Tetrahedral-Based Vector Generalized Finite Element Method and Its Applications

Vector generalized finite element method was first introduced as a meshless method. Its application to practical problems was stymied by the fact that one needs information of intersection of the partition of unity domains with the boundaries of the problem domain. The framework presented in Tuncer 's work (IEEE Trans. Antennas Propag., vol. 58, no. 3, 887-899, Mar. 2010) overcame this bottleneck. In this letter, the framework is extended to tetrahedral meshes and applied to a number of electromagnetic problems. These examples are chosen so as to highlight some features of the method such as higher-order convergence, flexibility in the choice of basis functions, and use of different types of basis functions or mixed polynomial orders within a simulation.