Tree gauging in lossy high frequency FEM models

Wave propagation problems involving both high conductivity materials and large non-conducting domains are solved in the frequency domain by the method of finite elements (FEM) using edge and nodal basis functions and applying the A,V-formulation. The singular matrix of the resulting algebraic equation system is regularized by tree gauging to facilitate its direct solution. It is shown that choosing a random tree can result in erroneous solutions even if a highly sophisticated sparse parallel direct equation system solver is used. This problem is overcome by generating the tree by a special algorithm taking account of the presence of high conductivity materials. Two numerical examples are investigated: an academic 1D wave propagation problem and a real-world 3D antenna.