Numerical Solution of a Surface Hypersingular Integral Equation by Piecewise Linear Approximation and Collocation Methodsстатья
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 12 сентября 2019 г.
Аннотация:A linear hypersingular integral equation is considered on a surface (closed or nonclosed
with a boundary). This equation arises when the Neumann boundary value problem for the Laplace
equation is solved by applying the method of boundary integral equations and the solution is represented
in the form of a double-layer potential. For such an equation, a numerical scheme is constructed
by triangulating the surface, approximating the solution by a piecewise linear function, and
applying the collocation method at the vertices of the triangles approximating the surface. As a result,
a system of linear equations is obtained that has coefficients expressed in terms of integrals over partition
cells containing products of basis functions and a kernel with a strong singularity. Analytical formulas
for finding these coefficients are derived. This requires the computation of the indicated integrals.
For each integral, a neighborhood of the singular point is traversed so that the system of linear
equations approximates the integrals of the unknown function at the collocation points in the sense of
the Hadamard finite part. The method is tested on some examples.