Performance of heterogeneous computing with graphics processing unit and many integrated core for hartree potential calculations on a numerical grid

We investigated the performance of heterogeneous computing with graphics processing units (GPUs) and many integrated core (MIC) with 20 CPU cores (20×CPU). As a practical example toward large scale electronic structure calculations using grid‐based methods, we evaluated the Hartree potentials of silver nanoparticles with various sizes (3.1, 3.7, 4.9, 6.1, and 6.9 nm) via a direct integral method supported by the sinc basis set. The so‐called work stealing scheduler was used for efficient heterogeneous computing via the balanced dynamic distribution of workloads between all processors on a given architecture without any prior information on their individual performances. 20×CPU + 1GPU was up to ～1.5 and ～3.1 times faster than 1GPU and 20×CPU, respectively. 20×CPU + 2GPU was ～4.3 times faster than 20×CPU. The performance enhancement by CPU + MIC was considerably lower than expected because of the large initialization overhead of MIC, although its theoretical performance is similar with that of CPU + GPU. © 2016 Wiley Periodicals, Inc.     

Acceleration of the GAMESS‐UK electronic structure package on graphical processing units

The approach used to calculate the two‐electron integral by many electronic structure packages including generalized atomic and molecular electronic structure system‐UK has been designed for CPU‐based compute units. We redesigned the two‐electron compute algorithm for acceleration on a graphical processing unit (GPU). We report the acceleration strategy and illustrate it on the (ss|ss) type integrals. This strategy is general for Fortran‐based codes and uses the Accelerator compiler from Portland Group International and GPU‐based accelerators from Nvidia. The evaluation of (ss|ss) type integrals within calculations using Hartree Fock ab initio methods and density functional theory are accelerated by single and quad GPU hardware systems by factors of 43 and 153, respectively. The overall speedup for a single self consistent field cycle is at least a factor of eight times faster on a single GPU compared with that of a single CPU. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Acceleration of a QM/MM‐QMC simulation using GPU

We accelerated an ab initio molecular QMC calculation by using GPGPU. Only the bottle‐neck part of the calculation is replaced by CUDA subroutine and performed on GPU. The performance on a (single core CPU + GPU) is compared with that on a (single core CPU with double precision), getting 23.6 (11.0) times faster calculations in single (double) precision treatments on GPU. The energy deviation caused by the single precision treatment was found to be within the accuracy required in the calculation, ～10^?5 hartree. The accelerated computational nodes mounting GPU are combined to form a hybrid MPI cluster on which we confirmed the performance linearly scales to the number of nodes. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Best bang for your buck: GPU nodes for GROMACS biomolecular simulations

The molecular dynamics simulation package GROMACS runs efficiently on a wide variety of hardware from commodity workstations to high performance computing clusters. Hardware features are well‐exploited with a combination of single instruction multiple data, multithreading, and message passing interface (MPI)‐based single program multiple data/multiple program multiple data parallelism while graphics processing units (GPUs) can be used as accelerators to compute interactions off‐loaded from the CPU. Here, we evaluate which hardware produces trajectories with GROMACS 4.6 or 5.0 in the most economical way. We have assembled and benchmarked compute nodes with various CPU/GPU combinations to identify optimal compositions in terms of raw trajectory production rate, performance‐to‐price ratio, energy efficiency, and several other criteria. Although hardware prices are naturally subject to trends and fluctuations, general tendencies are clearly visible. Adding any type of GPU significantly boosts a node's simulation performance. For inexpensive consumer‐class GPUs this improvement equally reflects in the performance‐to‐price ratio. Although memory issues in consumer‐class GPUs could pass unnoticed as these cards do not support error checking and correction memory, unreliable GPUs can be sorted out with memory checking tools. Apart from the obvious determinants for cost‐efficiency like hardware expenses and raw performance, the energy consumption of a node is a major cost factor. Over the typical hardware lifetime until replacement of a few years, the costs for electrical power and cooling can become larger than the costs of the hardware itself. Taking that into account, nodes with a well‐balanced ratio of CPU and consumer‐class GPU resources produce the maximum amount of GROMACS trajectory over their lifetime. © 2015 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Grid‐based algorithm to search critical points,in the electron density,accelerated by graphics processing units

