The Numerical Solution of First Kind Integral Equation for the Helmholtz Equation on Smooth Open Arcs
Year: 2001
Author: Wei-Jun Tang, Hong-Yuan Fu, Long-Jun Shen
Journal of Computational Mathematics, Vol. 19 (2001), Iss. 5 : pp. 489–500
Abstract
Consider solving the Dirichlet problem of Helmholtz equation on unbounded region $R^2$\Γ with Γ a smooth open curve in the plane. We use simple-layer potential to construct a solution. This leads to the solution of a logarithmic integral equation of the first kind for the Helmholtz equation. This equation is reformulated using a special change of variable, leading to a new first kind equation with a smooth solution function. This new equation is split into three parts. Then a quadrature method that takes special advantage of the splitting of the integral equation is used to solve the equation numerically. An error analysis in a Sobolev space setting is given. And numerical results show that fast convergence is clearly exhibited.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2001-JCM-9001
Journal of Computational Mathematics, Vol. 19 (2001), Iss. 5 : pp. 489–500
Published online: 2001-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Helmholtz equation Quadrature method.