Novel volume integral equations for broad frequency and material parameter electromagnetic analysis

Background. The ability to determine EM phenomena inside highly heterogeneous media that have regions with a large electric and/or negative permittivity has many potential biological, geophysical, metamaterial, and plasma applications. Currently, volume integral equations (VIEs) are used to analyze EM scattering from highly heterogeneous materials. Unfortunately, when used to analyze EM scattering from materials with a much different electric permittivity than that of their surrounding medium (i.e., high or negative permittivity objects), their discretization calls for very fine meshes and results in ill-conditioned systems of equations. 

Objective. This project aims to develop a volume integral equation solver that is stable for analysis of low-frequency and high/low/negative-permittivity.

Approach. We introduce a novel internally combined volume-surface integral equation (ICVSIE) that involves a judicious combination of volume along with surface equivalent principles.  When approximated using standard Galerkin methods, the ICVSIE yields matrices with condition numbers that are unaffected by the materials’ maximum permittivity and its sign. 

Main result. Unlike other methods, the ICVSIE method can be used to determine EM phenomena occurring inside objects with arbitrarily high permittivity and at a broad range of frequencies, enabling its use as the first general-purpose tool for EM analysis of medical applications. Furthermore, the ICVSIE is negative-permittivity stable and it is the first solver capable of analyzing the blackout that occurs whenever space vehicles travel through negative-permittivity plasma regions of the Earth’s atmosphere. 

Significance. A general-purpose EM solver enables medical professionals with little background in EM to accurately conduct EM analyses of their medical procedures and improve them, thereby streamlining new technological development. This technology will aid in designing new antennas that generate EM signals that can penetrate the plasma and do not cause a communication blackout.