Markus Faustmann

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We study the question of approximability of the inverse of the FEM stiffness matrix for the Laplace problem with Dirichlet boundary conditions by blockwise low rank matrices such as those given by the H-matrix format introduced in [Hac99]. We show that exponential convergence in the local block rank r can be achieved. Unlike prior works [BH03, Bör10a], our(More)
We consider the question of approximating the inverse W = V of the Galerkin stiffness matrix V obtained by discretizing the simple-layer operator V with piecewise constant functions. The block partitioning of W is assumed to satisfy any of the standard admissibility criteria that are employed in connection with clustering algorithms to approximate the(More)
We consider discretizations of the hyper-singular integral operator on closed surfaces and show that the inverses of the corresponding system matrices can be approximated by blockwise low-rank matrices at an exponential rate in the block rank. We cover in particular the data-space format of H-matrices. We show the approximability result for two types of(More)
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