Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 396, Issue -, Pages 761-784Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2019.07.005
Keywords
Volume computation; Numerical quadrature; Laplace-Beltrami
Funding
- 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
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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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