The stationary monochromatic radiative transfer equation is posed in five dimensions, with the intensity depending on both a position in a three-dimensional domain as well as a direction. For nonscattering radiative transfer, sparse finite elements [2007, “Sparse Finite Elements for Non-Scattering Radiative Transfer in Diffuse Regimes,” ICHMT Fifth International Symposium of Radiative Transfer, Bodrum, Turkey; 2008, “Sparse Adaptive Finite Elements for Radiative Transfer,” J. Comput. Phys., 227(12), pp. 6071–6105] have been shown to be an efficient discretization strategy if the intensity function is sufficiently smooth. Compared with the discrete ordinates method, they make it possible to significantly reduce the number of degrees of freedom in the discretization with almost no loss of accuracy. However, using a direct solver to solve the resulting linear system requires operations. In this paper, an efficient solver based on the conjugate gradient method 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 in the discretization.
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An Efficient Sparse Finite Element Solver for the Radiative Transfer Equation
Gisela Widmer
Gisela Widmer
Seminar for Applied Mathematics,
e-mail: gisela.widmer@math.ethz.ch
ETH Zürich
, Rämistrasse 101, Zurich CH-8092, Switzerland
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Gisela Widmer
Seminar for Applied Mathematics,
ETH Zürich
, Rämistrasse 101, Zurich CH-8092, Switzerlande-mail: gisela.widmer@math.ethz.ch
J. Heat Transfer. Feb 2010, 132(2): 023403 (7 pages)
Published Online: December 2, 2009
Article history
Received:
October 30, 2008
Revised:
April 30, 2009
Online:
December 2, 2009
Published:
December 2, 2009
Citation
Widmer, G. (December 2, 2009). "An Efficient Sparse Finite Element Solver for the Radiative Transfer Equation." ASME. J. Heat Transfer. February 2010; 132(2): 023403. https://doi.org/10.1115/1.4000190
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