High Order Numerical Methods to Two Dimensional Heaviside Function Integrals

High Order Numerical Methods to Two Dimensional Heaviside Function Integrals

Year:    2011

Journal of Computational Mathematics, Vol. 29 (2011), Iss. 3 : pp. 305–323

Abstract

In this paper we design and analyze a class of high order numerical methods to two dimensional Heaviside function integrals. Inspired by our high order numerical methods to two dimensional delta function integrals [19], the methods comprise approximating the mesh cell restrictions of the Heaviside function integral. In each mesh cell the two dimensional Heaviside function integral can be rewritten as a one dimensional ordinary integral with the integrand being a one dimensional Heaviside function integral which is smooth on several subsets of the integral interval. Thus the two dimensional Heaviside function integral is approximated by applying standard one dimensional high order numerical quadratures and high order numerical methods to one dimensional Heaviside function integrals. We establish error estimates for the method which show that the method can achieve any desired accuracy by assigning the corresponding accuracy to the sub-algorithms. Numerical examples are presented showing that the second- to fourth-order methods implemented in this paper achieve or exceed the expected accuracy.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1010-m3285

Journal of Computational Mathematics, Vol. 29 (2011), Iss. 3 : pp. 305–323

Published online:    2011-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:    Heaviside function integral High order numerical method Irregular domain

  1. An algorithm for approximating implicit functions by polynomials without using higher order differentiability information

    Rim, Kyung Soo

    Numerical Algorithms, Vol. (2024), Iss.

    https://doi.org/10.1007/s11075-024-01833-9 [Citations: 0]
  2. Solving Poisson-type equations with Robin boundary conditions on piecewise smooth interfaces

    Bochkov, Daniil | Gibou, Frederic

    Journal of Computational Physics, Vol. 376 (2019), Iss. P.1156

    https://doi.org/10.1016/j.jcp.2018.10.020 [Citations: 28]
  3. Gradient augmented reinitialization scheme for the level set method

    Anumolu, Lakshman | Trujillo, Mario F.

    International Journal for Numerical Methods in Fluids, Vol. 73 (2013), Iss. 12 P.1011

    https://doi.org/10.1002/fld.3834 [Citations: 14]