High Order Numerical Quadratures to One Dimensional Delta Function Integrals

Abstract. We study high order numerical quadratures to one dimensional delta function integrals in this paper. This is motivated by the fact that traditional numerical quadratures give only first order accuracy in general. We provide criteria on discrete delta functions and support size formulas which ensure any desired accuracy of the numerical quadratures. Discrete delta functions and support size formulas satisfying these criteria are designed. Numerical examples are presented to verify the performed analysis and the high order accuracy of the proposed numerical quadratures. Key words. delta function integral, discrete delta function, discrete moment condition, regularity condition, level set method AMS subject classification. 65Jxx DOI. 10.1137/070682939

• Type: Journal
• Year: 2008
• Where: SIAMSC
• Authors: Xin Wen
• Keywords: Delta Functions, Discrete Delta Functions, Numerical Quadratures, SIAMSC 2008