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At least 1,207 records · Page 67
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Optimizing Communication in 2D Grid-Based MPI Applications at Exascale

The new reality of exascale computing faces many challenges in achieving optimal performance on large numbers of nodes. A key challenge is the efficient utilization of the message-passing interface (MPI), a critical component for process communication. This paper explores communication optimization strategies to harness the GPU-accelerated architectures of these supercomputers. We focus on MPI applications where processors form a two-dimensional process grid, a common arrangement in applications involving dense matrix operations. This configuration offers a unique opportunity to implement innovative strategies to improve performance and maintain effective load distribution. We study two applications— Dist-FW (Apsp:all-pair-shortest-path) and HPL-MxP (LU factorization with Mixed precision)—on two accelerated systems: Summit (IBM Power and NVIDIA V100) and Frontier (AMD EPYC and MI250X). These supercomputers are operated by the Oak Ridge Leadership Computing Facility (OLCF) and are currently ranked #1 and #5 on the Top500 list. We show how to scale up both applications to exascale levels and tackle the MPI challenges related to implementation, synchronization, and performance. We also compare the performance of several communication strategies at an unprecedented scale. Accurately predicting application performance becomes crucial for cost reduction as the computational scale grows. To address this, we suggest a hyperbolic model as a better alternative to the traditional one-sided asymptotic model for predicting future application performance at such large scales.

Lu, Hao↗
DOE OSTI2020

Materials Data on LuH24C4N4Cl7 by Materials Project

(LuCl6)2(CH3NH3)8Cl2 is Silicon tetrafluoride-derived structured and crystallizes in the monoclinic P2 space group. The structure is zero-dimensional and consists of two hydrochloric acid molecules, eight methylammonium molecules, and two LuCl6 clusters. In each LuCl6 cluster, Lu3+ is bonded in an octahedral geometry to six Cl1- atoms. There are a spread of Lu–Cl bond distances ranging from 2.56–2.65 Å. There are three inequivalent Cl1- sites. In the first Cl1- site, Cl1- is bonded in a single-bond geometry to one Lu3+ atom. In the second Cl1- site, Cl1- is bonded in a single-bond geometry to one Lu3+ atom. In the third Cl1- site, Cl1- is bonded in a single-bond geometry to one Lu3+ atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Lu2MgSe4 by Materials Project

MgLu2Se4 is Spinel structured and crystallizes in the cubic Fd-3m space group. The structure is three-dimensional. Mg2+ is bonded to four equivalent Se2- atoms to form MgSe4 tetrahedra that share corners with twelve equivalent LuSe6 octahedra. The corner-sharing octahedral tilt angles are 57°. All Mg–Se bond lengths are 2.61 Å. Lu3+ is bonded to six equivalent Se2- atoms to form LuSe6 octahedra that share corners with six equivalent MgSe4 tetrahedra and edges with six equivalent LuSe6 octahedra. All Lu–Se bond lengths are 2.82 Å. Se2- is bonded in a distorted rectangular see-saw-like geometry to one Mg2+ and three equivalent Lu3+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on LuP by Materials Project

PLu is Halite, Rock Salt structured and crystallizes in the cubic Fm-3m space group. The structure is three-dimensional. Lu3+ is bonded to six equivalent P3- atoms to form a mixture of corner and edge-sharing LuP6 octahedra. The corner-sharing octahedral tilt angles are 0°. All Lu–P bond lengths are 2.77 Å. P3- is bonded to six equivalent Lu3+ atoms to form a mixture of corner and edge-sharing PLu6 octahedra. The corner-sharing octahedral tilt angles are 0°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on LuS2 by Materials Project

LuS2 is Cubic Laves structured and crystallizes in the cubic Fd-3m space group. The structure is three-dimensional. Lu3+ is bonded in a 12-coordinate geometry to twelve equivalent S+1.50- atoms. All Lu–S bond lengths are 3.21 Å. S+1.50- is bonded to six equivalent Lu3+ and six equivalent S+1.50- atoms to form a mixture of corner, edge, and face-sharing SLu6S6 cuboctahedra. All S–S bond lengths are 2.74 Å.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on RbLuSe2 by Materials Project

