A High-Order Accurate Parallel Solver for Maxwell’s Equations on Overlapping Grids

Authors:
William D. Henshaw
Affiliations:
-
Venue:
SIAM Journal on Scientific Computing
Year:
2006

Citing 0
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Abstract

A scheme for the solution of the time-dependent Maxwell’s equations on composite overlapping grids is described. The method uses high-order accurate approximations in space and time for Maxwell’s equations written as a second-order vector wave equation. High-order accurate symmetric difference approximations to the generalized Laplace operator are constructed for curvilinear component grids. The modified equation approach is used to develop high-order accurate approximations that use only three time levels and have the same time-stepping restriction as the second-order scheme. Discrete boundary conditions for perfect electrical conductors and for material interfaces are developed and analyzed. The implementation is optimized for component grids that are Cartesian, resulting in a fast and efficient method. The solver runs on parallel machines with each component grid distributed across one or more processors. Numerical results in two and three dimensions are presented for the fourth-order accurate version of the method. These results demonstrate the accuracy and efficiency of the approach.