Numerical Integration Over Implicitly Defined Domains with Topological Guarantee

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.

Keywords

Isogeometric analysis / Numerical integration / Implicitly defined domains / Topological guarantee / Interval arithmetic / Local error estimate / Hierarchical subdivision

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Funding

National Natural Science Foundation of China(No.11771420)