Discrete Quasi-Helmholtz Decomposition for 3-D High-Contrast Lossy Dielectric Problems

By applying Loop-Star decomposition of basis functions to form orthogonal transformation matrices, an efficient method for the analysis of electromagnetic scattering from three-dimensional dielectric and lossy objects, especially with high-contrast parameters to the background media, has been presented in this letter. The analysis of the diagonal blocks of the impedance matrix shows that the vector potential and scalar potential subspaces scale differently in relation to the material parameters, which may have a negative effect on the conditioning of the matrix and iteration efficiency. Therefore, new equations corresponding to the exterior and interior equations have been presented, respectively, by constructing discrete quasi-Helmholtz projection operators, based on the traditional dielectric integral formulations, i.e., Poggio-Miller-Chang-Harrington-Wu-Tsai. Numerical examples show that the proposed method is effective for high-contrast lossy dielectric objects by improving the condition number and decreasing the number of iterations.