Numerical integration over implicitly defined domains with topological guarantee
Numerical Analysis
2024-12-20 v1 Numerical Analysis
Abstract
Numerical integration over the implicitly defined domains is challenging due to topological variances of implicit functions. In this paper, we use interval arithmetic to identify the boundary of the integration domain exactly, thus getting the correct topology of the domain. Furthermore, a geometry-based local error estimate is explored to guide the hierarchical subdivision and save the computation cost. Numerical experiments are presented to demonstrate the accuracy and the potential of the proposed method.
Cite
@article{arxiv.1901.03498,
title = {Numerical integration over implicitly defined domains with topological guarantee},
author = {Tianhui Yang and Ammar Qarariyah and Hongmei Kang and Jiansong Deng},
journal= {arXiv preprint arXiv:1901.03498},
year = {2024}
}