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High-order quadrature on multi-component domains implicitly defined by multivariate polynomials

2021
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Journal of Computational Physics
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A high-order quadrature algorithm is presented for computing integrals over curved surfaces and volumes whose geometry is implicitly defined by the level sets of (one or more) multivariate polynomials. The algorithm recasts the implicitly defined geometry as the graph of an implicitly defined, multi-valued height function, and applies a dimension reduction approach needing only one-dimensional quadrature. In particular, we explore the use of Gauss-Legendre and tanh-sinh methods and demonstrate

doi:10.1016/j.jcp.2021.110720
fatcat:lpgkwwtg7fhyddaqfp77mbpsby