A Volume-Surface Integral Equation for Electromagnetic Modeling
Conventional methods for solving 3-D volume integral equations in electromagnetic (EM) modeling produce matrices that are ill-conditioned when the conductivity contrast between the target and the host is large or when the host resistivity itself is small. This problem is especially acute when pulse basis functions represent the scattering currents because the artificial discontinuities in the current create spurious charges in homogeneous conductive regions (where there are no physical charges). Basis functions with higher-order continuity do not entirely eliminate this problem. The field of these charges is amplified at high host resistivities by Green’s tensor and artificially attenuates the physical vortex currents. We present a new formulation that eliminates these spurious charges analytically by replacing the volume integral for the field caused by charges (on the boundary of homogeneous regions) with a surface integral, while retaining the volume integral for the field of the induced currents. This formulation is mathematically closer to the physics of EM induction and effectively removes a major source of error. Also, condition numbers of matrix systems without artificial charges are also much smaller than those of the conventional method.