Two approaches for the numerical determination of electromagnetic fields near material interfaces using radial basis functions in a meshless method

This article discusses the use of radial basis functions in the solution of partial differential equations. In particular, an investigation of how to implement boundary conditions at material interfaces is presented. A comparison is made of solutions obtained using only radial basis functions with those obtained using either jump functions or elliptical functions in conjunction with standard radial basis functions. The purpose of adding either jump functions or elliptical functions is to alleviate the inaccurate handling of the boundary conditions at material interfaces. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010