Turek, S. A generalized mean intensity approach for the numerical solution of the radiative transfer equation. (English) Zbl 0822.65129 Computing 54, No. 1, 27-38 (1995). From the author’s summary: Using the concept of the generalized mean intensity, the dimension of the system can be drastically diminished, without losing any information. The corresponding system matrices are positive definite under appropriate conditions on the choice of the discrete ordinates and, therefore, the classical conjugate gradient iteration is converging. In connection with local preconditioners, we develop robust and efficient methods of conjugate gradient type, which are superior to the classical approximate \(\Lambda\)-iteration, but with about the same numerical effort. Reviewer: C.L.Koul (Jaipur) Cited in 1 ReviewCited in 8 Documents MSC: 65R20 Numerical methods for integral equations 45K05 Integro-partial differential equations 85A25 Radiative transfer in astronomy and astrophysics Keywords:radiative transfer equation; astrophysics; generalized mean intensity; conjugate gradient iteration; local preconditioners PDFBibTeX XMLCite \textit{S. Turek}, Computing 54, No. 1, 27--38 (1995; Zbl 0822.65129) Full Text: DOI References: [1] Führer, Chr.: A comparative study of finite element solvers for hyperbolic problems with applications to radiative transfer. Technical report SFB 359, 65, University Heidelberg, 1993. [2] Johnson, C., Pitkäranta, J.: Convergence of a fully discrete scheme for two-dimensional neutron transport. SIAM J. Numer. Anal.20, 951–966 (1983). · Zbl 0538.65097 [3] Kalkofen, W.: Numerical radiative transfer, Cambridge: Cambridge University Press 1987. · Zbl 1170.85300 [4] Mihalas, D., Weibel-Mihalas, B.: Foundations of radiation hydrodynamics. Oxford: Oxford University Press, 1984. · Zbl 0651.76005 [5] Steiner, O.: A rapidly converging temperature correction procedure using operator perturbation. Astron. Astrophys.231, 278–288 (1990). [6] Turek, S.: Tools for simulating nonstationary incompressible flow via discretely divergence-free finite element models. Int. J. Numer. Meth. Fluids.18, 71–105 (1994). · Zbl 0794.76051 [7] Turek, S.: An efficient solution technique for the radiative transfer equation. Imp. Comput. Sci. Eng.5, 201–214 (1993). · Zbl 0786.65125 [8] Turek, S., Wehrse, R.: Spectral appearance of dust enshrouded stars: A combination of a strongly accelerated solution technique with a finite element approach for 2D radiative transfer, Astron. Astrophys. in press (1994). [9] Van der Vorst, H.: BI-CGSTAB: A fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Stat. Comput.13, 631–644 (1992). · Zbl 0761.65023 [10] Väth, H. M.: Three-dimensional radiative transfer on a massively parallel computer. Astron. Astrophys.284, 319–331 (1994). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.