A NULL SPACE FREE JACOBI-DAVIDSON ITERATION FOR MAXWELL'S OPERATOR

作者：Huang Yin Liang^*; Huang Tsung Ming; Lin Wen Wei; Wang Wei Cheng

来源：SIAM Journal on Scientific Computing, 2015, 37(1): A1-A29.

DOI：10.1137/140954714

• time harmonic Maxwell's equations
• Yee's scheme
• edge elements
• generalized eigenvalue problem
• discrete vector potential
• discrete deRham complex
• Poincare Lemma
• Jacobi-Davidson method

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.

• 出版日期2015
• 单位清华大学