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

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

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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Bordas, Dr Stephane and Natarajan, Mr Sundararajan
• Authors: Natarajan, S., Bordas, S., and Mahapatra, D.R.
• Subjects: T Technology > TA Engineering (General). Civil engineering (General)
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: International Journal for Numerical Methods in Engineering
• ISSN: 1097-0207