A Novel Combination of Kernel Radial Basis Function and Finite Element Methods for 2-D Time-Harmonic Eddy Current Problems

This article proposes a novel numerical technique based on the combination of the kernel radial basis function (RBF) and traditional finite element methods (FEMs) for solving the integro-differential equation of 2-D time-harmonic eddy current problems. In this technique, the kernel RBF method is used to formulate the term of the differential operator, and the term of the integral operator is formulated by the FEM. In particular, these two methods use the same points generated by the finite element mesh in the entire computational domain. In addition, for increasing the accuracy of the proposed combination method, the algorithm of choosing shape parameters for our kernel RBFs is also used. To evaluate and demonstrate the advantages of the proposed approach, a benchmark integro-differential equation and the eddy currents in a three-phase busbar system in the 2-D domain are both investigated. The obtained numerical results demonstrate that the proposed numerical approach compares favorably with the traditional FEM.