TY - GEN

T1 - High-performance computation of initial boundary value problems

AU - Il’in, Valery

N1 - Publisher Copyright: © 2018, Springer Nature Switzerland AG.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - Domain decomposition

KW - High-order approximations

KW - Initial guess

KW - Iterative processes

KW - Nonstationary boundary value problems

KW - Scalable parallelism

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=85053200722&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-99673-8_14

DO - 10.1007/978-3-319-99673-8_14

M3 - Conference contribution

AN - SCOPUS:85053200722

SN - 9783319996721

T3 - Communications in Computer and Information Science

SP - 186

EP - 199

BT - Parallel Computational Technologies - 12th International Conference, PCT 2018, Revised Selected Papers

A2 - Sokolinsky, L

A2 - Zymbler, M

PB - Springer-Verlag GmbH and Co. KG

T2 - 12th International Scientific Conference on Parallel Computational Technologies, PCT 2018

Y2 - 2 April 2018 through 6 April 2018

ER -