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

Jiang Le, Huang Jin, Xiao-Guang Lv, Qing-Song Cheng
2011 ANZIAM Journal  
A preconditioned iterative method for the two-dimensional Helmholtz equation with Robbins boundary conditions is discussed. Using a finite-difference method to discretize the Helmholtz equation leads to a sparse system of equations which is too large to solve directly. The approach taken in this paper is to precondition this linear system with a sine transform based preconditioner and then solve it using the generalized minimum residual method (GMRES). An analytical formula for the eigenvalues
more » ... or the eigenvalues of the preconditioned matrix is derived and it is shown that the eigenvalues are clustered around 1 except for some outliers. Numerical results are reported to demonstrate the effectiveness of the proposed method. 2000 Mathematics subject classification: primary 65F10.
doi:10.21914/anziamj.v52i0.2782 fatcat:e3stdwjemnagdigoef25thusfi