N. Angleitner, M. Faustmann, J. Melenk:

"Approximating inverse FEM matrices on non-uniform meshes with H-matrices";

in: "ASC Report 14/2020", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2020, ISBN: 978-3-902627-13-1, 1 - 21.

We consider the approximation of the inverse of the finite element stiffness matrix in the data sparse H-matrix format. For a large class of shape regular but possibly non-uniform meshes including graded meshes, we prove that the inverse of the stiffness matrix can be approximated in the H-matrix format at an exponential rate in the block rank. Since the storage complexity of the hierarchical matrix is logarithmic-linear and only grows linearly

in the block-rank, we obtain an efficient approximation that can be used, e.g., as an approximate direct solver or preconditioner for iterative solvers.

FEM, H-matrices, Approximability, Non-uniform meshes

http://www.asc.tuwien.ac.at/preprint/2020/asc14x2020.pdf

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