Edge Meshless Method Applied to Vector Electromagnetic Problems

A challenge in meshless methods dealing with vector electromagnetic problems is to produce numerical solutions that are free of spurious modes given that the generated vector field does not satisfy the condition of zero divergence. The edge meshless method (EMM) constructs its approximations using special shape functions based on edges to produce vector fields that are divergence free and to guarantee the continuity of the tangential field components. This paper presents the application of the EMM to solve vector electromagnetic problems. The 2-D Maxwell eigenvalue problem with anisotropic medium is tested to demonstrate that the technique produces correct numerical solution without spurious modes.