A Multi-Resolution Moment Method for Wire-Surface Objects

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Abstract
We present a multi-resolution (MR) basis for the method of moments (MoM) analysis of the electric field integral equation (EFIE) for fully arbitrary 3-D conductors composed of wires connected to surfaces. Representation of the unknown current with the MR basis results in a physics-based preconditioner, especially for geometrically complex and/or finely meshed structures, and/or low frequency problems. The proposed MR basis is constructed as a linear combination of the basis functions usually employed in the MoM-based codes, namely the piecewise linear (PWL) functions for wires modelled via line segments, the Rao-Wilton-Glisson (RWG) functions for surfaces modelled with triangles, and junction basis functions for modelling their connections. The key challenge and the novelty of the present work is the construction of multi-resolution basis functions defined on arbitrary cells formed by triangles and line segments modelling surfaces, wires and junctions that coherently include all three types of conventional basis functions. Application of the MR basis results in a basis change, algorithmically equivalent to a purely multiplicative algebraic preconditioner of the EFIE, that can be easily interfaced with pre-existing MoM codes.

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