期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 396, 期 -, 页码 761-784出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2019.07.005
关键词
Volume computation; Numerical quadrature; Laplace-Beltrami
资金
- Graduate School of Computational Engineering at Technical University Darmstadt, Germany [GSC 233]
- German Research Foundation (DFG) [SFB-TRR 75]
- Excellence Initiative of the German Federal and State Governments
This paper introduces a novel method for the efficient and accurate computation of the volume of a domain whose boundary is given by an orientable hypersurface which is implicitly given as the iso-contour of a sufficiently smooth level-set function. After spatial discretization, local approximation of the hypersurface and application of the GAUSSIAN divergence theorem, the volume integrals are transformed to surface integrals. Application of the surface divergence theorem allows for a further reduction to line integrals which are advantageous for numerical quadrature. We discuss the theoretical foundations and provide details of the numerical algorithm. Finally, we present numerical results for convex and non-convex hypersurfaces embedded in cuboidal domains, showing both high accuracy and third-to fourth-order convergence in space. (C) 2019 Elsevier Inc. All rights reserved.
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