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arXiv · 1901.03498

Numerical integration over implicitly defined domains with topological guarantee

Tianhui Yang·Ammar Qarariyah·Hongmei Kang·Jiansong Deng
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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.

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Tianhui Yang, Ammar Qarariyah, Hongmei Kang, Jiansong Deng. 2019-01-11. Numerical integration over implicitly defined domains with topological guarantee. https://arxiv.org/abs/1901.03498

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