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arXiv · 2005.04999

Approximating inverse FEM matrices on non-uniform meshes with $\mathcal{H}$-matrices

Niklas Angleitner·Markus Faustmann·Jens Markus Melenk
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Abstract

We consider the approximation of the inverse of the finite element stiffness matrix in the data sparse $\mathcal{H}$-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 $\mathcal{H}$-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.

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Niklas Angleitner, Markus Faustmann, Jens Markus Melenk. 2020-05-11. Approximating inverse FEM matrices on non-uniform meshes with $\mathcal{H}$-matrices. https://doi.org/10.1007/s10092-021-00413-w

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