Locality-aware parallel block-sparse matrix-matrix multiplication using the Chunks and Tasks programming model

We present a method for parallel block-sparse matrix-matrix multiplication on distributed memory clusters. By using a quadtree matrix representation, data locality is exploited without prior information about the matrix sparsity pattern. A distributed quadtree matrix representation is straightforward to implement due to our recent development of the Chunks and Tasks programming model [Parallel Comput. 40, 328 (2014)]. The quadtree representation combined with the Chunks and Tasks model leads to favorable weak and strong scaling of the communication cost with the number of processes, as shown both theoretically and in numerical experiments. Matrices are represented by sparse quadtrees of chunk objects. The leaves in the hierarchy are block-sparse submatrices. Sparsity is dynamically detected by the matrix library and may occur at any level in the hierarchy and/or within the submatrix leaves. In case graphics processing units (GPUs) are available, both CPUs and GPUs are used for leaf-level multiplication work, thus making use of the full computing capacity of each node. The performance is evaluated for matrices with different sparsity structures, including examples from electronic structure calculations. Compared to methods that do not exploit data locality, our locality-aware approach reduces communication significantly, achieving essentially constant communication per node in weak scaling tests.Comment: 35 pages, 14 figure

Siesta: Recent developments and applications

A review of the present status, recent enhancements, and applicability of the SIESTA program is presented. Since its debut in the mid-1990s, SIESTA’s flexibility, efficiency, and free distribution have given advanced materials simulation capabilities to many groups worldwide. The core methodological scheme of SIESTA combines finite-support pseudo-atomic orbitals as basis sets, norm-conserving pseudopotentials, and a realspace grid for the representation of charge density and potentials and the computation of their associated matrix elements. Here, we describe the more recent implementations on top of that core scheme, which include full spin–orbit interaction, non-repeated and multiple-contact ballistic electron transport, density functional theory (DFT)+U and hybrid functionals, time-dependent DFT, novel reduced-scaling solvers, density-functional perturbation theory, efficient van der Waals non-local density functionals, and enhanced molecular-dynamics options. In addition, a substantial effort has been made in enhancing interoperability and interfacing with other codes and utilities, such as WANNIER90 and the second-principles modeling it can be used for, an AiiDA plugin for workflow automatization, interface to Lua for steering SIESTA runs, and various post-processing utilities. SIESTA has also been engaged in the Electronic Structure Library effort from its inception, which has allowed the sharing of various low-level libraries, as well as data standards and support for them, particularly the PSeudopotential Markup Language definition and library for transferable pseudopotentials, and the interface to the ELectronic Structure Infrastructure library of solvers. Code sharing is made easier by the new open-source licensing model of the program. This review also presents examples of application of the capabilities of the code, as well as a view of on-going and future developments. Published under license by AIP Publishing.Siesta development was historically supported by different Spanish National Plan projects (Project Nos. MEC-DGES-PB95-0202, MCyT-BFM2000-1312, MEC-BFM2003-03372, FIS2006-12117, FIS2009-12721, FIS2012-37549, FIS2015-64886-P, and RTC-2016-5681-7), the latter one together with Simune Atomistics Ltd. We are thankful for financial support from the Spanish Ministry of Science, Innovation and Universities through Grant No. PGC2018-096955-B. We acknowledge the Severo Ochoa Center of Excellence Program [Grant Nos. SEV-2015-0496 (ICMAB) and SEV-2017-0706 (ICN2)], the GenCat (Grant No. 2017SGR1506), and the European Union MaX Center of Excellence (EU-H2020 Grant No. 824143). P.G.-F. acknowledges support from Ramón y Cajal (Grant No. RyC-2013-12515). J.I.C. acknowledges Grant No. RTI2018-097895-B-C41. R.C. acknowledges the European Union’s Horizon 2020 Research and Innovation Program under Marie Skłodoswka-Curie Grant Agreement No. 665919. D.S.P, P.K., and P.B. acknowledge Grant No. MAT2016-78293-C6, FET-Open No. 863098, and UPV-EHU Grant No. IT1246-19. V. W. Yu was supported by a MolSSI Fellowship (U.S. NSF Award No. 1547580), and V.B. and V.W.Y. were supported by the ELSI Development by the NSF (Award No. 1450280). We also acknowledge Honghui Shang and Xinming Qin for giving us access to the honpas code, where a preliminary version of the hybrid functional support described here was implemented. We are indebted to other contributors to the Siesta project whose names can be seen in the Docs/Contributors.txt file of the Siesta distribution, and we thank those, too many to list, contributing fixes, comments, clarifications, and documentation for the code.Peer reviewe

Siesta: Recent developments and applications

A review of the present status, recent enhancements, and applicability of the Siesta program is presented. Since its debut in the mid-1990s, Siesta?s flexibility, efficiency, and free distribution have given advanced materials simulation capabilities to many groups worldwide. The core methodological scheme of Siesta combines finite-support pseudo-atomic orbitals as basis sets, norm-conserving pseudopotentials, and a real-space grid for the representation of charge density and potentials and the computation of their associated matrix elements. Here, we describe the more recent implementations on top of that core scheme, which include full spin?orbit interaction, non-repeated and multiple-contact ballistic electron transport, density functional theory (DFT)+U and hybrid functionals, time-dependent DFT, novel reduced-scaling solvers, density-functional perturbation theory, efficient van der Waals non-local density functionals, and enhanced molecular-dynamics options. In addition, a substantial effort has been made in enhancing interoperability and interfacing with other codes and utilities, such as wannier90 and the second-principles modeling it can be used for, an AiiDA plugin for workflow automatization, interface to Lua for steering Siesta runs, and various post-processing utilities. Siesta has also been engaged in the Electronic Structure Library effort from its inception, which has allowed the sharing of various low-level libraries, as well as data standards and support for them, particularly the PSeudopotential Markup Language definition and library for transferable pseudopotentials, and the interface to the ELectronic Structure Infrastructure library of solvers. Code sharing is made easier by the new open-source licensing model of the program. This review also presents examples of application of the capabilities of the code, as well as a view of on-going and future developments.SIESTA development was historically supported by different Spanish National Plan projects (Project Nos. MEC-DGES-PB95-0202, MCyT-BFM2000-1312, MEC-BFM2003-03372, FIS2006-12117, FIS2009-12721, FIS2012-37549, FIS2015-64886-P, and RTC-2016-5681-7), the latter one together with Simune Atomistics Ltd. We are thankful for financial support from the Spanish Ministry of Science, Innovation and Universities through Grant No. PGC2018-096955-