Using a grid‐based method to search the critical points in electron density, we show how to accelerate such a method with graphics processing units (GPUs). When the GPU implementation is contrasted with that used on central processing units (CPUs), we found a large difference between the time elapsed by both implementations: the smallest time is observed when GPUs are used. We tested two GPUs, one related with video games and other used for high‐performance computing (HPC). By the side of the CPUs, two processors were tested, one used in common personal computers and other used for HPC, both of last generation. Although our parallel algorithm scales quite well on CPUs, the same implementation on GPUs runs around 10× faster than 16 CPUs, with any of the tested GPUs and CPUs. We have found what one GPU dedicated for video games can be used without any problem for our application, delivering a remarkable performance, in fact; this GPU competes against one HPC GPU, in particular when single‐precision is used. © 2014 Wiley Periodicals, Inc.     

Accelerating molecular dynamic simulation on graphics processing units

We describe a complete implementation of all‐atom protein molecular dynamics running entirely on a graphics processing unit (GPU), including all standard force field terms, integration, constraints, and implicit solvent. We discuss the design of our algorithms and important optimizations needed to fully take advantage of a GPU. We evaluate its performance, and show that it can be more than 700 times faster than a conventional implementation running on a single CPU core. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Computation of induced dipoles in molecular mechanics simulations using graphics processors

In this work, we present a tentative step toward the efficient implementation of polarizable molecular mechanics force fields with GPU acceleration. The computational bottleneck of such applications is found in the treatment of electrostatics, where higher-order multipoles and a self-consistent treatment of polarization effects are needed. We have implemented a GPU accelerated code, based on the Tinker program suite, for the computation of induced dipoles. The largest test system used shows a speedup factor of over 20 for a single precision GPU implementation, when comparing to the serial CPU version. A discussion of the optimization and parametrization steps is included. Comparison between different graphic cards and CPU-GPU embedding is also given. The current work demonstrates the potential usefulness of GPU programming in accelerating this field of applications.     

GPU accelerated implementation of NCI calculations using promolecular density

The NCI approach is a modern tool to reveal chemical noncovalent interactions. It is particularly attractive to describe ligand–protein binding. A custom implementation for NCI using promolecular density is presented. It is designed to leverage the computational power of NVIDIA graphics processing unit (GPU) accelerators through the CUDA programming model. The code performances of three versions are examined on a test set of 144 systems. NCI calculations are particularly well suited to the GPU architecture, which reduces drastically the computational time. On a single compute node, the dual‐GPU version leads to a 39‐fold improvement for the biggest instance compared to the optimal OpenMP parallel run (C code, icc compiler) with 16 CPU cores. Energy consumption measurements carried out on both CPU and GPU NCI tests show that the GPU approach provides substantial energy savings. © 2017 Wiley Periodicals, Inc.     

Porting ONETEP to graphical processing unit‐based coprocessors. 1. FFT box operations

We present the first graphical processing unit (GPU) coprocessor‐enabled version of the Order‐N Electronic Total Energy Package (ONETEP) code for linear‐scaling first principles quantum mechanical calculations on materials. This work focuses on porting to the GPU the parts of the code that involve atom‐localized fast Fourier transform (FFT) operations. These are among the most computationally intensive parts of the code and are used in core algorithms such as the calculation of the charge density, the local potential integrals, the kinetic energy integrals, and the nonorthogonal generalized Wannier function gradient. We have found that direct porting of the isolated FFT operations did not provide any benefit. Instead, it was necessary to tailor the port to each of the aforementioned algorithms to optimize data transfer to and from the GPU. A detailed discussion of the methods used and tests of the resulting performance are presented, which show that individual steps in the relevant algorithms are accelerated by a significant amount. However, the transfer of data between the GPU and host machine is a significant bottleneck in the reported version of the code. In addition, an initial investigation into a dynamic precision scheme for the ONETEP energy calculation has been performed to take advantage of the enhanced single precision capabilities of GPUs. The methods used here result in no disruption to the existing code base. Furthermore, as the developments reported here concern the core algorithms, they will benefit the full range of ONETEP functionality. Our use of a directive‐based programming model ensures portability to other forms of coprocessors and will allow this work to form the basis of future developments to the code designed to support emerging high‐performance computing platforms.Copyright © 2013 Wiley Periodicals, Inc.     

More bang for your buck: Improved use of GPU nodes for GROMACS 2018

We identify hardware that is optimal to produce molecular dynamics (MD) trajectories on Linux compute clusters with the GROMACS 2018 simulation package. Therefore, we benchmark the GROMACS performance on a diverse set of compute nodes and relate it to the costs of the nodes, which may include their lifetime costs for energy and cooling. In agreement with our earlier investigation using GROMACS 4.6 on hardware of 2014, the performance to price ratio of consumer GPU nodes is considerably higher than that of CPU nodes. However, with GROMACS 2018, the optimal CPU to GPU processing power balance has shifted even more toward the GPU. Hence, nodes optimized for GROMACS 2018 and later versions enable a significantly higher performance to price ratio than nodes optimized for older GROMACS versions. Moreover, the shift toward GPU processing allows to cheaply upgrade old nodes with recent GPUs, yielding essentially the same performance as comparable brand-new hardware. © 2019 Wiley Periodicals, Inc.     

GPU accelerated numerical simulations of viscoelastic phase separation model

We introduce a complete implementation of viscoelastic model for numerical simulations of the phase separation kinetics in dynamic asymmetry systems such as polymer blends and polymer solutions on a graphics processing unit (GPU) by CUDA language and discuss algorithms and optimizations in details. From studies of a polymer solution, we show that the GPU-based implementation can predict correctly the accepted results and provide about 190 times speedup over a single central processing unit (CPU). Further accuracy analysis demonstrates that both the single and the double precision calculations on the GPU are sufficient to produce high-quality results in numerical simulations of viscoelastic model. Therefore, the GPU-based viscoelastic model is very promising for studying many phase separation processes of experimental and theoretical interests that often take place on the large length and time scales and are not easily addressed by a conventional implementation running on a single CPU.     

High-performance transformation of protein structure representation from internal to Cartesian coordinates

We present a highly parallel algorithm to convert internal coordinates of a polymeric molecule into Cartesian coordinates. Traditionally, converting the structures of polymers (e.g., proteins) from internal to Cartesian coordinates has been performed serially, due to an inherent linear dependency along the polymer chain. We show this dependency can be removed using a tree-based concatenation of coordinate transforms between segments, and then parallelized efficiently on graphics processing units (GPUs). The conversion algorithm is applicable to protein engineering and fitting protein structures to experimental data, and we observe an order of magnitude speedup using parallel processing on a GPU compared to serial execution on a CPU.     

A fast parallel clustering algorithm for molecular simulation trajectories

We implemented a GPU‐powered parallel k‐centers algorithm to perform clustering on the conformations of molecular dynamics (MD) simulations. The algorithm is up to two orders of magnitude faster than the CPU implementation. We tested our algorithm on four protein MD simulation datasets ranging from the small Alanine Dipeptide to a 370‐residue Maltose Binding Protein (MBP). It is capable of grouping 250,000 conformations of the MBP into 4000 clusters within 40 seconds. To achieve this, we effectively parallelized the code on the GPU and utilize the triangle inequality of metric spaces. Furthermore, the algorithm's running time is linear with respect to the number of cluster centers. In addition, we found the triangle inequality to be less effective in higher dimensions and provide a mathematical rationale. Finally, using Alanine Dipeptide as an example, we show a strong correlation between cluster populations resulting from the k‐centers algorithm and the underlying density. © 2012 Wiley Periodicals, Inc.     

New ways to boost molecular dynamics simulations

We describe a set of algorithms that allow to simulate dihydrofolate reductase (DHFR, a common benchmark) with the AMBER all‐atom force field at 160 nanoseconds/day on a single Intel Core i7 5960X CPU (no graphics processing unit (GPU), 23,786 atoms, particle mesh Ewald (PME), 8.0 Å cutoff, correct atom masses, reproducible trajectory, CPU with 3.6 GHz, no turbo boost, 8 AVX registers). The new features include a mixed multiple time‐step algorithm (reaching 5 fs), a tuned version of LINCS to constrain bond angles, the fusion of pair list creation and force calculation, pressure coupling with a “densostat,” and exploitation of new CPU instruction sets like AVX2. The impact of Intel's new transactional memory, atomic instructions, and sloppy pair lists is also analyzed. The algorithms map well to GPUs and can automatically handle most Protein Data Bank (PDB) files including ligands. An implementation is available as part of the YASARA molecular modeling and simulation program from www.YASARA.org . © 2015 The Authors Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Efficient calculation of two‐electron integrals for high angular basis functions

