Development of a parallel molecular dynamics code on SIMD computers: Algorithm for use of pair list criterion

In recent years several implementations of molecular dynamics (MD) codes have been reported on multiple instruction multiple data (MIMD) machines. However, very few implementations of MD codes on single instruction multiple data (SIMD) machines have been reported. The difficulty in using pair lists of nonbonded interactions is the major problem with MD codes for SIMD machines, such that, generally, the full connectivity computation has been used. We present an algorithm, the global cut-off algorithm (GCA), which permits the use of pair lists on SIMD machines. GCA is based on a probabilistic approach and requires the cut-off condition to be simultaneously verified on all nodes of the machine. The MD code used was taken from the GROMOS package; only the routines involved in the pair lists and in the computation of nonbonded interactions were rewritten for a parallel architecture. The remaining calculations were performed on the host computer. The algorithm has been tested on Quadrics computers for configurations of 32, 128, and 512 processors and for systems of 4000, 8000, 15,000, and 30,000 particles. Quadrics was developed by Istituto Nazionale di Fisica Nucleare (INFN) and marketed by Alenia Spazio. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 685–694, 1998     

Data parallel large-scale molecular dynamics for liquids

An efficient data parallel computational scheme is presented for large-scale molecular dynamics (MD ) simulations of liquids with short-range interactions. The method is based on decomposition of the simulation cell into equally sized subcells, with the shortest side length equal to the cutoff radius. Inter- and intracell interactions are calculated in a coarse-grained manner. A geometric sorting procedure, based on particle distances to subcell boundaries, is used to minimize the overall computations and the nonproductive communications. Using only nearest-neighbor communications, an efficient scheme is developed for periodic updates of the contents of subcells due to the migration of particles. Special “null-particles” are introduced, which act as buffers during the periodic updates and allow for a globally uniform algorithm during the calculations. Communication cost is about 7% of the total CPU time. The method is found to be linearly scalable with the number of particles, performing better as the ratio of virtual to physical processors increases. The MD code is written in Fortran 90 and implemented on a CM-200. The overall speed is approximately 5.9 μs. per MD step and per particle for 1 million particles and 5.5 μs for 5 million particles. The method should be easily transferred to other massively parallel computers of SIMD and MIMD type. © 1993 John Wiley & Sons, Inc.     

SMART: A solvent-accessible triangulated surface generator for molecular graphics and boundary element applications

Summary An algorithm is presented for generating a representation of the solvent-accessible molecular surface as a smooth triangulated manifold. The algorithm, called SMART (SMooth moleculAR surface Triangulator), divides the contact and reentrant portions of the solvent-accessible molecular surface into curvilinear three-sided elements. In contrast to the author's earlier implementation of this general approach [Zauhar, R.J. and Morgan, R.S., J. Comput. Chem., 11 (1990) 603], the SMART algorithm defines elements directly on the appropriate geometric surface types (rather than using interpolation over cubic elements), and has special features to handle highly distorted regions which often appear in deep crevices and internal cavities. While the method is designed for use with boundary element techniques in continuum electrostatics, it can also be applied to the accurate computation of molecular surface areas and volumes, and the generation of shaded surfaces for display with interactive computer graphics. Availability: Programs (in C) for surface generation, area and volume computation are available from the author. Also available is a graphics display program which runs on Silicon Graphics workstations.     

Hybrid particle‐field molecular dynamics simulations: Parallelization and benchmarks

The parallel implementation of a recently developed hybrid scheme for molecular dynamics (MD) simulations (Milano and Kawakatsu, J Chem Phys 2009, 130, 214106) where self‐consistent field theory (SCF) and particle models are combined is described. Because of the peculiar formulation of the hybrid method, considering single particles interacting with density fields, the most computationally expensive part of the hybrid particle‐field MD simulation can be efficiently parallelized using a straightforward particle decomposition algorithm. Benchmarks of simulations, including comparisons of serial MD and MD‐SCF program profiles, serial MD‐SCF and parallel MD‐SCF program profiles, and parallel benchmarks compared with efficient MD program GROMACS 4.5.4 are tested and reported. The results of benchmarks indicate that the proposed parallelization scheme is very efficient and opens the way to molecular simulations of large scale systems with reasonable computational costs. © 2012 Wiley Periodicals, Inc.     

