Open Access

ARTICLE

Fast Boundary Knot Method for Solving Axisymmetric Helmholtz Problems with HighWave Number

J. Lin¹, W. Chen^1,2, C. S. Chen³, X. R. Jiang⁴
1 College of Mechanics and Materials, Hohai University, Nanjing, P.R. China, 210098
2 Corresponding to: chenwen@hhu.edu.cn
3 Department of Mathematics, University of Southern Mississippi, USA
4 Nanjing Les Information Technology Co.,Ltd, Nanjing, P.R. China, 210007

Computer Modeling in Engineering & Sciences 2013, 94(6), 485-505. https://doi.org/10.3970/cmes.2013.094.485

Abstract

To alleviate the difficulty of dense matrices resulting from the boundary knot method, the concept of the circulant matrix has been introduced to solve axi-symmetric Helmholtz problems. By placing the collocation points in a circular form on the surface of the boundary, the resulting matrix of the BKM has the block structure of a circulant matrix, which can be decomposed into a series of smaller matrices and solved efficiently. In particular, for the Helmholtz equation with high wave number, a large number of collocation points is required to achieve desired accuracy. In this paper, we present an efficient circulant boundary knot method algorithm for solving Helmholtz problems with high wave number.

---

Keywords

boundary knot method, Helmholtz problem, circulant matrix, axisymmetric.

---