Department of Mathematics and Statistics¹
University of West Florida
Pensacola. Florida
Department of Mathematics²
Borough of Manhattan Community College
The City University of New York (CUNY)
New York, New York

Preconditioned Iterative Solvers for the 2D Helmholtz Equation Via Radial Basis Functions

In this paper, we consider a linear system of equations arising from the discretization of the 2D Helmholtz equation through radial basis functions. The coefficient matrix A that is generated from the discretization is dense and often ill-conditioned. We apply different preconditioners to improve the conditioning of the problem for computation. Numerical experiments are conducted using the General Minimal Residual method (GMRES) to compare the convergence rates among various preconditioners. Besides, we applied the new discretization strategy to improve the accuracy and we found the best preconditioner with GMRES for the 2D Helmholtz equation based on the radial basis functions.

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