Integral equation analysis of complex (M)MIC-structures with optimized system matrix decomposition and novel quadrature techniques

Using integral equation methods for the analysis of complex (M)MIC structures, the computation and storage effort for the solution of the linear systems of equations with their fully populated matrices still forms the main bottleneck. In the last years, remarkable improvements could be achieved by means of diakoptic methods and related preconditiners. In this contribution, we present a method based on the optimized decomposition of the system matrix depending on the circuit topology. The system matrix is splitted in a densely populated matrix and a mainly blockdiagonal matrix with overlapping submatrices. The latter matrix is used for the generation of high performance preconditioners within Krylov subspace methods using sparsified matrix storage methods, adaptive Cholesky decompositions and optimized forward/backward substitutions. Furthermore, we present an integration technique using a complete analytical treatment for the strongly oscillating parts of the spectral domain integrands allowing the analysis of very large structures as compared to the wavelength.