Numerical cubature on scattered data by adaptive interpolation

TL;DR

This paper introduces a novel approach for numerical integration on scattered data using adaptive interpolation techniques, offering a promising alternative to existing meshless cubature methods.

Contribution

It develops a new method for constructing cubature formulas on scattered data through resampling and adaptive interpolation, enhancing flexibility and potential accuracy.

Findings

Effective construction of cubature formulas on scattered data

Demonstrates advantages over existing meshless methods

Provides a flexible framework for numerical integration

Abstract

We construct cubature methods on scattered data via resampling on the support of known algebraic cubature formulas, by different kinds of adaptive interpolation (polynomial, RBF, PUM). This approach gives a promising alternative to other recent methods, such as direct meshless cubature by RBF or least-squares cubature formulas.