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.
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”, Mat. Model., 29:2 (2017), 3–22; Math. Models Comput. Simul., 9:5 (2017), 529–543
This publication is cited in the following 27 articles:
V. F. Tishkin, M. E. Ladonkina, “The Discontinuous Galerkin Method and its Implementation in the RAMEG3D Software Package”, CMIT, 7:2 (2023), 7
S. A. Soukov, “Methods for Improving and Evaluating the Performance of Unstructured CFD Algorithms”, Math Models Comput Simul, 15:4 (2023), 717
S. A. Sukov, “Methods for improving and evaluating the performance of unstructured CFD-algorithms”, Matem. Mod., 35:2 (2023), 30–42
R. V. Zhalnin, V. F. Masyagin, V. F. Tishkin, “Reshenie dvumernykh zadach gazovoi dinamiki s ispolzovaniem neyavnoi skhemy dlya metoda Galerkina s razryvnymi bazisnymi funktsiyami na nestrukturirovannykh treugolnykh setkakh”, Sib. zhurn. vychisl. matem., 25:1 (2022), 19–32
M. M. Krasnov, M. E. Ladonkina, O. A. Neklyudova, V. F. Tishkin, “O vliyanii vybora chislennogo potoka na reshenie zadach s udarnymi volnami razryvnym metodom Galerkina”, Preprinty IPM im. M. V. Keldysha, 2022, 091, 21 pp.
Alexander Sukhinov, Alexander Chistyakov, Inna Kuznetsova, Yulia Belova, Elena Rahimbaeva, “Solving Hydrodynamic Problems Based on a Modified Upwind Leapfrog Scheme in Areas with Complex Geometry”, Mathematics, 10:18 (2022), 3248
M. D. Bragin, O. A. Kovyrkina, M. E. Ladonkina, V. V. Ostapenko, V. F. Tishkin, N. A. Khandeeva, “Combined numerical schemes”, Comput. Math. Math. Phys., 62:11 (2022), 1743–1781
Marina Ladonkina, Olga Nekliudova, Vladimir Tishkin, INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING ICCMSE 2021, 2611, INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING ICCMSE 2021, 2022, 050004
V. F. Masyagin, R. V. Zhalnin, M. E. Ladonkina, O. N. Terekhina, V. F. Tishkin, “Primenenie entropiinogo limitera dlya resheniya uravnenii gazovoi dinamiki s ispolzovaniem neyavnoi skhemy razryvnogo metoda Galerkina”, Preprinty IPM im. M. V. Keldysha, 2021, 007, 18 pp.
M. E. Ladonkina, O. A. Nekliudova, V. F. Tishkin, “Hybrid numerical flux for solving the problems of supersonic flow of solid bodies”, Math. Models Comput. Simul., 13:6 (2021), 1116–1121
N. M. Evstigneev, O. I. Ryabkov, “Application of the AmgX library to the discontinuous Galerkin methods for elliptic problems”, Parallel Computational Technologies, Communications in Computer and Information Science, 1437, eds. L. Sokolinsky, M. Zymbler, Springer, 2021, 178–193
V. Balashov, “A regularized isothermal phase-field model of two-phase solid-fluid mixture and its spatial dissipative discretization”, Russ. J. Numer. Anal. Math. Model, 36:4 (2021), 197–217
V. A. Balashov, E. B. Savenkov, “Regulyarizovannaya model tipa fazovogo polya dlya opisaniya sistemy «zhidkost–tverdoe telo» s uchetom khimicheskikh reaktsii”, Preprinty IPM im. M. V. Keldysha, 2021, 082, 20 pp.
A. V. Nikitina, A. E. Chistyakov, A. M. Atayan, “NUMERICAL IMPLEMENTATION OF A PARALLEL ALGORITHM FOR SOLVING THE PROBLEM OF POLLUTANT TRANSPORT IN A RESERVOIR ON A HIGH-PERFORMANCE COMPUTER SYSTEM”, vkit, 2021, no. 202, 27
A M Atayan, “Solving the diffusion-convection problem using MPI parallel computing technology”, J. Phys.: Conf. Ser., 1902:1 (2021), 012098
S. A. Sukov, “Load balancing method for heterogeneous CFD algorithms”, Zhurnal SVMO, 23:2 (2021), 193–206
A E Chistyakov, A V Strazhko, A M Atayan, S V Protsenko, “Software development for calculating the polluted by suspension and other impurities zones volumes on the basis of graphics accelerator”, IOP Conf. Ser.: Mater. Sci. Eng., 1029:1 (2021), 012084
Victor F. Masyagin, Communications in Computer and Information Science, 1413, Mathematical Modeling and Supercomputer Technologies, 2021, 33
A I Sukhinov, A E Chistyakov, E A Protsenko, V V Sidoryakina, S V Protsenko, “Wave hydrodynamics discrete models construction and research”, IOP Conf. Ser.: Mater. Sci. Eng., 1029:1 (2021), 012086
V. F. Tishkin, V. A. Gasilov, N. V. Zmitrenko, P. A. Kuchugov, M. E. Ladonkina, Yu. A. Poveschenko, “Modern methods of mathematical modeling of the development of hydrodynamic instabilities and turbulent mixing”, Math. Models Comput. Simul., 13:2 (2021), 311–327
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