Abstract
We present an efficient null space free Jacobi-Davidson method to compute the positive eigenvalues of time harmonic Maxwell's equations. We focus on a class of spatial discretizations that guarantee the existence of discrete vector potentials, such as Yee's scheme and the edge elements. During the Jacobi-Davidson iteration, the correction process is applied to the vector potential instead. The correction equation is solved approximately as in the standard Jacobi-Davidson approach. The computational cost of the transformation from the vector potential to the corrector is negligible. As a consequence, the expanding subspace automatically stays out of the null space and no extra projection step is needed. Numerical evidence confirms that the proposed scheme indeed outperforms the standard and projection-based Jacobi-Davidson methods by a significant margin.
Original language | English |
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Pages (from-to) | A1-A29 |
Journal | SIAM Journal on Scientific Computing |
Volume | 37 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2015 |
Keywords
- Discrete deRham complex
- Discrete vector potential
- Edge elements
- Generalized eigenvalue problem
- Jacobi-Davidson method
- Poincaré Lemma
- Time harmonic Maxwell's equations
- Yee's scheme
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics