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An Efficient Sparse Finite Element Solver for the Radiative Transfer Equation

[+] Author Affiliations
Gisela Widmer

Federal Institute of Technology, Zürich, Switzerland

Paper No. HT2009-88140, pp. 137-145; 9 pages
doi:10.1115/HT2009-88140
From:
  • ASME 2009 Heat Transfer Summer Conference collocated with the InterPACK09 and 3rd Energy Sustainability Conferences
  • Volume 1: Heat Transfer in Energy Systems; Thermophysical Properties; Heat Transfer Equipment; Heat Transfer in Electronic Equipment
  • San Francisco, California, USA, July 19–23, 2009
  • Conference Sponsors: Heat Transfer Division
  • ISBN: 978-0-7918-4356-7 | eISBN: 978-0-7918-3851-8
  • Copyright © 2009 by ASME

abstract

The stationary monochromatic radiative transfer equation (RTE) is posed in five dimensions, with the intensity depending on both a position in a three-dimensional domain as well as a direction. For non-scattering radiative transfer, sparse finite elements [1, 2] have been shown to be an efficient discretization strategy if the intensity function is sufficiently smooth. Compared to the discrete ordinates method, they make it possible to significantly reduce the number of degrees of freedom N in the discretization with almost no loss of accuracy. However, using a direct solver to solve the resulting linear system requires O(N3 ) operations. In this paper, an efficient solver based on the conjugate gradient method (CG) with a subspace correction preconditioner is presented. Numerical experiments show that the linear system can be solved at computational costs that are nearly proportional to the number of degrees of freedom N in the discretization.

Copyright © 2009 by ASME

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