Maxwell's curl equations in the time domain are solved using an explicit linear finite-element approach implemented on unstructured tetrahedral meshes. For the simulation of scattering problems, a perfectly matched layer is added at the artificial far-field boundary, created by the truncation of the physical domain prior to the numerical solution. The complete solution procedure is parallelized. The computational challenges that are encountered when attempting simulations at higher frequencies suggest that the implementation of a hybrid algorithm could have certain advantages. The hybrid approach adopted uses a combination of the finite-element procedure and the well-known low operation count/low storage finite-difference time-domain method. Examples are included to demonstrate the numerical performance of the techniques that are described.
SUMMARYThe numerical simulation of practical electromagnetic scattering problems often involves geometries that are complex in shape and that may contain small scale features. The result is a large scale simulation and this requires solution techniques that are e cient, in terms of both computer time and computer memory requirements. In addition, it is advantageous if the method adopted exhibits a high degree of exibility from the viewpoint of mesh generation. Hybrid methods, based upon the coupling of the structured grid ÿnite di erence time domain approach with an unstructured ÿnite element or ÿnite volume time domain procedure, appear ideally suited to meet these requirements. The structured grid method is memory and time e cient, while the unstructured grid methods readily handle general geometries, allowing detailed deÿnition of small scale features. This paper presents the results of an initial investigation into the possibility exploiting these advantages in electromagnetic scattering simulations.
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