Numerical Integration Over Implicitly Defined Domains with Topological Guarantee
Tianhui Yang , Ammar Qarariyah , Hongmei Kang , Jiansong Deng
Communications in Mathematics and Statistics ›› 2019, Vol. 7 ›› Issue (4) : 459 -474.
Numerical Integration Over Implicitly Defined Domains with Topological Guarantee
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.
Isogeometric analysis / Numerical integration / Implicitly defined domains / Topological guarantee / Interval arithmetic / Local error estimate / Hierarchical subdivision
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