A Simple Way to Enforce Boundary Conditions in the Solution of Volume-Surface Integral Equation

In the numerical modeling of composite perfect electric conductor (PEC)-dielectric objects using the volume-surface integral equation (VSIE), both normal and tangential boundary conditions (BCs) of electric field are enforced on the PEC-dielectric interfaces (PDIs) through an explicit formula. When solving the BC-enforced VSIE with the method of moments (MoM), the BC equation is discretized and tested by the commonly used SWG functions. An extremely sparse sub-matrix is then generated, which will take the place of the conventional fully-populated one yielded by the traditional VSIE. The memory usage is thereby reduced significantly, accompanied with less matrix filling and matrix-vector product time. Compared with existing BC-enforced VSIE methods, the proposed one not only features a simpler implementation, but also saves more core memory. The explicit enforcement of BCs also reduces numerical modeling error, which accelerates the convergence of iterative solvers.