Numerical integration over arbitrary polygonal domains based on Schwarz–Christoffel conformal mapping | Zendy

Natarajan Sundararajan | Zendy; Bordas Stéphane | Zendy; Roy Mahapatra D. | Zendy

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Numerical integration over arbitrary polygonal domains based on Schwarz–Christoffel conformal mapping

Author(s) -

Natarajan Sundararajan,

Bordas Stéphane,

Roy Mahapatra D.

Publication year - 2009

Publication title -

international journal for numerical methods in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.421

H-Index - 168

eISSN - 1097-0207

pISSN - 0029-5981

DOI - 10.1002/nme.2589

Subject(s) - conformal map , jacobian matrix and determinant , unit disk , christoffel symbols , context (archaeology) , domain (mathematical analysis) , numerical integration , mathematics , benchmark (surveying) , geometry , algorithm , computer science , mathematical analysis , geology , paleontology , geodesy

This paper presents a new numerical integration technique on arbitrary polygonal domains. The polygonal domain is mapped conformally to the unit disk using Schwarz–Christoffel mapping and a midpoint quadrature rule defined on this unit disk is used. This method eliminates the need for a two‐level isoparametric mapping usually required. Moreover, the positivity of the Jacobian is guaranteed. Numerical results presented for a few benchmark problems in the context of polygonal finite elements show that the proposed method yields accurate results. Copyright © 2009 John Wiley & Sons, Ltd.

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