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

An adaptive mesh refinement procedure is presented in order to address efficiently low-frequency electromagnetic problems with the unstructured partial element equivalent circuit (PEEC) method. A posteriori error estimator based on an equilibrated energy criterion is proposed, which means that two dual solutions are necessary. In fact, 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 ensure 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 is the TEAM Workshop problem no°7. Second, a circuit coupling test case is a laminated busbar, this last one being treated for a low-frequency case and also for the dc case. The adaptive mesh refinement procedure has shown great potential and makes the unstructured PEEC method much more functional and attractive for modeling complex devices.