Optimality of the Boundary Knot Method for Numerical Solutions of 2D Helmholtz-Type Equations
WANG Fuzhang1, ZHENG Kehong2, LI Congcong3† , ZHANG Juan11. School of Mathematical Sciences, Huaibei Normal University, Huaibei 235000, Anhui, China; 2. College of Water Conservancy and Ecological Engineering, Nanchang Institute of Technology, Nanchang 330099, Jiangxi, China; 3. Department of Mathematics, University of Macau, Avenida da Universidade, Taipa, Macau, China
The boundary knot method (BKM) is a boundary-type meshfree method. Only non-singular general solutions are used during the whole solution procedures. The effective condition number (ECN), which depends on the right-hand side vector of a linear system, is considered as an alternative criterion to the traditional condition number. In this paper, the effective condition number is used to help determine the position and distribution of the collocation points as well as the quasi-optimal collocation point numbers. During the solution process, we propose an NMN-search algorithm. Numerical examples show that the ECN is reliable to measure the feasibility of the BKM.
Key words:boundary knot method; effective condition number; non-singular general solution
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