A Highly Scalable Boundary Integral Equation and Walk-On-Spheres (BIE-WOS) Method for the Laplace Equation with Dirichlet Data

2021 ◽  
Vol 29 (5) ◽  
pp. 1446-1468
Author(s):  
Changhao Yan
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Laplace Equation ◽  
Boundary Integral ◽  
Dirichlet Data

Haar Wavelet for the Natural Boundary Integral Equation

2014 ◽  
Vol 635-637 ◽  
pp. 1569-1573
Author(s):  
Zhe Wang
Keyword(s):  
Integral Equation ◽  
Numerical Solution ◽  
Explicit Expression ◽  
Boundary Integral Equation ◽  
Laplace Equation ◽  
Haar Wavelet ◽  
Boundary Integral ◽  
Natural Boundary ◽  
Wavelet Method ◽  
Numerical Example

In this paper, we construct Haar wavelet and apply it to investigate the numerical solution of the natural boundary integral equation of the Laplace equation in the concave angle domains. Haar wavelet has better stability and good explicit expression. Moreover, they are mutual orthogonal. We make full use of their mutual orthogonal to cope with the natural boundary integral equation. Taking advantage of Galerkin-wavelet method in discretizing the natural boundary integral equation. Finally, a numerical example is shown and the feasibility and validity of the method are proved.

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