Keywords: computational electromagnetics, scattering, time domain, hybrid algorithm, overlapping meshes, parallelisation.

This paper considers the solution of large scale problems in electromagnetics in the time domain. The selected application area is the simulation of the interaction between a plane electromagnetic wave by a general layered scatterer. 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. Information is transferred accurately and efficiently between the two solution algorithms by overlapping the meshes in such a way that the vertices of the two meshes coincide in the overlap region. 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 and the efficiency of the parallelisation is demonstrated. The results obtained for the simulation of a problem of scattering by a perfectly conducting UAV configuration are described and the computational performance that can be achieved is presented.

[1]

K. Morgan, O. Hassan, 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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