Additive Schwarz Methods for the hp Version of the Boundary Element Method in ℝ3
For the Galerkin matrices of the hypersingular and weakly singular first kind integral equations on plane surfaces we present preconditioners obtained by additive Schwarz methods. When those integral equations are solved numerically by the Galerkin boundary element method the resulting matrices become ill-conditioned. Hence, for an efficient solution procedure appropriate preconditioners are necessary to reduce the number of CG-iterations. We consider the hp version of the boundary element method and show how to decompose the boundary element spaces such that the resulting preconditioned Galerkin matrices have in the worst case condition numbers which are only polylogarithmically growing with respect to the discretization parameters, i.e. the mesh size h and the polynomial degree p.
KeywordsBoundary Element Method Single Layer Potential Hypersingular Integral Equation Interior Function Wire Basket
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