The computation of electron repulsion integrals (ERIs) is the most time‐consuming process in the density functional calculation using Gaussian basis set. Many temporal ERIs are calculated, and most are stored on slower storage, such as cache or memory, because of the shortage of registers, which are the fastest storage in a central processing unit (CPU). Moreover, the heavy register usage makes it difficult to launch many concurrent threads on a graphics processing unit (GPU) to hide latency. Hence, we propose to optimize the calculation order of one‐center ERIs to minimize the number of registers used, and to calculate each ERI with three or six co‐operating threads. The performance of this method is measured on a recent CPU and a GPU. The proposed approach is found to be efficient for high angular basis functions with a GPU. When combined with a recent GPU, it accelerates the computation almost 4‐fold. © 2014 Wiley Periodicals, Inc.     

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

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.     

libKEDF: An accelerated library of kinetic energy density functionals

Kinetic energy density functionals (KEDFs) approximate the kinetic energy of a system of electrons directly from its electron density. They are used in electronic structure methods that lack direct access to orbitals, for example, orbital‐free density functional theory (OFDFT) and certain embedding schemes. In this contribution, we introduce libKEDF, an accelerated library of modern KEDF implementations that emphasizes nonlocal KEDFs. We discuss implementation details and assess the performance of the KEDF implementations for large numbers of atoms. We show that using libKEDF, a single computing node or (GPU) accelerator can provide easy computational access to mesoscale chemical and materials science phenomena using OFDFT algorithms. © 2017 Wiley Periodicals, Inc.     

Accelerated Simulation Study of Space Charge Effects in Quadrupole Ion Traps Using GPU Techniques

Space charge effects play important roles in the performance of various types of mass analyzers. Simulation of space charge effects is often limited by the computation capability. In this study, we evaluate the method of using graphics processing unit (GPU) to accelerate ion trajectory simulation. Simulation using GPU has been compared with multi-core central processing unit (CPU), and an acceleration of about 390 times have been obtained using a single computer for simulation of up to 10⁵ ions in quadrupole ion traps. Characteristics of trapped ions can be investigated at detailed levels within a reasonable simulation time. Space charge effects on the trapping capacities of linear and 3D ion traps, ion cloud shapes, ion motion frequency shift, mass spectrum peak coalescence effects between two ion clouds of close m/z are studied with the ion trajectory simulation using GPU.     

分子动力学模拟计算在通用图形处理芯片上的实现

将在计算生物分子中广泛应用的CHARMM力场应用于Windows computer cluster server(WCCS)环境下, 并实现了该力场及分子动力学模拟程序的通用显卡(GPU)并行计算. 对一些多肽链的动力学模拟结果显示, 与CPU计算相比, GPU计算在计算速度上有巨大的提升. 与64位Athlon 2.0G相比, 在NVIDIA GeForce 8800 GT显卡上的动力学模拟速度提高了至少10倍, 而且这个效率比会随着模拟体系及每块尺寸的增大而增大. 模拟体系的增大使得GPU并行单元的计算空载相对减少, 块尺寸的增大使缓存区尺寸相对减少, 单块计算效率得以提高. 在测试样本中, 该效率比最高可达到28倍以上. 利用GPU计算还对一条含有397个原子的多肽链进行了分子动力学模拟, 给出了氢键分布随时间的变化结果.     

Quantum supercharger library: Hyper‐parallelism of the Hartree–Fock method

We present here a set of algorithms that completely rewrites the Hartree–Fock (HF) computations common to many legacy electronic structure packages (such as GAMESS‐US, GAMESS‐UK, and NWChem) into a massively parallel compute scheme that takes advantage of hardware accelerators such as Graphical Processing Units (GPUs). The HF compute algorithm is core to a library of routines that we name the Quantum Supercharger Library (QSL). We briefly evaluate the QSL's performance and report that it accelerates a HF 6‐31G Self‐Consistent Field (SCF) computation by up to 20 times for medium sized molecules (such as a buckyball) when compared with mature Central Processing Unit algorithms available in the legacy codes in regular use by researchers. It achieves this acceleration by massive parallelization of the one‐ and two‐electron integrals and optimization of the SCF and Direct Inversion in the Iterative Subspace routines through the use of GPU linear algebra libraries. © 2015 Wiley Periodicals, Inc.