Three-dimensional numerical simulation of viscoelastic phase separation under shear: the roles of bulk and shear relaxation moduli

The morphological, dynamic and rheological characteristics in the viscoelastic phase separation(VPS) of sheared polymer solutions are investigated by three-dimensional(3D) numerical simulations of viscoelastic model. The simulations are accelerated by graphic process unit(GPU) to break through the limitation of computation power. Firstly, the morphological and dynamic characteristics of VPS under shear are presented by comparing with those in classic phase separation(CPS). The results show that the phase inversion and phase shrink take place in VPS under shear. Then, the roles of bulk and shear relaxation moduli in VPS are investigated in details. The bulk relaxation modulus slows down the phase separation process under shear, but not affects the dynamic path of VPS. The dynamic path can be divided into three stages: freezing stage, growth stage and stable stage. The second overshoot phenomenon in the shear stress is observed, and explained by the breakdown and reform of string structures. The shear modulus affects morphology evolution in the late stage of VPS under shear.     

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.     

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.     

Routine Microsecond Molecular Dynamics Simulations with AMBER on GPUs. 1. Generalized Born

We present an implementation of generalized Born implicit solvent all-atom classical molecular dynamics (MD) within the AMBER program package that runs entirely on CUDA enabled NVIDIA graphics processing units (GPUs). We discuss the algorithms that are used to exploit the processing power of the GPUs and show the performance that can be achieved in comparison to simulations on conventional CPU clusters. The implementation supports three different precision models in which the contributions to the forces are calculated in single precision floating point arithmetic but accumulated in double precision (SPDP), or everything is computed in single precision (SPSP) or double precision (DPDP). In addition to performance, we have focused on understanding the implications of the different precision models on the outcome of implicit solvent MD simulations. We show results for a range of tests including the accuracy of single point force evaluations and energy conservation as well as structural properties pertainining to protein dynamics. The numerical noise due to rounding errors within the SPSP precision model is sufficiently large to lead to an accumulation of errors which can result in unphysical trajectories for long time scale simulations. We recommend the use of the mixed-precision SPDP model since the numerical results obtained are comparable with those of the full double precision DPDP model and the reference double precision CPU implementation but at significantly reduced computational cost. Our implementation provides performance for GB simulations on a single desktop that is on par with, and in some cases exceeds, that of traditional supercomputers.     

Exploiting graphical processing units to enable quantum chemistry calculation of large solvated molecules with conductor-like polarizable continuum models

The conductor-like polarizable continuum model (C-PCM) with switching/Gaussian smooth discretization is a widely used implicit solvation model in quantum chemistry. We have previously implemented C-PCM solvation for Hartree-Fock (HF) and density functional theory (DFT) on graphical processing units (GPUs), enabling the quantum mechanical treatment of large solvated biomolecules. Here, we first propose a GPU-based algorithm for the PCM conjugate gradient linear solver that greatly improves the performance for very large molecules. The overhead for PCM-related evaluations now consumes less than 15% of the total runtime for DFT calculations on large molecules. Second, we demonstrate that our algorithms tailored for ground state C-PCM are transferable to excited state properties. Using a single GPU, our method evaluates the analytic gradient of the linear response PCM time-dependent density functional theory energy up to 80× faster than a conventional central processing unit (CPU)-based implementation. In addition, our C-PCM algorithms are transferable to other methods that require electrostatic potential (ESP) evaluations. For example, we achieve speed-ups of up to 130× for restricted ESP-based atomic charge evaluations, when compared to CPU-based codes. We also summarize and compare the different PCM cavity discretization schemes used in some popular quantum chemistry packages as a reference for both users and developers.     

A GPU solvent–solvent interaction calculation accelerator for biomolecular simulations using the GROMOS software

During the past few years, graphics processing units (GPUs) have become extremely popular in the high performance computing community. In this study, we present an implementation of an acceleration engine for the solvent–solvent interaction evaluation of molecular dynamics simulations. By careful optimization of the algorithm speed‐ups up to a factor of 54 (single‐precision GPU vs. double‐precision CPU) could be achieved. The accuracy of the single‐precision GPU implementation is carefully investigated and does not influence structural, thermodynamic, and dynamic quantities. Therefore, the implementation enables users of the GROMOS software for biomolecular simulation to run the solvent–solvent interaction evaluation on a GPU, and thus, to speed‐up their simulations by a factor 6–9. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

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     

Excited-State Electronic Structure with Configuration Interaction Singles and Tamm-Dancoff Time-Dependent Density Functional Theory on Graphical Processing Units

Excited-state calculations are implemented in a development version of the GPU-based TeraChem software package using the configuration interaction singles (CIS) and adiabatic linear response Tamm-Dancoff time-dependent density functional theory (TDA-TDDFT) methods. The speedup of the CIS and TDDFT methods using GPU-based electron repulsion integrals and density functional quadrature integration allows full ab initio excited-state calculations on molecules of unprecedented size. CIS/6-31G and TD-BLYP/6-31G benchmark timings are presented for a range of systems, including four generations of oligothiophene dendrimers, photoactive yellow protein (PYP), and the PYP chromophore solvated with 900 quantum mechanical water molecules. The effects of double and single precision integration are discussed, and mixed precision GPU integration is shown to give extremely good numerical accuracy for both CIS and TDDFT excitation energies (excitation energies within 0.0005 eV of extended double precision CPU results).     

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.     

