Keywords: electromagnetic wave scattering, Maxwell's curl equations, hybrid algorithm, time domain, explicit-implicit.

There are a number of practical problems, involving complex geometries and materials, that require the numerical solution of Maxwell's equations. In this paper, we concentrate on one selected application area, which is the simulation of scattering of plane electromagnetic waves by a perfectly conducting obstacle. We develop a hybrid solution procedure, which couples a modification of a finite element time domain approach [1], used on an unstructured grid in the vicinity of the scatterer, with the explicit finite difference time domain method [2], used for the remainder of free space on a Cartesian grid. This approach requires the solution of the hybrid mesh generation problem and needs to account for inter-mesh transfer of information. The far field boundary condition is imposed by the addition of an artificial perfectly matched layer, located at a finite distance from the obstacle. Automatically generated unstructured meshes can contain a number of small elements, because of the constraints that may be imposed due to the complexity of the geometry. With an explicit solution scheme, the appearance of these elements results in a severe limitation on the size of the allowable time step and a corresponding significant rise in the CPU time. We will demonstrate how this effect may be alleviated, and computational efficiency maintained, by adopting an implicit-explicit implementation on the unstructured portion of the mesh. The complete simulation process is parallelised to enable the solution of large scale problems. The results obtained for the simulation of a problem of scattering by a perfectly conducting cone-sphere configuration are described and the computational performance that can be achieved is demonstrated.

1

K. Morgan, O. Hassan and J. Peraire, An unstructured grid algorithm for the solution of Maxwell's equations in the time domain, International Journal for Numerical Methods in Fluids, 19, 849-863, 1994. doi:10.1002/fld.1650190907

2

K. S. Yee, Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media, IEEE Transactions on Antennas and Propagation, 14, 302-307, 1966. doi:10.1109/TAP.1966.1138693

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