TY - GEN

T1 - On an Integrated Computational Environment for Numerical Algebra

AU - Il’in, Valery

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Computational algebra

KW - Domain decomposition

KW - Heterogeneous supercomputer

KW - High performance

KW - Iterative method

KW - Krylov subspaces

KW - Scalable parallelism

KW - Sparse matrix

UR - http://www.scopus.com/inward/record.url?scp=85070648597&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-28163-2_7

DO - 10.1007/978-3-030-28163-2_7

M3 - Conference contribution

AN - SCOPUS:85070648597

SN - 9783030281625

T3 - Communications in Computer and Information Science

SP - 91

EP - 106

BT - Parallel Computational Technologies - 13th International Conference, PCT 2019, Revised Selected Papers

A2 - Sokolinsky, Leonid

A2 - Zymbler, Mikhail

PB - Springer-Verlag GmbH and Co. KG

T2 - 13th International Scientific Conference on Parallel Computational Technologies, PCT 2019

Y2 - 2 April 2019 through 4 April 2019

ER -