Publications in Scientific Journals:
N. Angleitner, M. Faustmann, J. Melenk:
"Approximating inverse FEM matrices on non-uniform meshes with H-matrices";
Calcolo,
3
(2021),
31;
1
- 36.
English abstract:
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.
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1007/s10092-021-00413-w
Created from the Publication Database of the Vienna University of Technology.