Non-Sibsonian interpolation on arbitrary system of points in Euclidean space and adaptive generating isolines algorithm

Numerical Grid Generation in Computational Field Simulations, Ed. M. Cross., B. K. Soni, J. F. Thompson, J. Hauser, P. R. Eiseman, Proceedings of the 6th International Conference, held at the University of Greenwich, pp.277-286, July 1998

MESHING
RESEARCH
CORNER

Vitali V. Belikov
Computing Centre, Russian Academy of Sciences
40 Vavilov Street, Moscow 117333, Russia

Andrei Yu. Semenov
General Physics Institute, Russian Academy of Sciences
38 Vavilov Street, Moscow 117942, Russia
E-mail: say@lpl.gpi.ru

Abstract
A new method of interpolation of the function values on the set of arbitrary points in a finite-dimensional Eucidean space E^n that differs from the well- known Sibson method is presented. A number of properties of the method are described, including harmonic property. The application of nonSibsonian interpolation and comparison with the Sibson interpolation and with the interpolation based on the Delaunay triangulation are reviewed. The new fast effective economic algorithm for isolines generation based on the non-Sibsonian and the Delaunay interpolations without any isolines intersections and numerical information losses is presented.