RbLuSe2 is Caswellsilverite structured and crystallizes in the trigonal R-3m space group. The structure is three-dimensional. Rb1+ is bonded to six equivalent Se2- atoms to form distorted RbSe6 octahedra that share corners with six equivalent LuSe6 octahedra, edges with six equivalent RbSe6 octahedra, and edges with six equivalent LuSe6 octahedra. The corner-sharing octahedral tilt angles are 13°. All Rb–Se bond lengths are 3.44 Å. Lu3+ is bonded to six equivalent Se2- atoms to form LuSe6 octahedra that share corners with six equivalent RbSe6 octahedra, edges with six equivalent RbSe6 octahedra, and edges with six equivalent LuSe6 octahedra. The corner-sharing octahedral tilt angles are 13°. All Lu–Se bond lengths are 2.85 Å. Se2- is bonded to three equivalent Rb1+ and three equivalent Lu3+ atoms to form a mixture of corner and edge-sharing SeRb3Lu3 octahedra. The corner-sharing octahedral tilt angles are 0°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on LuN by Materials Project

LuN is Halite, Rock Salt structured and crystallizes in the cubic Fm-3m space group. The structure is three-dimensional. Lu3+ is bonded to six equivalent N3- atoms to form a mixture of edge and corner-sharing LuN6 octahedra. The corner-sharing octahedral tilt angles are 0°. All Lu–N bond lengths are 2.38 Å. N3- is bonded to six equivalent Lu3+ atoms to form a mixture of edge and corner-sharing NLu6 octahedra. The corner-sharing octahedral tilt angles are 0°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on LuCuS2 by Materials Project

LuCuS2 crystallizes in the orthorhombic Pnma space group. The structure is three-dimensional. Lu3+ is bonded to six S2- atoms to form LuS6 octahedra that share corners with four equivalent LuS6 octahedra, corners with six equivalent CuS4 tetrahedra, edges with four equivalent LuS6 octahedra, and edges with three equivalent CuS4 tetrahedra. The corner-sharing octahedral tilt angles are 51°. There are a spread of Lu–S bond distances ranging from 2.61–2.75 Å. Cu1+ is bonded to four S2- atoms to form CuS4 tetrahedra that share corners with six equivalent LuS6 octahedra, corners with two equivalent CuS4 tetrahedra, edges with three equivalent LuS6 octahedra, and edges with two equivalent CuS4 tetrahedra. The corner-sharing octahedra tilt angles range from 13–61°. There are a spread of Cu–S bond distances ranging from 2.30–2.42 Å. There are two inequivalent S2- sites. In the first S2- site, S2- is bonded in a distorted rectangular see-saw-like geometry to three equivalent Lu3+ and one Cu1+ atom. In the second S2- site, S2- is bonded to three equivalent Lu3+ and three equivalent Cu1+ atoms to form distorted edge-sharing SLu3Cu3 octahedra.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on CsLuCdTe3 by Materials Project

CsLuCdTe3 crystallizes in the orthorhombic Cmcm space group. The structure is three-dimensional. Cs1+ is bonded in a 8-coordinate geometry to eight Te2- atoms. There are a spread of Cs–Te bond distances ranging from 3.95–4.14 Å. Lu3+ is bonded to six Te2- atoms to form LuTe6 octahedra that share corners with two equivalent LuTe6 octahedra, edges with two equivalent LuTe6 octahedra, and edges with four equivalent CdTe4 tetrahedra. The corner-sharing octahedral tilt angles are 41°. There are four shorter (3.09 Å) and two longer (3.15 Å) Lu–Te bond lengths. Cd2+ is bonded to four Te2- atoms to form CdTe4 tetrahedra that share corners with two equivalent CdTe4 tetrahedra and edges with four equivalent LuTe6 octahedra. There are two shorter (2.81 Å) and two longer (2.87 Å) Cd–Te bond lengths. There are two inequivalent Te2- sites. In the first Te2- site, Te2- is bonded in a 6-coordinate geometry to three equivalent Cs1+, two equivalent Lu3+, and one Cd2+ atom. In the second Te2- site, Te2- is bonded in a 6-coordinate geometry to two equivalent Cs1+, two equivalent Lu3+, and two equivalent Cd2+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Ba2LuNbO6 by Materials Project