A new parallel method for molecular dynamics simulation of macromolecular systems

Short-range molecular dynamics simulations of molecular systems are commonly parallelized by replicated-data methods, in which each processor stores a copy of all atom positions. This enables computation of bonded 2-, 3-, and 4-body forces within the molecular topology to be partitioned among processors straightforwardly. A drawback to such methods is that the interprocessor communication scales as N (the number of atoms) independent of P (the number of processors). Thus, their parallel efficiency falls off rapidly when large numbers of processors are used. In this article a new parallel method for simulating macromolecular or small-molecule systems is presented, called force-decomposition. Its memory and communication costs scale as N/√P, allowing larger problems to be run faster on greater numbers of processors. Like replicated-data techniques, and in contrast to spatial-decomposition approaches, the new method can be simply load balanced and performs well even for irregular simulation geometries. The implementation of the algorithm in a prototypical macromolecular simulation code ParBond is also discussed. On a 1024-processor Intel Paragon, ParBond runs a standard benchmark simulation of solvated myoglobin with a parallel efficiency of 61% and at 40 times the speed of a vectorized version of CHARMM running on a single Cray Y-MP processor. © 1996 by John Wiley & Sons, Inc.     

Reduced variable molecular dynamics

This article describes an extension to previously developed constraint techniques. These enhanced constraint methods will enable the study of large computational chemistry problems that cannot be easily handled with current constrained molecular dynamics (MD) methods. These methods are based on an O(N) solution to the constrained equations of motion. The benefits of this approach are that (1) the system constraints are solved exactly at each time step, (2) the solution algorithm is noniterative, (3) the algorithm is recursive and scales as O(N), (4) the algorithm is numerically stable, (5) the algorithm is highly amenable to parallel processing, and (6) potentially greater integration step sizes are possible. It is anticipated that application of this methodology will provide a 10- to 100-improvement in the speed of a large molecular trajectory as compared with the time required to run a conventional atomistic unconstrained simulation. It is, therefore, anticipated that this methodology will provide an enabling capacity for pursuing the drug discovery process for large molecular systems. © 1995 John Wiley & Sons, Inc.     

Consideration of data load time on modern processors for the Verlet table and linked-cell algorithms

Neighbor search algorithms are widely used in molecular dynamics for the direct computation of short‐range pairwise interatomic potentials. These algorithms are based on the Verlet table (VT) and linked‐cell (LC) methods. It is widely believed that the VT is more efficient than the LC. The analysis of these methods shows that in case when the average number of interactions per particle is relatively large, or more specifically, the particle density ρ and skin radius r_skin meet the condition (4π/6) ρr/27 ? 1, which may be true for most simulations of liquids, the number of memory data load operations in the LC is much less than that in the VT. Because memory access on modern processors is a bottleneck, this advantage of the LC should be and was in fact used, and a code outperforming the VT by a factor of almost 2 was obtained. Some modifications of the VT were proposed to reduce its disadvantage concerning memory data loading. The key modifications included automated skin radius tuning during simulations and compression of the VT to minimize duplications of atom identifiers in its nearby rows. Although these modifications had improved the performance, the VT failed to regain the superiority over the LC. The methods were tested in the MOLKERN simulation software by using SIMD and multithreading. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Protein calculations on parallel processors. I. Parallel algorithm for the potential energy

We investigate and test an algorithm suitable for the parallel calculation of the potential energy of a protein, or its spatial gradient, when the protein atoms interact via pair potentials. This algorithm is similar to one previously proposed, but it is more efficient, having half the interprocessor communications costs. For a given protein, we show that there is an optimal number of processors that gives a maximum speedup of the potential energy calculation compared to a sequential machine. (Using more than the optimum number of processors actually increases the computation time). With the optimum number the computation time is proportional to the protein size N. This is a considerable improvement in performance compared to sequential machines, where the computation time is proportional to N². We also show that the dependence of the maximum speedup on the message latency time is relatively weak.     

