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High order numerical methods to a type of delta function integrals. (English) Zbl 1125.65024
Summary: 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 partial differential equations. 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 an interpolation approach. Numerical examples are presented to verify the efficiency and accuracy of our methods.

MSC:
65D32 Numerical quadrature and cubature formulas
41A55 Approximate quadratures
41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)
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