Commun. Comput. Phys., 5 (2009), pp. 126-141.

A Hybrid Finite Element-Laplace Transform Method for the Analysis of Transient Electromagnetic Scattering by an Over-Filled Cavity in the Ground Plane

Junqi Huang 1, Aihua W. Wood 1*, Michael J. Havrilla 1

1 Air Force Institute of Technology, 2950 Hobson Way, Wright-Patterson AFB, OH 45433, USA.

Received 29 November 2007; Accepted (in revised version) 1 May 2008
Available online 15 July 2008


A hybrid finite element-Laplace transform method is implemented to analyze the time domain electromagnetic scattering induced by a 2-D overfilled cavity embedded in the infinite ground plane. The algorithm divides the whole scattering domain into two, interior and exterior, sub-domains. In the interior sub-domain which covers the cavity, the problem is solved via the finite element method. The problem is solved analytically in the exterior sub-domain which slightly overlaps the interior sub-domain and extends to the rest of the upper half plane. The use of the Laplace transform leads to an analytical link condition between the overlapping sub-domains. The analytical link guides the selection of the overlapping zone and eliminates the need to use the conventional Schwartz iteration. This dramatically improves the efficiency for solving transient scattering problems. Numerical solutions are tested favorably against analytical ones for a canonical geometry. The perfect link over the artificial boundary between the finite element approximation in the interior and analytical solution in the exterior further indicates the reliability of the method. An error analysis is also performed.

AMS subject classifications: 35M10, 65M60

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Key words: Overfilled cavity, time domain electromagnetic scattering, Laplace transform, finite element method.

*Corresponding author.
Email: (J. Huang), (A. W. Wood), (M. J. Havrilla)

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