Application of two radial basis function-pseudospectral meshfree methods to three-dimensional electromagnetic problems
In this study the authors present an application of the radial basis function-pseudospectral (RBF-PS) meshfree method as well as a least squares variant thereof to a three-dimensional (3D) benchmark engineering problem defined by the Laplace equation. To their knowledge this is the first such study. The RBF-PS method is a version of the radial basis function (RBF) collocation method formulated in the vein of traditional pseudospectral methods. The least squares RBF-PS method introduced here as a modification of the RBF-PS method allows the authors to work with fewer RBFs while maintaining a high number of collocation points. In addition, the authors use a leave-one-out cross validation algorithm to choose an ‘optimal’ shape parameter for their basis functions. In order to evaluate the accuracy, effectiveness and applicability of their new approach, the authors apply it to a 3D benchmark electromagnetic problem. Their numerical results demonstrate that the proposed methods compare favourably to the finite difference and finite element methods.
