An integral-collocation-based fictitious-domain technique for solving elliptic problems

Authors

  • N. Mai-Duy,

    Corresponding author
    1. Computational Engineering and Science Research Centre (CESRC), The University of Southern Queensland, Toowoomba, Qld. 4350, Australia
    • Computational Engineering and Science Research Centre (CESRC), The University of Southern Queensland, Toowoomba, Qld. 4350, Australia
    Search for more papers by this author
  • H. See,

    1. School of Chemical & Biomolecular Engineering, The University of Sydney, Sydney, NSW 2006, Australia
    Search for more papers by this author
  • T. Tran-Cong

    1. Computational Engineering and Science Research Centre (CESRC), The University of Southern Queensland, Toowoomba, Qld. 4350, Australia
    Search for more papers by this author

Abstract

This paper presents a new fictitious-domain technique for numerically solving elliptic second-order partial differential equations (PDEs) in complex geometries. The proposed technique is based on the use of integral-collocation schemes and Chebyshev polynomials. The boundary conditions on the actual boundary are implemented by means of integration constants. The method works for both Dirichlet and Neumann boundary conditions. Several test problems are considered to verify the technique. Numerical results show that the present method yields spectral accuracy for smooth (analytic) problems. Copyright © 2007 John Wiley & Sons, Ltd.

Ancillary