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High-Order Discrete Helmholtz Decompositions for the Electric Field Integral Equation

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2 Author(s)
Michael J. Bluck ; Dept. of Mech. Eng., Imperial Coll. of Sci., Technol. & Med., London ; Simon P. Walker

We develop a differential form based formalism to address the problem of low-frequency breakdown of the electric field integral equation (EFIE). Note, in this formalism we approximate the surface magnetic field, not the surface current as is conventionally the case. A discrete Helmholtz decomposition is achieved for both triangular and quadrilateral curvilinear meshes based on a star-cotree decomposition. These decompositions are based upon the construction of a canonical basis which ab-initio possess the required separation into irrotational and nonirrotational spaces. This makes the process of construction clear and generally applicable. The construction of appropriate bases is demonstrated for a range of interpolation orders. The effects of these constructions is demonstrated on a simple flat PEC plate problem

Published in:

IEEE Transactions on Antennas and Propagation  (Volume:55 ,  Issue: 5 )