A Null-space free Jacobi-Davidson Method for Maxwell's equation


Prof. Wei-Cheng Wang (National TsingHua University, Taiwan)


2012.02.03 14:00-15:00


601 Pao Yue-Kong Library


We present an efficient null-space free method to compute the positive eigenvalues of the degenerate elliptic operator arising from time-harmonic Maxwell’s equations. We focus on a class of spatially compatible discretizations such as Yee’s scheme, co-volume discretization and the edge elements, which guarantees the existence of a discrete vector potential. During the Jacobi-Davidson iteration, a new correction equation is derived and solver for the the correction. The correction equation only needs to be solved approximately as in the standard Jacobi-Davidson approach.The computational cost of the transformation from the vector potential back to the correcting vector is negligible. As a consequence, the corrected subspace automatically stays out of the (huge) null-space and no extra Helmholtz projection step is needed. Numerical evidence confirms that the new method outperforms standard projection-based Jacobi-Davidson method by a significant margin.