The Multilevel Krylov-Multigrid Method for the Helmholtz Equation Preconditioned by the Shifted Laplacian

2017 ◽  
pp. 113-139
Author(s):  
Yogi A. Erlangga ◽  
Luis García Ramos ◽  
Reinhard Nabben
Keyword(s):  
Helmholtz Equation ◽  
Multigrid Method

scholarly journals Multigrid Method for Solution of 3D Helmholtz Equation Based on HOC Schemes

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Fazal Ghaffar ◽  
Noor Badshah ◽  
Saeed Islam
Keyword(s):  
Difference Scheme ◽  
Helmholtz Equation ◽  
Multigrid Method ◽  
Three Dimensional ◽  
Uniform Mesh ◽  
Sparse Linear Systems ◽  
Compact Difference Scheme ◽  
Order Accuracy ◽  
Compact Difference ◽  
Fifth Order

A higher order compact difference (HOC) scheme with uniform mesh sizes in different coordinate directions is employed to discretize a two- and three-dimensional Helmholtz equation. In case of two dimension, the stencil is of 9 points while in three-dimensional case, the scheme has 27 points and has fourth- to fifth-order accuracy. Multigrid method using Gauss-Seidel relaxation is designed to solve the resulting sparse linear systems. Numerical experiments were conducted to test the accuracy of the sixth-order compact difference scheme with Multigrid method and to compare it with the standard second-order finite-difference scheme and fourth-order compact difference scheme. Performance of the scheme is tested through numerical examples. Accuracy and efficiency of the new scheme are established by using the errors normsl2.

scholarly journals A Multigrid Method for the Helmholtz Equation with Optimized Coarse Grid Corrections

2014 ◽  
Vol 36 (6) ◽  
pp. A2819-A2841 ◽  
Author(s):  
Christiaan C. Stolk ◽  
Mostak Ahmed ◽  
Samir Kumar Bhowmik
Keyword(s):  
Helmholtz Equation ◽  
Multigrid Method ◽  
Coarse Grid

A preconditioned method for the solution of the Robbins problem for the Helmholtz equation

2011 ◽  
Vol 51 ◽  
pp. 87
Author(s):  
Jiang Le ◽  
Huang Jin ◽  
Xiao-Guang Lv ◽  
Qing-Song Cheng
Keyword(s):  
Helmholtz Equation
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