Vector Nodal Meshless Method for 3D Magnetostatic Applications

Traditional meshless methods use scalar-based functions and therefore, present difficulties in approximating vector fields. The Vector Nodal Meshless Method (VNMM) constructs its approximations using shape functions based on edges whose length tends to zero in order to reproduce vector fields. The VNMM has been applied to solve two-dimensional electromagnetic problems [1]. This paper presents the construction of VNMM functions for use in three dimensions vectorial problems. The formulation is tested using a magnetostatic shielding problem with analytical solution.