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     

Molecular dynamics simulations using the drude polarizable force field on GPUs with OpenMM: Implementation,validation, and benchmarks

Presented is the implementation of the Drude force field in the open‐source OpenMM simulation package allowing for access to graphical processing unit (GPU) hardware. In the Drude model, electronic degrees of freedom are represented by negatively charged particles attached to their parent atoms via harmonic springs, such that extra computational overhead comes from these additional particles and virtual sites representing lone pairs on electronegative atoms, as well as the associated thermostat and integration algorithms. This leads to an approximately fourfold increase in computational demand over additive force fields. However, by making the Drude model accessible to consumer‐grade desktop GPU hardware it will be possible to perform simulations of one microsecond or more in less than a month, indicating that the barrier to employ polarizable models has largely been removed such that polarizable simulations with the classical Drude model are readily accessible and practical.     

GALAMOST: GPU‐accelerated large‐scale molecular simulation toolkit

GALAMOST [graphics processing unit (GPU)‐accelerated large‐scale molecular simulation toolkit] is a molecular simulation package designed to utilize the computational power of GPUs. Besides the common features of molecular dynamics (MD) packages, it is developed specially for the studies of self‐assembly, phase transition, and other properties of polymeric systems at mesoscopic scale by using some lately developed simulation techniques. To accelerate the simulations, GALAMOST contains a hybrid particle‐field MD technique where particle–particle interactions are replaced by interactions of particles with density fields. Moreover, the numerical potential obtained by bottom‐up coarse‐graining methods can be implemented in simulations with GALAMOST. By combining these force fields and particle‐density coupling method in GALAMOST, the simulations for polymers can be performed with very large system sizes over long simulation time. In addition, GALAMOST encompasses two specific models, that is, a soft anisotropic particle model and a chain‐growth polymerization model, by which the hierarchical self‐assembly of soft anisotropic particles and the problems related to polymerization can be studied, respectively. The optimized algorithms implemented on the GPU, package characteristics, and benchmarks of GALAMOST are reported in detail. © 2013 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.     

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.     

Phase separation and gelation of polymer-dispersed liquid crystals

Polymerization-induced phase separation in polymer-dispersed liquid crystal is studied by computer simulations in two dimensions. The domain morphology resulting from phase separation is investigated by solving the coupled set of equations for the local volume fraction and the nematic order parameter, taking into account the viscoelastic effects and gelation due to polymerization. Comparing the morphology of phase separation by temperature quench, it is shown that the viscoelastic effects and gelation enable the polymer-rich phase to form a stable interconnected domain even when the polymer component is minority. The experimental evidence consistent with this characteristic feature is also given.     

GPU-Accelerated Large-Scale Excited-State Simulation Based on Divide-and-Conquer Time-Dependent Density-Functional Tight-Binding

The present study implemented the divide-and-conquer time-dependent density-functional tight-binding (DC-TDDFTB) code on a graphical processing unit (GPU). The DC method, which is a linear-scaling scheme, divides a total system into several fragments. By separately solving local equations in individual fragments, the DC method could reduce slow central processing unit (CPU)-GPU memory access, as well as computational cost, and avoid shortfalls of GPU memory. Numerical applications confirmed that the present code on GPU significantly accelerated the TDDFTB calculations, while maintaining accuracy. Furthermore, the DC-TDDFTB simulation of 2-acetylindan-1,3-dione displays excited-state intramolecular proton transfer and provides reasonable absorption and fluorescence energies with the corresponding experimental values. © 2019 Wiley Periodicals, Inc.     

Accelerating molecular modeling applications with graphics processors

Molecular mechanics simulations offer a computational approach to study the behavior of biomolecules at atomic detail, but such simulations are limited in size and timescale by the available computing resources. State-of-the-art graphics processing units (GPUs) can perform over 500 billion arithmetic operations per second, a tremendous computational resource that can now be utilized for general purpose computing as a result of recent advances in GPU hardware and software architecture. In this article, an overview of recent advances in programmable GPUs is presented, with an emphasis on their application to molecular mechanics simulations and the programming techniques required to obtain optimal performance in these cases. We demonstrate the use of GPUs for the calculation of long-range electrostatics and nonbonded forces for molecular dynamics simulations, where GPU-based calculations are typically 10-100 times faster than heavily optimized CPU-based implementations. The application of GPU acceleration to biomolecular simulation is also demonstrated through the use of GPU-accelerated Coulomb-based ion placement and calculation of time-averaged potentials from molecular dynamics trajectories. A novel approximation to Coulomb potential calculation, the multilevel summation method, is introduced and compared with direct Coulomb summation. In light of the performance obtained for this set of calculations, future applications of graphics processors to molecular dynamics simulations are discussed.     

Molecular dynamics simulations of aqueous ions at the liquid–vapor interface accelerated using graphics processors

Molecular dynamics (MD) simulations are a vital tool in chemical research, as they are able to provide an atomistic view of chemical systems and processes that is not obtainable through experiment. However, large‐scale MD simulations require access to multicore clusters or supercomputers that are not always available to all researchers. Recently, scientists have returned to exploring the power of graphics processing units (GPUs) for various applications, such as MD, enabled by the recent advances in hardware and integrated programming interfaces such as NVIDIA's CUDA platform. One area of particular interest within the context of chemical applications is that of aqueous interfaces, the salt solutions of which have found application as model systems for studying atmospheric process as well as physical behaviors such as the Hoffmeister effect. Here, we present results of GPU‐accelerated simulations of the liquid–vapor interface of aqueous sodium iodide solutions. Analysis of various properties, such as density and surface tension, demonstrates that our model is consistent with previous studies of similar systems. In particular, we find that the current combination of water and ion force fields coupled with the ability to simulate surfaces of differing area enabled by GPU hardware is able to reproduce the experimental trend of increasing salt solution surface tension relative to pure water. In terms of performance, our GPU implementation performs equivalent to CHARMM running on 21 CPUs. Finally, we address possible issues with the accuracy of MD simulaions caused by nonstandard single‐precision arithmetic implemented on current GPUs. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011