On an Integrated Computational Environment for Numerical Algebra

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This paper describes the conception, general architecture, data structure, and main components of an Integrated Computational Environment (ICE) for the high-performance solution of a wide class of numerical algebraic problems on heterogeneous supercomputers with distributed and hierarchical shared memory. The tasks considered include systems of linear algebraic equations (SLAEs), various eigenvalue problems, and transformations of algebraic objects with large sparse matrices. These tasks arise in various approximations of multidimensional initial boundary value problems on unstructured grids. A quite large variety of types of matrices, featuring diverse structural, spectral, and other properties are allowed; there can also be a wide diversity of algorithms for computational algebra. There are relevant issues associated with scalable parallelism through hybrid programming on heterogeneous multiprocessor systems, MPI-processes, multithread computing, and vectorization of operations, including those without formal constraints on the number of degrees of freedom and on the number of computing units. The numerical methods and technologies are implemented in the KRYLOV library, which provides the integrated subsystem of the ICE. There are various technical requirements imposed upon the software: extendibility of the set of problems and algorithms, adaptation to the evolution of supercomputer architecture, ability to reuse external products, and coordinated participation of development groups taking part in the project. The end goal of these requirements is to provide a product featuring a long life cycle, high performance, and general acceptance among end users of diverse professional backgrounds.

Original languageEnglish
Title of host publicationParallel Computational Technologies - 13th International Conference, PCT 2019, Revised Selected Papers
EditorsLeonid Sokolinsky, Mikhail Zymbler
PublisherSpringer-Verlag GmbH and Co. KG
Number of pages16
ISBN (Print)9783030281625
Publication statusPublished - 1 Jan 2019
Event13th International Scientific Conference on Parallel Computational Technologies, PCT 2019 - Kaliningrad, Russian Federation
Duration: 2 Apr 20194 Apr 2019

Publication series

NameCommunications in Computer and Information Science
ISSN (Print)1865-0929
ISSN (Electronic)1865-0937


Conference13th International Scientific Conference on Parallel Computational Technologies, PCT 2019
CountryRussian Federation


  • Computational algebra
  • Domain decomposition
  • Heterogeneous supercomputer
  • High performance
  • Iterative method
  • Krylov subspaces
  • Scalable parallelism
  • Sparse matrix

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