Ba2LuNbO6 is (Cubic) Perovskite-derived structured and crystallizes in the cubic Fm-3m space group. The structure is three-dimensional. Ba2+ is bonded to twelve equivalent O2- atoms to form BaO12 cuboctahedra that share corners with twelve equivalent BaO12 cuboctahedra, faces with six equivalent BaO12 cuboctahedra, faces with four equivalent LuO6 octahedra, and faces with four equivalent NbO6 octahedra. All Ba–O bond lengths are 2.99 Å. Lu3+ is bonded to six equivalent O2- atoms to form LuO6 octahedra that share corners with six equivalent NbO6 octahedra and faces with eight equivalent BaO12 cuboctahedra. The corner-sharing octahedral tilt angles are 0°. All Lu–O bond lengths are 2.20 Å. Nb5+ is bonded to six equivalent O2- atoms to form NbO6 octahedra that share corners with six equivalent LuO6 octahedra and faces with eight equivalent BaO12 cuboctahedra. The corner-sharing octahedral tilt angles are 0°. All Nb–O bond lengths are 2.03 Å. O2- is bonded in a distorted linear geometry to four equivalent Ba2+, one Lu3+, and one Nb5+ atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on LuTaO4 by Materials Project

LuTaO4 crystallizes in the monoclinic C2/c space group. The structure is three-dimensional. Lu3+ is bonded in a 8-coordinate geometry to eight O2- atoms. There are a spread of Lu–O bond distances ranging from 2.25–2.43 Å. Ta5+ is bonded in a 6-coordinate geometry to six O2- atoms. There are a spread of Ta–O bond distances ranging from 1.88–2.34 Å. There are two inequivalent O2- sites. In the first O2- site, O2- is bonded in a 4-coordinate geometry to two equivalent Lu3+ and two equivalent Ta5+ atoms. In the second O2- site, O2- is bonded in a 3-coordinate geometry to two equivalent Lu3+ and one Ta5+ atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Lu2O3 by Materials Project

Lu2O3 crystallizes in the trigonal P-3m1 space group. The structure is three-dimensional. Lu3+ is bonded in a 7-coordinate geometry to seven O2- atoms. There are a spread of Lu–O bond distances ranging from 2.14–2.52 Å. There are two inequivalent O2- sites. In the first O2- site, O2- is bonded to four equivalent Lu3+ atoms to form OLu4 tetrahedra that share corners with six equivalent OLu6 octahedra, corners with six equivalent OLu4 tetrahedra, edges with three equivalent OLu6 octahedra, and edges with three equivalent OLu4 tetrahedra. The corner-sharing octahedra tilt angles range from 19–55°. In the second O2- site, O2- is bonded to six equivalent Lu3+ atoms to form OLu6 octahedra that share corners with twelve equivalent OLu4 tetrahedra, edges with six equivalent OLu6 octahedra, and edges with six equivalent OLu4 tetrahedra.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on SrLuCuS3 by Materials Project

SrLuCuS3 crystallizes in the orthorhombic Cmcm space group. The structure is three-dimensional. Sr2+ is bonded in a 8-coordinate geometry to eight S2- atoms. There are a spread of Sr–S bond distances ranging from 2.99–3.49 Å. Lu3+ is bonded to six S2- atoms to form LuS6 octahedra that share corners with two equivalent LuS6 octahedra, edges with two equivalent LuS6 octahedra, and edges with four equivalent CuS4 tetrahedra. The corner-sharing octahedral tilt angles are 43°. There are two shorter (2.69 Å) and four longer (2.70 Å) Lu–S bond lengths. Cu1+ is bonded to four S2- atoms to form CuS4 tetrahedra that share corners with two equivalent CuS4 tetrahedra and edges with four equivalent LuS6 octahedra. There are two shorter (2.32 Å) and two longer (2.37 Å) Cu–S bond lengths. There are two inequivalent S2- sites. In the first S2- site, S2- is bonded to two equivalent Sr2+, two equivalent Lu3+, and two equivalent Cu1+ atoms to form a mixture of distorted edge and corner-sharing SSr2Lu2Cu2 octahedra. The corner-sharing octahedral tilt angles are 0°. In the second S2- site, S2- is bonded in a 6-coordinate geometry to three equivalent Sr2+, two equivalent Lu3+, and one Cu1+ atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on PrLuSe3 by Materials Project

