Error Estimation and Adaptive Mesh Refinement for the Unstructured Inductive PEEC Formulation

Abstract

An adaptive mesh refinement procedure is presented in order to address efficiently low frequencies electromagnetic problems with the unstructured PEEC method. An a posteriori error estimator based on an equilibrated energy criterion is proposed, which means that two dual solutions are necessary. Actually, knowing that there is no dual formulation for the PEEC method, an auxiliary method is proposed in order to calculate a second admissible solution. This method is based on a projection of the PEEC solution from facets to edges function space in order to ensures the continuity of the electric field in the mesh. Two test cases have been treated in order to show the efficiency of the procedure. First, an inductive coupling test case which is the TEAM Workshop problem no • 7. Second, a circuit coupling test case which is a laminated busbars, this last one being treated for a low frequency case and also for the DC case. Adaptive mesh refinement procedure has shown great potential and makes the unstructured PEEC method much more functional and attractive for modeling complex devices.