Density results with linear combinations of translates of fundamental solutions
Journal of Approximation Theory
The under-determined version of the MFS: Taking more sources than collocation points
Applied Numerical Mathematics
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The method of fundamental solutions (MFS) is a Trefftz–type technique in which the solution of an elliptic boundary value problem is approximated by a linear combination of translates of fundamental solutions with singularities placed on a pseudo–boundary, i.e., a surface embracing the domain of the problem under consideration. In this work, we develop a mathematical framework for the numerical implementation of the MFS in elliptic systems. We obtain density results, with respect to the C ℓ-norms, which establish the applicability of the method in certain systems arising from the theory of elastostatics and thermo-elastostatics. The domains in our density results may possess holes and they satisfy the segment condition.