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[In this chapter, we construct numerical solutions to the problems in the field of solid mechanics by combining theMethodBoundary Element Boundary Element Method (BEM) with interpolation by means ofRadial basis functions radial basis functions. The main task is to find an approximation to a particular solution of the corresponding elliptic system of partial differential equations. To construct the approximation, the differential operator is applied to a vector of radial basis functions. The resulting vectors are linearly combined to interpolate the function on the right-hand side. The solvability of the interpolation problem is established. Additionally, stability and accuracy estimates for the method are given. A fast numerical method for the solution of the interpolation problem is proposed. These theoretical results are then illustrated on several numerical examples related to theLamésystem Lamé system.]
Published: Feb 2, 2019
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