Parallel implementation of Galerkin technique in large-scale electromagnetic problems

An integral equation formulation in conjunction with a parallelised Galerkin technique is employed to solve large-scale electromagnetic (EM) problems. The proposed technique is applicable to EM structures consisting of similar conducting or dielectric parts, defined as 'elements'. Coupled integral equations are derived in the frequency domain, written in terms of the conductivity currents or the electric fields developed on the conducting or dielectric 'elements' surfaces, respectively. The system of integral equations is numerically solved via the parallel computed Galerkin technique, with convenient entire domain basis functions. Even for electrically large structures, the use of entire domain basis functions leads to relatively small order linear systems and the main computational cost refers to the matrix fill rather than the matrix solution. The parallelisation introduced to the computation of the matrix elements overcomes the limitation of using Method of Moments at lower and resonant frequencies. The inherent parallelism of the introduced technique allows for the results to be obtained with minimal additional to the sequential code programming effort. Two indicative electromagnetic compatibility applications are presented, concerning the coupling of incident waves with multiple conducting rectangular plates and the coupling phenomena occurring in a multi-element waveguide array looking into a layered lossy cylinder. Numerical results are presented, while the applicability/suitability of diverse High Performance Computing platforms is judged, based on both performance obtained and ease of code portation.