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

Natarajan, Sundararajan and Bordas, Stephane and Mahapatra, D Roy (2009) Numerical integration over arbitrary polygonal domains based on Schwarz-Christoffel conformal mapping. In: International Journal for Numerical Methods in Engineering, 80 (1). pp. 103-134.

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Abstract

This paper presents a new numerical integration technique oil arbitrary polygonal domains. The polygonal domain is mapped conformally to the unit disk using Schwarz-Christoffel mapping and a midpoint quadrature rule defined oil 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.

Item Type:	Journal Article
Publication:	International Journal for Numerical Methods in Engineering
Publisher:	John wiley
Additional Information:	Copyright for this article belongs to John wiley.
Keywords:	Schwarz-Christoffel mapping; polygonal finite element; quadrature; integration rule; finite element method; conformal mapping; Wachspress shape functions; numerical integration; discontinuities; natural element method; XFEM
Department/Centre:	Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited:	09 Dec 2009 10:54
Last Modified:	19 Sep 2010 05:52
URI:	http://eprints.iisc.ac.in/id/eprint/24917

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