Extended Meshfree Point Collocation Method for Electromagnetic Problems With Layered Singularity

A novel meshfree point collocation method for solving the electromagnetic potential problems with layered singularity is presented. The approximation based on the moving least squares technique is enriched by Heaviside step function, scissor function and wedge function. It effectively models discontinuities in electromagnetic potential and its gradient fields. Direct discretization of the partial differential equations yields the system of equations so that the computational speed is very fast compared to the Galerkin formulation. Solving the system provides the nodal solutions and jump strengths on the singular layer at the same time. Numerical results show that the developed method is highly efficient and reliable in solving electrostatic problems with charge layer or insulating layer.