Details
| Original language | English |
|---|---|
| Article number | 59 |
| Number of pages | 32 |
| Journal | Advances in Computational Mathematics |
| Volume | 48 |
| Issue number | 5 |
| Early online date | 13 Sept 2022 |
| Publication status | Published - Oct 2022 |
Abstract
The inverse of the stiffness matrix of the time-harmonic Maxwell equation with perfectly conducting boundary conditions is approximated in the blockwise low-rank format of H-matrices. Under a technical assumption on the mesh, we prove that root exponential convergence in the block rank can be achieved, if the block structure conforms to a standard admissibility criterion.
Keywords
- Finite element method, Helmholtz decompositions, Hierarchical matrices, Maxwell equations
ASJC Scopus subject areas
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Advances in Computational Mathematics, Vol. 48, No. 5, 59, 10.2022.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - H -matrix approximability of inverses of FEM matrices for the time-harmonic Maxwell equations
AU - Faustmann, Markus
AU - Melenk, Jens Markus
AU - Parvizi, Maryam
N1 - Funding Information: Open access funding provided by TU Wien (TUW). This work received financial support from the Austrian Science Fund (FWF) through the research program “Taming complexity in partial differential systems” (grant SFB F65) for JMM and through grant P 28367-N35 for JMM and MP and by the Deutsche Forschungsgemeinschaft (DFG) under Germany’s Excellence Strategy within the Cluster of Excellence PhoenixD (EXC 2122, Project ID 390833453) for MP. MP also acknowledges the financial support of the Alexander van Humboldt Foundation Project - matrix approximability of the inverses for FEM, BEM and FEM-BEM couplings of the electromagnetic problems.
PY - 2022/10
Y1 - 2022/10
N2 - The inverse of the stiffness matrix of the time-harmonic Maxwell equation with perfectly conducting boundary conditions is approximated in the blockwise low-rank format of H-matrices. Under a technical assumption on the mesh, we prove that root exponential convergence in the block rank can be achieved, if the block structure conforms to a standard admissibility criterion.
AB - The inverse of the stiffness matrix of the time-harmonic Maxwell equation with perfectly conducting boundary conditions is approximated in the blockwise low-rank format of H-matrices. Under a technical assumption on the mesh, we prove that root exponential convergence in the block rank can be achieved, if the block structure conforms to a standard admissibility criterion.
KW - Finite element method
KW - Helmholtz decompositions
KW - Hierarchical matrices
KW - Maxwell equations
UR - http://www.scopus.com/inward/record.url?scp=85138821964&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2103.14981
DO - 10.48550/arXiv.2103.14981
M3 - Article
AN - SCOPUS:85138821964
VL - 48
JO - Advances in Computational Mathematics
JF - Advances in Computational Mathematics
SN - 1019-7168
IS - 5
M1 - 59
ER -