Abstract
| Original language | Undefined |
|---|---|
| Article number | 10.1016/j.laa.2008.12.036 |
| Pages (from-to) | 300-317 |
| Number of pages | 26 |
| Journal | Linear algebra and its applications |
| Volume | 431 |
| Issue number | 3-4 |
| DOIs | |
| Publication status | Published - Jul 2009 |
Keywords
- EWI-17315
- MSC-65L05
- MSC-65L20
- MSC-65M12
- MSC-65M20
- IR-69760
- Krylov subspace iteration
- exponential integration
- implicit integration
- conjugate gradient iteration
- METIS-264501
- Maxwell's equations
Cite this
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Unconditionally stable integration of Maxwell's equations. / Verwer, J.G.; Bochev, Mikhail A.
In: Linear algebra and its applications, Vol. 431, No. 3-4, 10.1016/j.laa.2008.12.036, 07.2009, p. 300-317.Research output: Contribution to journal › Article › Academic › peer-review
TY - JOUR
T1 - Unconditionally stable integration of Maxwell's equations
AU - Verwer, J.G.
AU - Bochev, Mikhail A.
N1 - Please note different possible spellings of the first author name: "Botchev" or "Bochev".
PY - 2009/7
Y1 - 2009/7
N2 - Numerical integration of Maxwell's equations is often based on explicit methods accepting a stability step size restriction. In literature evidence is given that there is also a need for unconditionally stable methods, as exemplified by the successful alternating direction implicit finite difference time domain scheme. In this paper we discuss unconditionally stable integration for a general semi-discrete Maxwell system allowing non-Cartesian space grids as encountered in finite element discretizations. Such grids exclude the alternating direction implicit approach. Particular attention is given to the second-order trapezoidal rule implemented with preconditioned conjugate gradient iteration and to second-order exponential integration using Krylov subspace iteration for evaluating the arising phi-functions. A three-space dimensional test problem is used for numerical assessment and comparison with an economical second order implicit-explicit integrator. We further pay attention to the Chebyshev series expansion for computing the exponential operator for skew-symmetric matrices.
AB - Numerical integration of Maxwell's equations is often based on explicit methods accepting a stability step size restriction. In literature evidence is given that there is also a need for unconditionally stable methods, as exemplified by the successful alternating direction implicit finite difference time domain scheme. In this paper we discuss unconditionally stable integration for a general semi-discrete Maxwell system allowing non-Cartesian space grids as encountered in finite element discretizations. Such grids exclude the alternating direction implicit approach. Particular attention is given to the second-order trapezoidal rule implemented with preconditioned conjugate gradient iteration and to second-order exponential integration using Krylov subspace iteration for evaluating the arising phi-functions. A three-space dimensional test problem is used for numerical assessment and comparison with an economical second order implicit-explicit integrator. We further pay attention to the Chebyshev series expansion for computing the exponential operator for skew-symmetric matrices.
KW - EWI-17315
KW - MSC-65L05
KW - MSC-65L20
KW - MSC-65M12
KW - MSC-65M20
KW - IR-69760
KW - Krylov subspace iteration
KW - exponential integration
KW - implicit integration
KW - conjugate gradient iteration
KW - METIS-264501
KW - Maxwell's equations
U2 - 10.1016/j.laa.2008.12.036
DO - 10.1016/j.laa.2008.12.036
M3 - Article
VL - 431
SP - 300
EP - 317
JO - Linear algebra and its applications
JF - Linear algebra and its applications
SN - 0024-3795
IS - 3-4
M1 - 10.1016/j.laa.2008.12.036
ER -