Title

Fast Boundary Knot Method for Solving Axisymmetric Helmholtz Problems with High Wave Number

Document Type

Article

Publication Date

8-1-2013

Department

Mathematics

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.

Publication Title

CMES: Computer Modeling in Engineering & Sciences

Volume

94

Issue

6

First Page

485

Last Page

505

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