Massively parallel algorithm and implementation of RI-MP2 energy calculation for peta-scale many-core supercomputers

Abstract

A new parallel algorithm and its implementation for the RI-MP2 energy calculation utilizing peta-flop-class many-core supercomputers are presented. Some improvements from the previous algorithm (J. Chem. Theory Comput. 2013, 9, 5373) have been performed: (1) a dual-level hierarchical parallelization scheme that enables the use of more than 10,000 Message Passing Interface (MPI) processes and (2) a new data communication scheme that reduces network communication overhead. A multi-node and multi-GPU implementation of the present algorithm is presented for calculations on a central processing unit (CPU)/graphics processing unit (GPU) hybrid supercomputer. Benchmark results of the new algorithm and its implementation using the K computer (CPU clustering system) and TSUBAME 2.5 (CPU/GPU hybrid system) demonstrate high efficiency. The peak performance of 3.1 PFLOPS is attained using 80,199 nodes of the K computer. The peak performance of the multi-node and multi-GPU implementation is 514 TFLOPS using 1349 nodes and 4047 GPUs of TSUBAME 2.5. © 2016 Wiley Periodicals, Inc.

Coupled‐cluster singles, doubles and perturbative triples with density fitting approximation for massively parallel heterogeneous platforms

“…DF‐based MP2 method has reduced computational cost relative to the conventional MP2 approaches that utilize the 4‐center AO integrals (1) by reducing the cost of the integral evaluation (which is particularly significant for large basis sets with high‐angular momentum AOs) and (2) by reducing the prefactor of the step in integral transformation. Due to these advantages, DF has been the standard formalism in MP2 implementations, including the massively parallel variants., The DF approximation in CCSD and higher‐order methods does not substantially reduce the prefactor of the contribution to the cost; namely, the prefactor of O 2 V 4 term is unchanged, but one O 3 V 3 contribution can be evaluated with lower complexity by re‐factorization . Nevertheless, DF can be benefitial in the context of CCSD and CCSD(T) by reducing the AO/MO integral storage and bandwidth requirements and by reducing the computational cost of integral evaluation and transformation with large AO basis sets .…”

Quantum Chemistry in Dataflow: Density-Fitting MP2

“…[29][30][31] Interest in using GPUs as co-processors for quantum chemistry calculations has increased in recent years as double precision arithmetic is now supported and programming has become easier with CUDA and OpenCL. There are also highly parallel implementations [32][33][34][35] allowing one to calculate MP2 energies on systems as large nanographene sheets 32 and tetrapeptides, 33 as well as combining both highly parallel CPU and GPU heterogeneous architectures to achieve significant speed ups 36,37 on nano-sized molecules.…”

The GPU‐enabled divide‐expand‐consolidate RI‐MP2 method (DEC‐RI‐MP2)

“…The RI approximation was first applied to MP2 by Feyereisen et al [59] and is now an established technique implemented by many groups. [60][61][62][63][64][65][66][67][68][69][70][71] For reviews, the reader is referred to Refs. [72] and [71].…”

“…[60][61][62][63][64][65][66][67][68][69][70][71] For reviews, the reader is referred to Refs. [72] and [71]. Today the method is called RI-MP2, although it is really a misnomer and it should be called density-fitting MP2 (DF-MP2).…”