An integration scheme for electromagnetic scattering using plane wave edge elements |
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| Authors: | ME Honnor J Trevelyan P Bettess M El-hachemi O Hassan K Morgan JJ Shirron |
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| Affiliation: | 1. School of Engineering, Durham University, South Road, Durham DH1 3LE, UK;2. School of Engineering, Swansea University, Singleton Park, Swansea SA2 8PP, UK;3. Metron, Inc., Suite 800, 11911 Freedom Drive, Reston, Virginia, VA 20190, USA;1. School of Civil Engineering, Central South University, Changsha 410075, China;2. National Engineering Laboratory for High Speed Railway Construction, Changsha 410004, China;1. Department of Civil and Environmental Engineering, Northeastern University, Boston, MA, United States;2. Department of Civil and Construction Engineering, Western Michigan University, Kalamazoo, MI, United States;1. Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland;2. Institute of Mathematics, Lodz University of Technology, Wolczanska 215, 90-924 Lodz, Poland;1. Department of Architecture, Construction and Conservation, Università IUAV di Venezia, Dorsoduro 2206, Venice 30123, Italy;2. Department of Building Engineering, Tongji University, Shanghai 200092, China;3. College of Civil Engineering, Fuzhou University, Fuzhou, Fujian 350108, China |
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| Abstract: | Finite element techniques for the simulation of electromagnetic wave propagation are, like all conventional element based approaches for wave problems, limited by the ability of the polynomial basis to capture the sinusoidal nature of the solution. The Partition of Unity Method (PUM) has recently been applied successfully, in finite and boundary element algorithms, to wave propagation. In this paper, we apply the PUM approach to the edge finite elements in the solution of Maxwell’s equations. The electric field is expanded in a set of plane waves, the amplitudes of which become the unknowns, allowing each element to span a region containing multiple wavelengths. However, it is well known that, with PUM enrichment, the burden of computation shifts from the solver to the evaluation of oscillatory integrals during matrix assembly. A full electromagnetic scattering problem is not simulated or solved in this paper. This paper is an addition to the work of Ledger and concentrates on efficient methods of evaluating the oscillatory integrals that arise. A semi-analytical scheme of the Filon character is presented. |
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