Circulant Matrix and Conformal Mapping For Solving Partial Differential Equations

Document Type

Article

Publication Date

8-1-2014

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

In recent years, a fast radial basis function (RBF) solver for surface interpolation has been developed by Karageorghis et al. (2007). In this paper, we follow up their work by extending the idea of fast evaluation of the surface interpolation to efficiently solve various types of partial differential equations (PDEs). We look into the possibility of solving PDEs with conformal mapping to map the RBF circular points on a disk to the interior of an irregular domain. We also compare the pros and cons for these two approaches. In both approaches, the circulant matrix formulation and the matrix decomposition method are the central ideas of fast computation. In numerical experiments, we test these two approaches for solving PDEs using up to 160 000 RBF interpolation points with greater accuracy and efficiency. © 2014 Elsevier Ltd. All rights reserved.

Publication Title

Computers and Mathematics with Applications

Volume

68

Issue

3

First Page

67

Last Page

76

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