IJPAM: Volume 97, No. 4 (2014)

SOLVING THE DIRICHLET PROBLEM WITH
DISCONTINUOUS COEFFICIENTS IN BOUNDED MULTIPLY
CONNECTED REGIONS USING A BOUNDARY INTEGRAL
EQUATION WITH THE GENERALIZED NEUMANN KERNEL

M. Aghaeiboorkheili$^{1,3}$, Ali H.M. Murid$^{2,3}$
$^1$Department of Mathematical Sciences
Faculty of Science
Universiti Teknologi Malaysia
81310 UTM Johor Bahru,
Johor, MALAYSIA
$^2$UTM Centre for Industrial and Applied Mathematics
(UTM-CIAM), Universiti Teknologi Malaysia, 81310 UTM
Johor Bahru, Johor, MALAYSIA
$^3$Ibnu Sina Institute for Fundamental Science Studies
Universiti Teknologi Malaysia
81310 UTM Johor Bahru, Johor, MALAYSIA


Abstract. This paper presents a numerical method for solving the Dirichlet problem with discontinuous coefficients in bounded multiply connected regions. The method is based on reducing the problem of solving the Dirichlet problem with discontinuous coefficients to a problem of solving Dirichlet problem with continuous coefficients. The Dirichlet problem with continuous coefficients is then solved using a combination of a uniquely solvable boundary integral equation with generalized Neumann kernel and the Fast Multipole Method. Numerical results and comparison are given to illustrate the efficiency of the suggested method.

Received: March 5, 2014

AMS Subject Classification: 30E25, 31B10

Key Words and Phrases: Dirichlet problem with discontinuous coefficients, boundary integral equations, generalized Neumann kernel, simply connected region, multiply connected region

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DOI: 10.12732/ijpam.v97i4.6 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 97
Issue: 4
Pages: 447 - 479


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