Numerical integration over implicitly defined domains with topological guarantee
| Autor: | Tianhui Yang, Ammar Qarariyah, Jiansong Deng, Hongmei Kang |
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| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Implicit function Computer science business.industry Applied Mathematics Computation Boundary (topology) Numerical Analysis (math.NA) Topology 65G30 65D30 Numerical integration Interval arithmetic Domain (software engineering) Computational Mathematics FOS: Mathematics Mathematics - Numerical Analysis business Topology (chemistry) Subdivision |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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