Local boundary integral equation analysis of 2-dimensional potential problems using Fourier series. (English) Zbl 0673.65074
This paper presents an interesting variation of the boundary element technique which proves to be suited for local solution improvement at a particular region of the problem. The technique is based on the application of the standard interval point integral equation and a Fourier series expansion for the solution on the boundary coupled with its higher order derivatives at the internal point. Simple examples indicate considerable improvements in the performance when compared to a previous attempt which employed Taylor series expansion instead.
Reviewer: J.C.F.Telles
MSC:
65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |
65R20 | Numerical methods for integral equations |
35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
35C15 | Integral representations of solutions to PDEs |
45E10 | Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) |
Keywords:
boundary element method; boundary integral equation method; Laplace; equation; local solution improvement; interval point integral equation; Fourier series expansionReferences:
[1] | Fenner, Int. j. numer. methods eng. 26 pp 2517– (1988) |
[2] | and , Integral Equation Methods in Potential Theory and Elastostatics, Academic Press, London, 1977. · Zbl 0414.45001 |
[3] | and , Boundary Element Methods in Engineering Science, McGraw Hill, London, 1981. · Zbl 0499.73070 |
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