ISSN Print: 2381-1218  ISSN Online: 2381-1226
Computational and Applied Mathematics Journal  
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Numerical Solution of Boundary Value Problems for the Laplacian in R3 in the Case of Complex Boundary Surface
Computational and Applied Mathematics Journal
Vol.1 , No. 2, Publication Date: Feb. 15, 2015, Page: 29-35
1152 Views Since February 15, 2015, 438 Downloads Since Apr. 12, 2015
 
 
Authors
 
[1]    

Olexandr Polishchuk, Department of Nonlinear Mathematical Analysis, Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, Lviv, Ukraine.

 
Abstract
 

Potential theory is one of the ways to solve the boundary value problems for the Laplacian. Well-posed solvability of integral equations equivalent to boundary value problems allow to use for their solution well known projection methods. In many applied problems the boundary surfaces have complex geometry and contain the edges and corner points. Together with the singularity in the kernel this gives rise to a singularity in the searched density of the potential. The methods are proposed for removal of singularities in the kernels and unknown densities of potentials that significantly improve the accuracy of projection methods, as well as their numerical solution.


Keywords
 

Boundary Integral Equations, Projection Methods, Collocation, Removal of Singularity


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