Abstract
This paper is devoted to the conception and general structure of the integrated computational environment for constructing multi-dimensional large grids (with \(10^{10}\) nodes and more) for high-performance solutions of interdisciplinary direct and inverse mathematical modelling problems in computational domains with complicated geometrical boundaries and contrast material properties. This includes direct and inverse statements which are described by the system of differential and/or integral equations. The constructed computational grid domain consists of subdomains featuring a grid, which may be of different types (structured or non-structured); discretization at the internal boundaries can be consistent or non-consistent. The methodology of such quasi-structured meshes makes it possible to use various algorithms and codes in the subdomains, as well as different data structure formats and their conversion. The proposed technologies include grid quality control, the generation of dynamic grids adapted to singularities of input geometric data of structures and multigrid approaches with local refinements, taking into account information about the solution to be obtained. The balanced grid domain decomposition, based on hybrid programming at the heterogeneous clusters with distributed and hierarchical shared memory, supports scalable parallelization. In addition, the paper outlines the technological requirements to provide a successful long-life cycle for the proposed computational environment. In a sense, the considered development presents a stable software ecosystem (integrated grid generator DELAUNAY) for supercomputing modelling in the epoch of big data and artificial intellect.
V. Il’in—This work was supported by Russian Foundation of Basic Research grant 18-01-00295.
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References
Il’in, V.P.: Mathematical Modeling, Part I: Continuous and Discrete Models. SBRAS Publ, Novosibirsk (2017). (in Russian)
Godunov, S.K., Romenski, E.L., Chamakov, G.A.: Grid generate ioncomplicated domains by qusuconformal mapping. Trudy IM SBRAS Novosibirsk 18, 75–84 (1990). (in Russian)
Terekhov, K., Vassilevski, Y.: Mesh modification and adaption within INMOST programming platform. In: Proceedings of the 9th International Conference NUMGRID 2018, Moscow, LNCSE, vol. 131, pp. 243–255 (2018)
Garanzha, V.A.: Variational principles in grid generation and geometric modelling. Numer. Lin. Alg. 11, 535–563 (2003)
Bronina, T.N., Gasilova, I.A., Ushakova, O.V.: Algorihms fort hree- dimensional structured grid generation. Zh. Vychisl. Mat. Met. Fiz. 43, 875–883 (2003). (in Russian)
Fritzke, B.: Growing cell structuring - a self-organizing networks for unsupervised learning. Neural Netw. 7(9), 1441–1460 (1994)
Ivanenko, S.A.: On the existence of equation for description of the classes of nonsingular curvilinear coordinates on arbitrary domain. Zh. Vgchisl. Mat. Phys. 42, 47–52 (2002). (in Russian)
Liseikin, V.D.: Grid Generation Methods. SC. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-57846-0
Il’in, V.P.: DELAUNAY: technological media for grid generation. Sib. J. Industr. Appl. Math. 16, 83–97 (2013). (in Russian)
Funken, S.A., Schmidt, A.: Ameshref: a Matlab-toolbox for adaptive mesh refinement in two dimensions. In: Proceedings of the 9th International Conference NUMGRID 2018, Moscow, LNCSE, vol. 131, pp. 269–279 (2018)
Li, S.: Mesh curving refinement based on cubic bezier surface for high-order discontinuous Galerkin methods. In: Proceedings of the 9th International Conference NUMGRID 2018, Moscow, LNCSE, vol. 131, pp. 205–216 (2018)
Ushakova, O.V. (ed.): Advances in Grid Generations. Nova Sci. Publ, New York (2007)
Zint, D., Grosso, R., Aizinger, V., Kostler, H.: Generation of block structured grids on complex domains for high performance simulation. In: Proceedings of the 9th International Conference NUMGRID 2018, Moscow, LNCSE, vol. 131, pp. 87–99 (2018)
Khademi, A., Korotov, S., Vatne, J.E.: On equivalence of maximum angle conditions for tetrahedral finite element meshes. Performance Simulation. In: Proceedings of the 9th International Conference NUMGRID 2018, Moscow, LNCSE, vol. 131, pp. 101–108 (2018)
Gartner, K., Kamenski, L.: Why do we need voronoi cells and delaunay Meshes? In: Proceedings of the 9th International Conference NUMGRID 2018, Moscow, LNCSE, vol. 131, pp. 45–60 (2018)
International Meshing Roundtable: www.imr.sandia.gov/18imr
Internat. J. for Numer. Math. in Eng., 58(2), special issue “Trends in Unstructured Mesh Generation” (2003)
Schoberl, J.: Netgen-an advancing front 2D/3D-mesh generator based on abstract rules. Comput. Visualizat. Sci. 1, 41–52 (1997)
Geuzain, C., Remacle, J.-F.: Gmsh: a 3-D finite element mesh generator with built-in pre- and post-processing facilities. Int. J. Num. Methods Eng. 79, 1309–1331 (2009)
Meng, X., Duan, Z., Yang, Q., Liang, X.: Local PEBI grid generation method for reverse faults. Comput. Geosci. 110, 73–80 (2018)
Ponting, D.K.: Corner point geometry in reservoir simulation. In: Proceedings of the 1st European Conference on Mathematics in Oil Recovery, Cambridge, pp. 45–65 (1989)
DUNE.URL: http://www.dune-project.org. Accessed 15 Jan 2016
Il’in, V.P., Gladkih, V.S.: Basic system of modeling (BSM): the conception, architecture and methodology. In: Proceedings of the International Conference on Modern Problems of Mathematical Modeling, Image Processing and Parallel Computing. (MPMMIP & PC-2017) DSTU Publ. Rostov-Don, pp. 151–158 (2017). (in Russian)
Ilin, V.P.: The Conception, Requirements and Structure of the Integrated Computational Environment. In: Voevodin, Vladimir, Sobolev, Sergey (eds.) RuSCDays 2018. CCIS, vol. 965, pp. 653–665. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-05807-4_56
HERBARIUM. http://tflex.ru/about/publications/detail/index.php?ID=3846
Cottrell, J., Hughes, T., Bazilevs, Y.: "Isogeometric Analysis", Towards Integration of CAD and FEA. Wiley, Singapore (2009)
Delfour, M., Zolesio, J.-P.: Shape and Geometries. Metrics, Analysis, Differential Calculus, and Optimization, SIAM Publication, Philadelphia (2011)
ALGOWIKI. https://algowiki-project.org
Ilin, Valery: On an Integrated Computational Environment for Numerical Algebra. In: Sokolinsky, Leonid, Zymbler, Mikhail (eds.) PCT 2019. CCIS, vol. 1063, pp. 91–106. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-28163-2_7
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Il’in, V. (2020). Integrated Computational Environment for Grid Generation Parallel Technologies. In: Sokolinsky, L., Zymbler, M. (eds) Parallel Computational Technologies. PCT 2020. Communications in Computer and Information Science, vol 1263. Springer, Cham. https://doi.org/10.1007/978-3-030-55326-5_5
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