Geodesic
Discontinuous Galerkin method on three-dimensional tetrahedral meshes. The usage of the operator programming method
Matematičeskoe modelirovanie, Tome 29 (2017) no. 2, pp. 3-22

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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. 
@article{MM_2017_29_2_a0,
     author = {M. M. Krasnov and P. A. Kuchugov and M. E. Ladonkina and V. F. Tishkin},
     title = {Discontinuous {Galerkin} method on three-dimensional tetrahedral meshes. {The} usage of the operator programming method},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--22},
     publisher = {mathdoc},
     volume = {29},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2017_29_2_a0/}
}
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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. Matematičeskoe modelirovanie, Tome 29 (2017) no. 2, pp. 3-22. http://geodesic.mathdoc.fr/item/MM_2017_29_2_a0/