Selection of Basis Functions for Volume-Surface Integral Equation Using Spanning Tree

Problem of electromagnetic scattering by a system of wires, conductive surfaces and magnitodielectric volumes is solved. It is reduced to solution of volume-surface integral equations (VSIE). For approximation of equivalent electric and magnetic currents basis functions based on Rao-Wilton-Glisson (RWG) and Shaubert-Wilton-Glisson (SWG) functions are used. Integral equations are used in a form which unites formulations for different regions. To ensure linear independence of basis functions and absence of artificial charges inside volume elements the spanning tree of the graph representing topology of the mesh is constructed. Proposed method coupled with multilevel fast multipole algorithm (MLFMA) is applied to scattering on perfectly conducting sphere coated by dielectric layer.