High-performance computation of initial boundary value problems

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This paper considers the efficient methods and high- performance parallel technologies for the numerical solution of the multi-dimensional initial boundary value problems, with a complicated geometry of a computational domain and contrast properties of a material on the heterogeneous multi-processor systems with distributed and hierarchical shared memory. The approximations with respect to time and space are carried out by implicit schemes on the quasi-structured grids. At each time step, the iterative algorithms are used for solving the systems of linear or nonlinear equations that, in general, are non-symmetric with a special choice of the initial guess. The scalable parallelism is provided by two-level iterative domain decomposition methods, with parameterized intersection of subdomains in the Krylov subspaces, which are accelerated by means of a coarse grid correction and polynomial or other types of preconditioning. A comparative analysis of the performance and speed up of the computational processes is presented, based on a simple model of parallel computing and data structures.

Original languageEnglish
Title of host publicationParallel Computational Technologies - 12th International Conference, PCT 2018, Revised Selected Papers
EditorsL Sokolinsky, M Zymbler
PublisherSpringer-Verlag GmbH and Co. KG
Number of pages14
ISBN (Print)9783319996721
Publication statusPublished - 1 Jan 2018
Event12th International Scientific Conference on Parallel Computational Technologies, PCT 2018 - Rostov-on-Don, Russian Federation
Duration: 2 Apr 20186 Apr 2018

Publication series

NameCommunications in Computer and Information Science
ISSN (Print)1865-0929


Conference12th International Scientific Conference on Parallel Computational Technologies, PCT 2018
CountryRussian Federation


  • Domain decomposition
  • High-order approximations
  • Initial guess
  • Iterative processes
  • Nonstationary boundary value problems
  • Scalable parallelism
  • Stability


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