A Gradient Weighted Finite Element Method (GW-FEM) for Static and Quasi-Static Electromagnetic Field Computation

This paper presented a Gradient Weighted Finite Element Method (GW-FEM) for solving electromagnetic problems. First, the analysis domain is discretized into a set of triangular or tetrahedral elements which are easy to automatically generate. Then, Gradient Weighted influence domains are further constructed by the center element with all the adjacent elements. The Galerkin Weak form is evaluated based on these influence domains. The GW-FEM is employed here for the solution of static and quasi-static electromagnetic problems by using linear triangular or tetrahedral elements. All the properties of GW-FEM are proved theoretically and analyzed in detail. Consistency between four benchmark results is obtained by GW-FEM and analytical results verify the accuracy, stability, and potential of this method. It turns out that GW-FEM possesses potentials in the applications of electromagnetic problems.