期刊文献+

HIGH ORDER NUMERICAL METHODS TO TWO DIMENSIONAL HEAVISIDE FUNCTION INTEGRALS

HIGH ORDER NUMERICAL METHODS TO TWO DIMENSIONAL HEAVISIDE FUNCTION INTEGRALS
原文传递
导出
摘要 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 dimen- sional 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 inte- gral is approximated by applying standard one dimensional high order numerical quadra- tures 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 in this paper achieve or exceed the expected second to fourth-order methods implemented accuracy. 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 dimen- sional 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 inte- gral is approximated by applying standard one dimensional high order numerical quadra- tures 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 in this paper achieve or exceed the expected second to fourth-order methods implemented accuracy.
作者 Xin Wen
机构地区 LSEC
出处 《Journal of Computational Mathematics》 SCIE CSCD 2011年第3期305-323,共19页 计算数学(英文)
关键词 Heaviside function integral High order numerical method Irregular domain. Heaviside function integral, High order numerical method, Irregular domain.
  • 相关文献

参考文献20

  • 1I J.T. Beale, A proof that a discrete delta function is second-order accurate, J. Comput. Phys., 227 (2008), 2195-2197.
  • 2Y. Di, R. Li, T. Tang and P.W. Zhang, Level set calculations for incompressible two-phase flows on a dynamically adaptive grid, J. Sci. Comput., 31 (2006), 75-98.
  • 3B. Engquist, A.K. Tornberg and R. Tsai, Discretization of dirac delta functions in level set methods, J. Comput. Phys., 207:1 (2005), 28-51.
  • 4C. Min and F. Gibou, Geometric integration over irregular domains with application to level-set methods, J. Comput. Phys., 226 (2007), 1432-1443.
  • 5C. Min and F. Gibou, Robust second-order accurate discretizations of the multi-dimensional Heaviside and Dirac delta functions, J. Comput. Phys., 227 (2008), 9686-9695.
  • 6C.S. Peskin, Numerical analysis of blood flow in the heart, J. Comput. Phys., 25 (1977), 220-252.
  • 7C.S. Peskin, The immersed boundary method, Acta Numerica, 11 (2002)( 479-511.
  • 8P. Smereka, The numerical approximation of a delta function with application to level set meth- ods, J. Comput. Phys., 211 (2006), 77-90.
  • 9A.K. Tornberg, Interface Tracking Methods with Applications to Multiphase Flows, Ph.D. Thesis, Royal Institute of Technology, Stockholm, Sweden, 2000.
  • 10A.K. Tornberg, Multi-dimensional quadrature of singular and discontinuous functions, BIT, 42 (2002), 644-669.

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部