Novel 3D orthogonal basis functions for the vector wave equation solution

Abstract

New three-dimension orthogonal basis functions for finite element solution of the vectorial wave equation are presented. These functions, based on the Whitney edge elements, maintain the same characteristics as those of conventional basis functions with the advantage of naturally generating diagonal matrices during calculation. This approach completely eliminates the necessity of solving a linear system of equations at each time step, as it is required by conventional numerical methods.