Recent Progress in the Radial Integration Boundary Integral and Integro-Differential Equation Methods for Numerical Solution of Problems withVariable Coefficients

[摘要] The Boundary Element Method (BEM) has become an efficient andpopular alternative to the Finite Element Method (FEM) because of itsability, at least for some problems with constant coefficients, of reducinga Boundary Value Problems (BVP) for a linear Partial DifferentialEquation (PDE) defined in a domain to an integral equation definedon the boundary, leading to a simplified discretisation process withboundary elements only. The main requirement for the reduction ofthe PDE to a Boundary Integral Equation (BIE) is that a fundamentalsolution to the PDE must be available. Such fundamental solutions arewell known for many PDEs with constant coefficients, see [1-4], butare not generally available when the coefficients of the original PDEare variable.