arXiv subjects

Denis Demidov

Publications and source records attributed to Denis Demidov.

8 recordsLinked to original sources

arXiv2022

Efficient solution of 3D elasticity problems with smoothed aggregation algebraic multigrid and block arithmetics

Efficient solution of 3D elasticity problems is an important part of many industrial and scientific applications. Smoothed aggregation algebraic multigrid using rigid body modes for the tentative prolongation operator construction is an efficient and robust choice for the solution of linear systems arising from the discretization of elasticity equations. The system matrices on every level of the multigrid hierarchy have block structure, so using block representation and block arithmetics should significantly improve the solver efficiency. However, the tentative prolongation operator construction may only be done using scalar representation. The paper proposes a couple of practical approaches for enabling the use of block arithmetics with smoothed aggregation algebraic multigrid based on the open-source AMGCL library. It is shown on the example of two real-world model problems that the suggested improvements may speed up the solution by 50% and reduce the memory requirements for the preconditioner by 30%. The implementation is straightforward and only requires a minimal amount of code.

cs.MS↗

arXiv2020

Accelerating linear solvers for Stokes problems with C++ metaprogramming

The efficient solution of large sparse saddle point systems is very important in computational fluid mechanics. The discontinuous Galerkin finite element methods have become increasingly popular for incompressible flow problems but their application is limited due to high computational cost. We describe the C++ programming techniques that may help to accelerate linear solvers for such problems. The approach is based on the policy-based design pattern and partial template specialization, and is implemented in the open source AMGCL library. The efficiency is demonstrated with the example of accelerating an iterative solver of a discontinuous Galerkin finite element method for the Stokes problem. The implementation allows selecting algorithmic components of the solver by adjusting template parameters without any changes to the codebase. It is possible to switch the system matrix to use small statically sized blocks to store the nonzero values, or use a mixed precision solution, which results in up to 4 times speedup, and reduces the memory footprint of the algorithm by about 40\%. We evaluate both monolithic and composite preconditioning strategies for the 3 benchmark problems. The performance of the proposed solution is compared with a multithreaded direct Pardiso solver and a parallel iterative PETSc solver.

cs.MS↗

arXiv2019

Thermoelectric properties of Wigner crystal in two-dimensional periodic potential

We study numerically transport and thermoelectric properties of electrons placed in a two-dimensional (2D) periodic potential. Our results show that the transition from sliding to pinned phase takes place at a certain critical amplitude of lattice potential being similar to the Aubry transition for the one-dimensional Frenkel-Kontorova model. We show that the 2D Aubry pinned phase is characterized by high values of Seebeck coefficient S = 12. At the same time we find that the value of Seebeck coefficient is significantly influenced by the geometry of periodic potential. We discuss possibilities to test the properties of 2D Aubry phase with electrons on a surface of liquid helium.

cond-mat.mes-hall↗

arXiv2019

Wigner crystal diode

We study the transport properties of a Wigner crystal in one- and two-dimensional asymmetric periodic potential. We show that the Aubry transition takes place above a certain critical amplitude of potential with the sliding and pinned phase below and above the transition. Due to the asymmetry the Aubry pinned phase is characterized by the diode charge transport of the Wigner crystal. We argue that the recent experimental observations of Aubry transition with cold ions and colloidal monolayers can be extended to asymmetric potentials making possible to observe Wigner crystal diode with these physical systems and electrons on liquid helium.

cond-mat.mes-hall↗

arXiv2019

What is the central bank of Wikipedia?

We analyze the influence and interactions of 60 largest world banks for 195 world countries using the reduced Google matrix algorithm for the English Wikipedia network with 5 416 537 articles. While the top asset rank positions are taken by the banks of China, with China Industrial and Commercial Bank of China at the first place, we show that the network influence is dominated by USA banks with Goldman Sachs being the central bank. We determine the network structure of interactions of banks and countries and PageRank sensitivity of countries to selected banks. We also present GPU oriented code which significantly accelerates the numerical computations of reduced Google matrix.

cs.SI↗

arXiv2018

AMGCL: an Efficient, Flexible, and Extensible Algebraic Multigrid Implementation

The paper presents AMGCL -- an opensource C++ library implementing the algebraic multigrid method (AMG) for solution of large sparse linear systems of equations, usually arising from discretization of partial differential equations on an unstructured grid. The library supports both shared and distributed memory computation, allows to utilize modern massively parallel processors via OpenMP, OpenCL, or CUDA technologies, has minimal dependencies, and is easily extensible. The design principles behind AMGCL are discussed and it is shown that the code performance is on par with alternative implementations.

cs.MS↗

arXiv2017

Subdomain Deflation Combined with Local AMG: a Case Study Using AMGCL Library

The paper proposes a combination of the subdomain deflation method and local algebraic multigrid as a scalable distributed memory preconditioner that is able to solve large linear systems of equations. The implementation of the algorithm is made available for the community as part of an open source AMGCL library. The solution targets both homogeneous (CPU-only) and heterogeneous (CPU/GPU) systems, employing hybrid MPI/OpenMP approach in the former and a combination of MPI, OpenMP, and CUDA in the latter cases. The use of OpenMP minimizes the number of MPI processes, thus reducing the communication overhead of the deflation method and improving both weak and strong scalability of the preconditioner. The examples of scalar, Poisson-like, systems as well as non-scalar problems, stemming out of the discretization of the Navier-Stokes equations, are considered in order to estimate performance of the implemented algorithm. A comparison with a traditional global AMG preconditioner based on a well-established Trilinos ML package is provided.

cs.DC↗

arXiv2013

Programming CUDA and OpenCL: A Case Study Using Modern C++ Libraries

We present a comparison of several modern C++ libraries providing high-level interfaces for programming multi- and many-core architectures on top of CUDA or OpenCL. The comparison focuses on the solution of ordinary differential equations and is based on odeint, a framework for the solution of systems of ordinary differential equations. Odeint is designed in a very flexible way and may be easily adapted for effective use of libraries such as Thrust, MTL4, VexCL, or ViennaCL, using CUDA or OpenCL technologies. We found that CUDA and OpenCL work equally well for problems of large sizes, while OpenCL has higher overhead for smaller problems. Furthermore, we show that modern high-level libraries allow to effectively use the computational resources of many-core GPUs or multi-core CPUs without much knowledge of the underlying technologies.

cs.MS↗