On a Well-Conditioned Electric Field Integral Operator for Multiply Connected Geometries

• Published in: IEEE transactions on antennas and propagation Vol. 61; no. 4; pp. 2077 - 2087
• Main Authors: Andriulli, F. P., Cools, K., Bogaert, I., Michielssen, E.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.2013; Institute of Electrical and Electronics Engineers
• Subjects: Applied classical electromagnetism; Calderón equations; EFIE; Electric breakdown; Electromagnetic wave propagation, radiowave propagation; Electromagnetism; electron and ion optics; Equations; Error analysis; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Integral equations; loop-star/tree bases; Mathematics; Matrix decomposition; MFIE; Numerical analysis; Numerical analysis. Scientific computation; Physics; Sciences and techniques of general use; Surface impedance; Vectors; Projector; MFIE; loop-star/tree bases; Electromagnetism; Discretization; Integral equations; Quasi static theory; Modelling; Topology; Calderón equations; EFIE; Calderon problem
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2012.2234072

All known integral equation techniques for simulating scattering and radiation from arbitrarily shaped, perfect electrically conducting objects suffer from one or more of the following shortcomings: (i) they give rise to ill-conditioned systems when the frequency is low (ii) and/or when the discretization density is high, (iii) their applicability is limited to the quasi-static regime, (iv) they require a search for global topological loops, (v) they suffer from numerical cancellations in the solution when the frequency is very low. This work presents an equation that does not suffer from any of the above drawbacks when applied to smooth and closed objects. The new formulation is obtained starting from a Helmholtz decomposition of two discretizations of the electric field integral operator obtained by using RWGs and dual bases respectively. The new decomposition does not leverage Loop and Star/Tree basis functions, but projectors that derive from them. Following the decomposition, the two discretizations are combined in a Calderon-like fashion resulting in a new overall equation that is shown to exhibit self-regularizing properties without suffering from the limitations of existing formulations. Numerical results show the usefulness of the proposed method both for closed and open structures.