LuPrSe3 crystallizes in the orthorhombic Cmcm space group. The structure is three-dimensional. Lu3+ is bonded to six Se2- atoms to form a mixture of edge and corner-sharing LuSe6 octahedra. The corner-sharing octahedral tilt angles are 48°. There are two shorter (2.74 Å) and four longer (2.83 Å) Lu–Se bond lengths. Pr3+ is bonded in a 8-coordinate geometry to eight Se2- atoms. There are a spread of Pr–Se bond distances ranging from 2.95–3.41 Å. There are two inequivalent Se2- sites. In the first Se2- site, Se2- is bonded to two equivalent Lu3+ and two equivalent Pr3+ atoms to form distorted corner-sharing SePr2Lu2 tetrahedra. In the second Se2- site, Se2- is bonded in a 5-coordinate geometry to two equivalent Lu3+ and three equivalent Pr3+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on NdLuSe3 by Materials Project

LuNdSe3 crystallizes in the orthorhombic Cmcm space group. The structure is three-dimensional. Lu3+ is bonded to six Se2- atoms to form a mixture of corner and edge-sharing LuSe6 octahedra. The corner-sharing octahedral tilt angles are 49°. There are two shorter (2.74 Å) and four longer (2.83 Å) Lu–Se bond lengths. Nd3+ is bonded in a 8-coordinate geometry to eight Se2- atoms. There are a spread of Nd–Se bond distances ranging from 2.93–3.40 Å. There are two inequivalent Se2- sites. In the first Se2- site, Se2- is bonded to two equivalent Lu3+ and two equivalent Nd3+ atoms to form distorted corner-sharing SeNd2Lu2 tetrahedra. In the second Se2- site, Se2- is bonded in a 5-coordinate geometry to two equivalent Lu3+ and three equivalent Nd3+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Lu3Al5O12 by Materials Project

Lu3Al5O12 crystallizes in the cubic Ia-3d space group. The structure is three-dimensional. Lu3+ is bonded in a distorted body-centered cubic geometry to eight equivalent O2- atoms. There are four shorter (2.29 Å) and four longer (2.41 Å) Lu–O bond lengths. There are two inequivalent Al3+ sites. In the first Al3+ site, Al3+ is bonded to six equivalent O2- atoms to form corner-sharing AlO6 octahedra. All Al–O bond lengths are 1.93 Å. In the second Al3+ site, Al3+ is bonded to four equivalent O2- atoms to form corner-sharing AlO4 tetrahedra. The corner-sharing octahedral tilt angles are 51°. All Al–O bond lengths are 1.78 Å. O2- is bonded in a 4-coordinate geometry to two equivalent Lu3+ and two Al3+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Lu3Ga5O12 by Materials Project

Lu3Ga5O12 crystallizes in the cubic Ia-3d space group. The structure is three-dimensional. Lu3+ is bonded in a body-centered cubic geometry to eight equivalent O2- atoms. There are four shorter (2.32 Å) and four longer (2.40 Å) Lu–O bond lengths. There are two inequivalent Ga3+ sites. In the first Ga3+ site, Ga3+ is bonded to six equivalent O2- atoms to form corner-sharing GaO6 octahedra. All Ga–O bond lengths are 2.01 Å. In the second Ga3+ site, Ga3+ is bonded to four equivalent O2- atoms to form corner-sharing GaO4 tetrahedra. The corner-sharing octahedral tilt angles are 55°. All Ga–O bond lengths are 1.86 Å. O2- is bonded in a 4-coordinate geometry to two equivalent Lu3+ and two Ga3+ atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Lu2MgS4 by Materials Project

MgLu2S4 is Spinel structured and crystallizes in the cubic Fd-3m space group. The structure is three-dimensional. Mg2+ is bonded to four equivalent S2- atoms to form MgS4 tetrahedra that share corners with twelve equivalent LuS6 octahedra. The corner-sharing octahedral tilt angles are 57°. All Mg–S bond lengths are 2.49 Å. Lu3+ is bonded to six equivalent S2- atoms to form LuS6 octahedra that share corners with six equivalent MgS4 tetrahedra and edges with six equivalent LuS6 octahedra. All Lu–S bond lengths are 2.68 Å. S2- is bonded in a distorted rectangular see-saw-like geometry to one Mg2+ and three equivalent Lu3+ atoms.

36 MATERIALS SCIENCE↗