Mechanical Quadrature Method and Splitting Extrapolation for Solving Dirichlet Boundary Integral Equation of Helmholtz Equation on PolygonsReportar como inadecuado




Mechanical Quadrature Method and Splitting Extrapolation for Solving Dirichlet Boundary Integral Equation of Helmholtz Equation on Polygons - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Journal of Applied MathematicsVolume 2014 2014, Article ID 812505, 7 pages

Research ArticleSchool of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China

Received 20 February 2014; Revised 20 June 2014; Accepted 22 June 2014; Published 10 July 2014

Academic Editor: Bo Yu

Copyright © 2014 Hu Li and Yanying Ma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the numerical solution of Helmholtz equation with Dirichlet boundary condition. Based on the potential theory, the problem can be converted into a boundary integral equation. We propose the mechanical quadrature method MQM using specific quadrature rule to deal with weakly singular integrals. Denote by the mesh width of a curved edge of polygons. Then, the multivariate asymptotic error expansion of MQM accompanied with for all mesh widths is obtained. Hence, once discrete equations with coarse meshes are solved in parallel, the higher accuracy order of numerical approximations can be at least by splitting extrapolation algorithm SEA. A numerical example is provided to support our theoretical analysis.





Autor: Hu Li and Yanying Ma

Fuente: https://www.hindawi.com/



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