Parallelization and benchmarks

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Transcription:

Parallelization and benchmarks

Content! Scalable implementation of the DFT/LCAO module! Plane wave DFT code! Parallel performance of the spin-free CC codes! Scalability of the Tensor Contraction Engine based CC implementations! iterative methods! non-iterative approaches 2

Gaussian DFT computational kernel Evaluation of XC potential matrix element my_next_task = SharedCounter() do i=1,max_i if(i.eq.my_next_task) then call ga_get() ρ(x (do work) q ) = µν D µν χ κ (x q ) χ ν (x q ) call ga_acc() F my_next_task = λσ += SharedCounter() q w q χ λ (x q ) V xc [ρ(x q )] χ σ (x q ) endif enddo barrier() D µν F λσ Both GA operations are greatly dependent on the communication latency 3

Parallel scaling of the DFT code 4 Si 28 O 148 H 66 3554 Basis functions LDA wavefunction XC build Benchmark run on Cray XK6

Parallel scaling of the DFT code 5 Si 159 O 264 H 110 7108 Basis functions LDA wavefunction XC build Benchmark run on Cray XK6

Parallel timings for AIMD simulation of UO 2 2+ +122H 2 O! Development of algorithms for AIMD has progressed in recent years! 0.1-10 seconds per step can be obtained on many of today s supercomputers for most AIMD simulations.! However, large numbers of cpus are often required! 5000 cpus * 10 days à 1.2 million cpu hours! Very easy to use up 1-2 million CPUs hours in a single simulation 6

Plane wave DFT Exact exchange timings 576 atom cell of water (cutoff energy=100ry). These calculations were performed on the Hopper Cray-XE6 computer system at NERSC. 7

CCSD(T) run on Cray XT5 : 24 water November 2009 Floating-Point performance at 223K cores: 1.39 PetaFLOP/s (H 2 O) 24 72 atoms 1224 basis functions Cc-pvtz(-f) basis

What is Tensor Contraction Engine (TCE)! Symbolic manipulation & program generator! Automates the derivation of complex working equations based on a well-defined second quantized many-electron theories! Synthesizing efficient parallel computer programs on the basis of these equations.! Granularity of the parallel CC TCE codes is provided by the so-called tiles, which define the partitioning of the whole spinorbital domain. 9

What is Tensor Contraction Engine (TCE) Tile structure: α β α β S1 S2 S1 S2 S1 S2. S1 S2. Occupied spinorbitals unoccupied spinorbitals Tile-induced block structure of the CC tensors: CPU1 CPU2 CPU3. i a T T [ h [ p n ] ] m CPU n 10

New elements of parallel design for the iterative CCSD/EOMCCSD method! Use of Global Arrays (GA) to implement a distributed memory model! Iterative CCSD/EOMCCSD methods (basic challenges)! Global memory requirements! Complex load balancing! Complicated communication pattern: use of one-sided ga_get,ga_put,ga_acc! Implementation improvements! New way of representing antysymmetric 2-electron integrals for the restricted (RHF) and restricted open-shell (ROHF) references! Replication of low-rank tensors! New task scheduling for the CCSD/EOMCCSD methods 11

Scalability of the iterative EOMCC methods! Alternative task schedulers! use global task pool! improve load balancing! reduce the number of synchronization steps to absolute minimum! larger tiles can be effectively used 12

New elements of parallel design for the non-iterative CR-EOMCCSD(T) method! Use of Global Arrays (GA) to implement a distributed memory model! Basic challenges for Non-Iterative CR-EOMCCSD(T) method! Local memory requirements: (tilesize) 4 (EOMCCSD) vs. M* (tilesize) 6 (CR-EOMCCSD(T))! Implementation improvements! Two-fold reduction of local memory use : 2*(tilesize) 6! New algorithms which enable the decomposition of sixdimensional tensors 13

Scalability of the non-iterative EOMCC code 94 %parallel efficiency using 210,000 cores! Scalability of the triples part of the CR- EOMCCSD(T) approach for the FBP-f-coronene system in the AVTZ basis set. Timings were determined from calculations on the Jaguar Cray XT5 computer system at NCCS. 14

Multireference CC methods! Multireference CC methods in NWChem (next release)! Strongly correlated excited states! Implemented MRCC approaches! Brillouin-Wigner MRCCSD! Mukherjee Mk-MRCCSD approach! State-Universal MRCCSD (under testing)! Perturbative triples corrections MRCCSD(T)! Novel paralellization strategies based on the processor groups! Demonstrated scalability of MRCCSD across 24,000 cores 15

16 Questions?

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