Numerical integration over arbitrary polygonal domains based on Schwarz–Christoffel conformal mapping
✍ Scribed by Sundararajan Natarajan; Stéphane Bordas; D. Roy Mahapatra
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 641 KB
- Volume
- 80
- Category
- Article
- ISSN
- 0029-5981
- DOI
- 10.1002/nme.2589
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✦ Synopsis
Abstract
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.