Geodesic
Solution of the self-adjoint radiative transfer equation on hybrid computer systems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 6, pp. 999-1007

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A new technique for simulating three-dimensional radiative energy transfer for the use in the software designed for the predictive simulation of plasma with high energy density on parallel computers is proposed. A highly scalable algorithm that takes into account the angular dependence of the radiation intensity and is free of the ray effect is developed based on the solution of a second-order equation with a self-adjoint operator. A distinctive feature of this algorithm is a preliminary transformation of rotation to eliminate mixed derivatives with respect to the spatial variables, simplify the structure of the difference operator, and accelerate the convergence of the iterative solution of the equation. It is shown that the proposed method correctly reproduces the limiting cases—isotropic radiation and the directed radiation with a $\delta$-shaped angular distribution. 
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     author = {V. A. Gasilov and P. A. Kuchugov and O. G. Olkhovskaya and B. N. Chetverushkin},
     title = {Solution of the self-adjoint radiative transfer equation on hybrid computer systems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     number = {6},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_6_a6/}
}
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V. A. Gasilov; P. A. Kuchugov; O. G. Olkhovskaya; B. N. Chetverushkin. Solution of the self-adjoint radiative transfer equation on hybrid computer systems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 6, pp. 999-1007. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_6_a6/