Block partitioned Gauss-Seidel PEEC solver accelerated by QR-based coupling matrix compression techniques

Abstract

Electromagnetic (EM) integral equation solvers based on the partial element equivalent circuit (PEEC) approach have proven to be well suited for modeling combined circuit and EM problems. The solution of the full-wave electromagnetic part is transformed to the circuit domain and general well-known circuit solver techniques are applied. However owing to the mutual couplings in the PEEC formulation, the MNA matrix is not sparse as in the case of general lumped circuits. This gives rise to a time and memory bottleneck. A Gauss-Seidel relaxation (GSR) solver is presented as an appropriate alternative to SPICE sparse LU solvers, for the PEEC class of problems in the frequency domain. Circuit based block partitioning schemes similar to the ones used in waveform relaxation methods with known convergence properties are used to insure fast convergence. Furthermore, circuit coupling thinning schemes based on QR compression techniques are used to accelerate the inter block updates and also intra block solutions.