Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 37, Issue 2, Pages A993-A1019Publisher
SIAM PUBLICATIONS
DOI: 10.1137/140966290
Keywords
quadrature; integration; implicit surfaces; level set function; level set methods; high order
Categories
Funding
- Luis W. Alvarez Postdoctoral Fellowship at Lawrence Berkeley National Laboratory
- Laboratory Directed Research and Development Program of LBNL
- Applied Mathematics Program of the U.S. DOE Office of Advanced Scientific Computing Research [DE-AC02-05CH11231]
- Office of Science of the U.S. DOE [DE-AC02-05CH11231]
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A high-order accurate numerical quadrature algorithm is presented for the evaluation of integrals over curved surfaces and volumes which are defined implicitly via a fixed isosurface of a given function restricted to a given hyperrectangle. By converting the implicitly defined geometry into the graph of an implicitly defined height function, the approach leads to a recursive algorithm on the number of spatial dimensions which requires only one-dimensional root finding and one-dimensional Gaussian quadrature. The computed quadrature scheme yields strictly positive quadrature weights and inherits the high-order accuracy of Gaussian quadrature: a range of different convergence tests demonstrate orders of accuracy up to 20th order. Also presented is an application of the quadrature algorithm to a high-order embedded boundary discontinuous Galerkin method for solving partial differential equations on curved domains.
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