Efficient partial elements computation for the non-orthogonal PEEC method including conductive, dielectrics and magnetic materials

The partial element equivalent circuit method is a well-known numerical technique that is used to solve Maxwell’s equations in their integral equation form. The application of the PEEC method to modeling domains with non-orthogonal three-dimensional geometries requires the computation of the interaction integrals to be performed numerically, thus slowing down the overall computation. This work presents a new technique that allows improving the computation of the interaction integrals of the PEEC method for non-orthogonal geometries under the quasi-static hypothesis. To this purpose, a voxelization approach that automatically decomposes non-orthogonal volumes in elementary parallelepipeds is used, allowing the implementation of closed-form formulas for the interaction integrals and completely avoiding numerical integration. The proposed approach is applied to three example problems exhibiting very good accuracy and excellent speed-up compared to the standard one using the numerical integration.

The partial-element equivalent circuit method is a well-known numerical technique that is used to solve Maxwell's equations in their integral equation form. The application of the partial-element equivalent circuit (PEEC) method to modeling domains with non-orthogonal three-dimensional geometries requires the computation of the interaction integrals to be performed numerically, thus slowing down the overall computation. This work presents a new technique that allows improving the computation of the interaction integrals of the PEEC method for non-orthogonal geometries under the quasi-static hypothesis. To this purpose, a voxelization approach that automatically decomposes non-orthogonal volumes in elementary parallelepipeds is used, allowing the implementation of closed-form formulas for the interaction integrals and completely avoiding numerical integration. The proposed approach is applied to three example problems exhibiting very good accuracy and excellent speed-up compared with the standard one using the numerical integration.