Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 226, Issue 2, Pages 1952-1967Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2007.06.025
Keywords
delta function integral; level set method; discrete delta function
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We study second to fourth order numerical methods to a type of delta function integrals in one to three dimensions. These delta function integrals arise from recent efficient level set methods for computing the multivalued solutions of nonlinear PDEs. We show that the natural quadrature approach with usual discrete delta functions and support size formulas to the two dimensional delta function integrals suffer from nonconvergence. We then design high order numerical methods to this type of delta function integrals based on interpolation approach. Numerical examples are presented to verify the efficiency and accuracy of our methods. (c) 2007 Elsevier Inc. All rights reserved.
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