## Application of two radial basis functionpseudospectral meshfree methods to three-dimensional electromagnetic problems

Vu, P, Fasshauer GE.  2011.

### Journal:

IET Science, Measurement & Technology

5

206–210

### Abstract:

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.

Citation:
Vu, P, Fasshauer GE.  2011.  Application of two radial basis functionpseudospectral meshfree methods to three-dimensional electromagnetic problems. IET Science, Measurement & Technology. 5:206–210.