Meshfree computation of electrostatics and related boundary value problems

Abstract

We discuss a meshfree method for solving boundary value problems in physics. The method uses random data interpolation and radial basis functions that depend on the distance, instead of the usual basis functions that depend on the position. As an example, we apply this method to the electrostatic problem of two parallel plates inside a conducting cylinder and discuss its convergence and robustness. The method is shown to be robust and flexible and can be an efficient alternative to mesh-based methods for solving computational problems involving irregular domains.