Novel Numerical Basis Sets for Electromagnetic Field Expansion in Arbitrary Inhomogeneous Objects

• Published in: IEEE transactions on antennas and propagation Vol. 70; no. 9; pp. 8227 - 8241
• Main Authors: Georgakis, Ioannis P., Villena, Jorge Fernandez, Polimeridis, Athanasios G., Lattanzi, Riccardo
• Format: Journal Article
• Language: English
• Published: United States IEEE 01-09-2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Accuracy; Characteristic modes (CMs); electromagnetic (EM) scattering; Electromagnetic fields; Green's functions; Indexes; inhomogeneous media; magnetic resonance (MR) imaging; Magnetic resonance imaging; Mathematical analysis; Measurement; Nonhomogeneous media; numerical basis; Numerical models; Radio frequency; Reduced order models; reduced-order systems; Signal to noise ratio; Singular value decomposition; surface integral equation (SIE); volume integral equation (VIE); Characteristic modes; magnetic resonance imaging; volume-surface integral equations; numerical basis; inhomogeneous media; electromagnetic scattering; reduced-order systems
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2022.3177566

We investigated how to construct low-order subspace basis sets to accurately represent electromagnetic (EM) fields generated within inhomogeneous arbitrary objects by radio frequency sources external to Huygen's surface. The basis generation relies on the singular value decomposition of Green's functions integrodifferential operators, which makes it feasible to derive a reduced-order yet stable model. We present a detailed study of the theoretical and numerical requisites for generating such basis and show how it can be used to calculate performance limits in magnetic resonance imaging applications. Finally, we propose a novel numerical framework for the computation of characteristic modes of arbitrary inhomogeneous objects. We validated accuracy and convergence properties of the numerical basis against a complete analytical basis in the case of a uniform spherical object. We showed that the discretization of Huygens's surface has a minimal effect on the accuracy of the calculations, which mainly depends on the EM solver resolution and order of approximation.