AdaptivSearch: A Novel Iterative Algorithm for the Generation of n-dimensional Hypersurfaces Using an Adaptive Numerical Strategy

Abstract

AdaptivSearch is the first adaptive strategy based algorithm for the rational and economical construction of n-dimensional hypersurfaces. AdaptivSearch works iteratively: At each step it parcels out the definition range into several triangles, evaluates the worst according to a built-in error criterion, and refines the approximation to the unknown function by choosing the barycenter of this partial area as the node to be calculated next. Based upon the error criterion, AdaptivSearch selectively approaches those parts of the hypersurface in which the curvature exhibits the strongest changes. Some examples of AdaptivSearch applications for both analytical functions and chemical model surfaces are given in order to demonstrate the behavior of the algorithm. These show its broad applicability and the usefulness, especially for chemical problems.