Wuhan University Journal of Natural Sciences

, Volume 24, Issue 4, pp 314–320

Optimality of the Boundary Knot Method for Numerical Solutions of 2D Helmholtz-Type Equations

Mathematics

Abstract

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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© Wuhan University and Springer-Verlag GmbH Germany 2019

Authors and Affiliations

• Fuzhang Wang
• 1
• Kehong Zheng
• 2
• Congcong Li
• 3
Email author
• Juan Zhang
• 1
1. 1.School of Mathematical SciencesHuaibei Normal UniversityHuaibei, AnhuiChina
2. 2.College of Water Conservancy and Ecological EngineeringNanchang Institute of TechnologyNanchang, JiangxiChina
3. 3.Department of MathematicsUniversity of MacauTaipa, MacauChina

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