Effective Preconditioners for Maxwell's equations on Unstructured Grids for Coupled Plasma-EM Wave Modeling

摘要

Numerical simulations of electromagnetic waves interacting with plasmas are useful in understanding the physics of plasma based photonic crystals and metamaterials and can assist the design of such materials. A computational model is developed for this purpose and it solves the Maxwell's and fluid plasma equations within an unstructured mesh framework. The curl-curl equation for electric field is discretized in space using the lowest order H(curl) conforming Nedelec elements of the first type. The chief bottleneck in the solution process is the time taken by the Krylov method to solve the linear system arising out of the curl-curl equation.This issue is addressed using a preconditioning technique based on the decomposition of the Nedelec edge element space into stable components in H~1 conforming finite elements on the same mesh infrastructure, introduced by Hiptmair and Xu. The preconditioner is implemented for a benchmark test problem and a practical simulation of electromagnetic wave interacting with a plasma slab in a rectangular wave guide. The preconditioned Krylov method performs significantly better than standard methods (ILU, block Jacobi) with respect to the number of iterations and wall clock time taken for the linear system to converge.