Application notes on a lossy medium model in the method of auxiliary sources and solving of eigenvalue problems

This paper describes numerical solving of the Laplace operator's eigenvalue problem for domain with space periodic boundaries, based on the Method of Auxiliary Sources (MAS) and with a lossy medium model. It discusses space periodic green function's representation in different sum and their convergence properties. A lossy medium model in the MAS is analyzed and assessed its applicability solveing eigenvalue problems in case of periodic boundaries of arbitrary shape.