Application Of Lopi Method To Solve Pdes.

Abstract

The Local Optimal Point Interpolation (LOPI) method is a “truly meshless” method
based on the boolean sum of a radial basis function interpolator and a least squares approximation
in a polynomials space. In this way, it can interpolate solutions in data points,
while at the same time fit exactly polynomial solutions up to certain degree. Systems of
PDEs can be solved in strong form using point collocation, without meshes or integration
cells. Essential boundary conditions (which cause problems in many other meshless methods)
are applied directly; and natural boundary conditions are implemented by means of
additional equations. This work presents a description of the method, and some examples
of applications.