkhoff et. alenAttribution-NonCommercial-ShareAlike 3.0 United StatesResearch Subject Categories::MATHEMATICS::Applied mathematicsmultigrid methodslope equationshifted-Laplacian preconditionerBi-CGSTAB algorithmMaster's thesis