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Matem. Mod., 2017, Volume 29, Number 2, Pages 3–22 (Mi mm3811)  

This article is cited in 3 scientific papers (total in 3 papers)

Discontinuous Galerkin method on three-dimensional tetrahedral meshes. The usage of the operator programming method

M. M. Krasnova, P. A. Kuchugova, M. E. Ladonkinaba, V. F. Tishkinab

a Keldysh Institute for Applied Mathematics RAS, Moscow
b Lavrentyev Institute of Hydrodynamics of SB RAS, Novosibirsk

Abstract: In the numerical simulation of gasdynamic flows in areas with complex geometry it is necessary to use detailed unstructured grids and numerical methods of high accuracy. Galerkin method with discontinuous basis functions or Discontinuous Galerkin Method (DGM) works well in dealing with such problems. This approach has several advantages inherent in both finite-element and finite-difference approximations. At the same time discontinuous Galerkin method has a significant computational complexity, so the corresponding implementation should efficiently use all available computational capacity. In order to speed up the calculations operator programming method was applied while creating the computational module.
Operator programming method allows writing mathematical formulas in programs in compact form and helps to port the programs to parallel architectures, such as NVidia CUDA and Intel Xeon Phi. Earlier the operator programming method was implemented for regular threedimensional Cartesian grids and tree-dimensional locally adaptive grids. In this work, the approach is applied to three-dimensional tetrahedron meshes. This demonstrates the possibility of implementation of the method on arbitrary tree-dimensional meshes. Besides, in this work we give the example of the usage of template metaptogramming methods of the C++ programming language to speed-up calculations.

Keywords: operator programming method, three-dimensional tetrahedral meshes, discontinuous Galerkin method, CUDA, template metaprogramming.

Funding Agency Grant Number
Russian Science Foundation 16-11-10033

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English version:
Mathematical Models and Computer Simulations, 2017, 9:5, 529–543

Received: 23.05.2016

Citation: M. M. Krasnov, P. A. Kuchugov, M. E. Ladonkina, V. F. Tishkin, “Discontinuous Galerkin method on three-dimensional tetrahedral meshes. The usage of the operator programming method”, Matem. Mod., 29:2 (2017), 3–22; Math. Models Comput. Simul., 9:5 (2017), 529–543

Citation in format AMSBIB
\by M.~M.~Krasnov, P.~A.~Kuchugov, M.~E.~Ladonkina, V.~F.~Tishkin
\paper Discontinuous Galerkin method on three-dimensional tetrahedral meshes. The usage of the operator programming method
\jour Matem. Mod.
\yr 2017
\vol 29
\issue 2
\pages 3--22
\jour Math. Models Comput. Simul.
\yr 2017
\vol 9
\issue 5
\pages 529--543

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    This publication is cited in the following articles:
    1. M. M. Krasnov, M. E. Ladonkina, V. F. Tishkin, “Realizatsiya razryvnogo metoda Galërkina v programmnom komplekse DGM”, Preprinty IPM im. M. V. Keldysha, 2018, 245, 31 pp.  mathnet  crossref  elib
    2. A. I. Sukhinov, A. E. Chistyakov, E. A. Protsenko, “Raznostnaya skhema dlya resheniya zadach gidrodinamiki pri bolshikh setochnykh chislakh Pekle”, Kompyuternye issledovaniya i modelirovanie, 11:5 (2019), 833–848  mathnet  crossref
    3. A. I. Sukhinov, A. E. Chistyakov, E. A. Protsenko, V. V. Sidoryakina, S. V. Protsenko, “Metod ucheta zapolnennosti yacheek dlya resheniya zadach gidrodinamiki so slozhnoi geometriei raschetnoi oblasti”, Matem. modelirovanie, 31:8 (2019), 79–100  mathnet  crossref  elib
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