Geodesic
The bicompact schemes for numerical solving of Reed problem using \emph{HOLO} algorithms
Matematičeskoe modelirovanie, Tome 33 (2021) no. 8, pp. 3-26

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The paper considers bicompact schemes for HOLO algorithms for solving the nonstationary transport equation. To accelerate the convergence of scattering iterations, not only the solution of the transfer equation with respect to the distribution function of high order (HO) is used, but also the quasi-diffusion equation of low order (LO). For both systems of kinetic equations semi-discrete bicompact schemes with the fourth order of approximation in space are used. Integration over time can be carried out with any order of approximation. The diagonal-implicit third order approximation method is used in the work, its each stage can be reduced to the implicit Euler method. The discretization of quasi-diffusion equations is described in detail. Two variants for the boundary conditions for the LO part are considered: the classical one using fractional-linear functionals for the flux and radiation density ratio, and also by the radiation density value from the HO part of the system. It is shown that the boundary conditions for the LO system of equations of quasi-diffusion reduces the order of convergence of the scheme in time to the second. Setting the boundary conditions for solving the transport equation preserves the third order of convergence in time, but worsens the efficiency of iteration acceleration in HOLO algorithm.
Mots-clés : transport equation, quasi-diffusion method
Keywords: bicompact scheme, HOLO algorithms for transport equation solving, diagonally implicit Runge-Kutta method, Reed problem. 
@article{MM_2021_33_8_a0,
     author = {E. N. Aristova and N. I. Karavaeva},
     title = {The bicompact schemes for numerical solving of {Reed} problem using {\emph{HOLO}} algorithms},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--26},
     publisher = {mathdoc},
     volume = {33},
     number = {8},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2021_33_8_a0/}
}
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E. N. Aristova; N. I. Karavaeva. The bicompact schemes for numerical solving of Reed problem using \emph{HOLO} algorithms. Matematičeskoe modelirovanie, Tome 33 (2021) no. 8, pp. 3-26. http://geodesic.mathdoc.fr/item/MM_2021_33_8_a0/