Inmost Singularities And
Appropriate Quadrature Rules In The
Boundary Element Method
Author(s)
E. E. Theotokoglou & G. Tsamasphyros
Abstract
The solution of singular integral equations (SIEs), taking into consideration the
particular behaviour of its regular kernel and its right hand side function, is
investigated in this paper. In particular, the problems appearing in the solution of
singular integral equations in the boundary element method are verified. It is
shown that the behaviour of singular integral equations does not depend only on
the behaviour of the regular kernel but on the behaviour of the unknown
function.
Keywords: singular integral equation, singularities, nearby poles, elasticity,
quadrature formula, numerical integration, boundary element method.
1 Introduction
Many problems in the boundary element method can be reduced to a singular
integral equation or to systems of singular integral equations [1]. For the solution
of these equations where the known functions are Hölder continuous,
approximate solutions through numerical techniques preserving the correct
nature of singularities of the unknown function, have been developed [1–10].
Problems in the numerical solution of singular integral equations appear
because of the Cauchy singularities, either from the unknown function or from of
the poles of the known functions. In addition the regular Kernels of the singular
integral equation may have either nearby poles, or branch points, or jump
discontinuities.
Keywords
singular integral equation, singularities, nearby poles, elasticity,
quadrature formula, numerical integration, boundary element method.
Related Book
Other papers in this volume
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