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The Boundary Element Method (BEM) has become an efficient and popular alternative to the Finite Element Method (FEM) because of its ability, at least for some problems with constant coefficients, of reducing a Boundary Value Problems (BVP) for a linear Partial Differential Equation (PDE) defined in a domain to an integral equation defined on the boundary, leading to a simplified discretisation process with boundary elements only. The main requirement for the reduction of the PDE to a Boundary Integral Equation (BIE) is that a fundamental solution to the PDE must be available. Such fundamental solutions are well known for many PDEs with constant coefficients, see, but are not generally available when the coefficients of the original PDE are variable.
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