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

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.