Adaptive Multilevel Methods for the Maxwell Eigenvalue Problem
This work addresses computational challenges in electromagnetic simulations for engineers and physicists, but it is incremental as it builds on existing multilevel and preconditioning techniques.
The authors tackled the Maxwell eigenvalue problem with singularities by proposing an adaptive multilevel preconditioned Helmholtz-Jacobi-Davidson method, achieving a quasi-optimal convergence factor independent of mesh sizes and levels, as confirmed by numerical experiments on complex domains.
In this paper, we propose an adaptive multilevel preconditioned Helmholtz-Jacobi-Davidson (PHJD) method for the Maxwell eigenvalue problem with singularities. The key idea in this work is to employ the local multilevel method for preconditioning the Jacobi-Davidson correction equation. It is shown that our convergence factor is quasi-optimal, which means the convergence factor is independent of mesh sizes and mesh levels provided the coarse mesh is sufficiently fine. Numerical experiments on complex domains are carried out to confirm the theoretical results and demonstrate the efficiency of the proposed method.