An efficient sparse finite element solver for the radiative transfer equatioe / Gisela Widmer in Journal of heat transfer, Vol. 132 N° 2 (n° spécial) (Fevrier 2010)  

Public ISBD [article]  inJournal of heat transfer > Vol. 132 N° 2 (n° spécial) (Fevrier 2010) . - pp. [023403-1/7] Titre : An efficient sparse finite element solver for the radiative transfer equatioe Type de document : texte imprimé Auteurs : Gisela Widmer, Auteur Article en page(s) : pp. [023403-1/7] Note générale : Physique Langues : Anglais (eng) Mots-clés : Radiative transfer equation Least-squares finite elements Preconditioning Sparse grids Index. décimale : 536 Chaleur. Thermodynamique Résumé : 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 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 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. DEWEY : 536 ISSN : 0022-1481 En ligne : http://asmedl.aip.org/vsearch/servlet/VerityServlet?KEY=JHTRAO&ONLINE=YES&smode= [...] [article] An efficient sparse finite element solver for the radiative transfer equatioe [texte imprimé] / Gisela Widmer, Auteur . - pp. [023403-1/7]. Physique Langues : Anglais (eng) in Journal of heat transfer > Vol. 132 N° 2 (n° spécial) (Fevrier 2010) . - pp. [023403-1/7] Mots-clés : Radiative transfer equation Least-squares finite elements Preconditioning Sparse grids Index. décimale : 536 Chaleur. Thermodynamique Résumé : 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 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 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. DEWEY : 536 ISSN : 0022-1481 En ligne : http://asmedl.aip.org/vsearch/servlet/VerityServlet?KEY=JHTRAO&ONLINE=YES&smode= [...]

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