Publications and Research
Document Type
Article
Publication Date
Summer 6-7-2022
Abstract
In this paper, we discuss the solution solver for the linear system of equations arising from the discretized 2D Helmholtz equation using the radial basis functions. The coefficient matrix A that is generated from the discretization is dense and often ill-conditioned. This paper uses preconditioned iterative methods such as the General Minimal Residual method (GMRES) to solve the linear system. Different preconditioners are compared. Numerical experiments are conducted in order to provide a comparison of the convergence rates among various preconditioned linear systems. A further observation is made into the eigenvalue distributions and the choice of the shaping parameters during the meshless discretization. We conclude the triangular preconditioner and the di agonal preconditioner are both good choices for the discretized 2D Helmholtz equation when we use the meshless discretizations.
Comments
This project was supported by grants. The author Professor Dr. Jia Liu would like to thank the grant support from the Hal Marcus College of Science and Engineering at the University of West Florida. The author Professor Dr. Lina Wu would like to thank the grant support provided by a PSC-CUNY Award, jointly funded by the Professional Staff Congress and The City University of New York.