Efficient Calculation of the Partial Elements for the Orthogonal PEEC Method With the Integer-Varying Nonuniform Meshes

A nonuniform orthogonal mesh generation scheme, namely, the integer-varying meshes, is proposed to model realistic conductor systems with the partial element equivalent circuit (PEEC) method in this article. The integer-varying meshes resolve the weak geometry description ability and unrealistic of uniform meshes, thus yielding frequency-independent circuits for skin-effect modelling. In comparison to generic nonuniform meshes, the calculation of the partial elements can be significantly accelerated by the integer-varying meshes in coordination with the partial inductance approximation scheme and tabulation. The accuracy of the partial inductance approximation scheme is validated for partial inductance units with a wide range of aspect ratios and relative distance. In addition, to deal with the cells with extreme aspect ratios generated by the integer-varying meshes, stable model order-reduced formulas for partial elements are adopted; such proposed model, at the same time, is able to speed up the calculation, when the formula for the partial self potential coefficient is modified for stability at extreme aspect ratios. Through three numerical examples, including an L-shaped trace over a ground, a single loop coil and a 3-D spiral inductor, the efficiency of the integer-varying meshes with the partial inductance approximation and tabulation is verified by comparison to the case without approximation or tabulation, and the results demonstrate good consistency to the references.