Approximating inverse FEM matrices on non-uniform meshes with $${\mathcal{H}}$$-matrices
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AbstractWe consider the approximation of the inverse of the finite element stiffness matrix in the data sparse $${\mathcal{H}}$$ H -matrix format. For a large class of shape regular but possibly non-uniform meshes including algebraically graded meshes, we prove that the inverse of the stiffness matrix can be approximated in the $${\mathcal{H}}$$ 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.
2011 ◽
Vol 47
(3)
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pp. 271-284
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2016 ◽
Vol 3
(5)
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pp. 16-00001-16-00001
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2021 ◽
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2017 ◽
Vol 13
(3)
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pp. 119-137
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1990 ◽
Vol 112
(4)
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pp. 481-483
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