Efficient particle labeling in atomistic simulations

The authors develop an efficient particle labeling procedure based on a linked cell algorithm which is shown to reduce the computing time for a molecular dynamics simulation by a factor of 3. They prove that the improvement of performance is due to the efficient fulfillment of both spatial and temporal locality principles, as implemented by the contiguity of labels corresponding to interacting atoms. Finally, they show that the present label reordering procedure can be used to devise an efficient parallel one-dimensional domain decomposition molecular dynamics scheme.     

Ab initio SCF calculations on [V10O28]6−: A benchmark for the classical calculation and processing of molecular integrals on large Gaussian basis sets

A vector efficient implementation of the McMurchie and Davidson algorithm for the calculation of one- and two-electron molecular integrals is presented, as available in the Cray version of the ASTERIX program system. The implementation and performance of a vector-oriented strategy for the generation and processing of the P supermatrix is also discussed. This program system has been applied to the ab initio SCF computation of the ground-state wave function for the [V₁₀O₂₈]^6? ion, with a basis set of triple-zeta quality for the valence shell of oxygen generating 1404 GTOS and 574 CGTOS for the complete system. The performance and the bottlenecks of the integral calculation are discussed as a function of the integral classes. Two-dimensional maps of the electrostatic potential are presented for this molecule and compared to experimental information about proton fixation.     

ORAC: A Molecular dynamics program to simulate complex molecular systems with realistic electrostatic interactions

In this study, we present a new molecular dynamics program for simulation of complex molecular systems. The program, named ORAC, combines state-of-the-art molecular dynamics (MD) algorithms with flexibility in handling different types and sizes of molecules. ORAC is intended for simulations of molecular systems and is specifically designed to treat biomolecules efficiently and effectively in solution or in a crystalline environment. Among its unique features are: (i) implementation of reversible and symplectic multiple time step algorithms (or r-RESPA, reversible reference system propagation algorithm) specifically designed and tuned for biological systems with periodic boundary conditions; (ii) availability for simulations with multiple or single time steps of standard Ewald or smooth particle mesh Ewald (SPME) for computation of electrostatic interactions; and (iii) possibility of simulating molecular systems in a variety of thermodynamic ensembles. We believe that the combination of these algorithms makes ORAC more advanced than other MD programs using standard simulation algorithms. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1848–1862, 1997     

Dynamic load balancing algorithms for replicated data molecular dynamics

Algorithms to enhance parallel performance of molecular dynamics simulations on parallel computers by dynamic load balancing are described. Load balancing is achieved by redistribution of work based on either a history of time spent computing per processor or on the number of pair interactions computed per processor. The two algorithms we detail are designed to yield optimal load balancing on both workstation clusters and parallel supercomputers. We illustrate these methods using a small molecular dynamics kernel developed for the simulation of rigid molecular solvents. In addition, we discuss our observation regarding global communications performance on workstation clusters with a fiber distributed data interface (FDDI) using a high-speed point-to-point switch (Gigaswitch) and the k-ary 3-cube of the Cray T3D. © 1995 by John Wiley & Sons, Inc.     

Parallel algorithm for efficient calculation of second derivatives of conformational energy function in internal coordinates

A parallel algorithm for efficient calculation of the second derivatives (Hessian) of the conformational energy in internal coordinates is proposed. This parallel algorithm is based on the master/slave model. A master processor distributes the calculations of components of the Hessian to one or more slave processors that, after finishing their calculations, send the results to the master processor that assembles all the components of the Hessian. Our previously developed molecular analysis system for conformational energy optimization, normal mode analysis, and Monte Carlo simulation for internal coordinates is extended to use this parallel algorithm for Hessian calculation on a massively parallel computer. The implementation of our algorithm uses the message passing interface and works effectively on both distributed-memory parallel computers and shared-memory parallel computers. We applied this system to the Newton–Raphson energy optimization of the structures of glutaminyl transfer RNA (Gln-tRNA) with 74 nucleotides and glutaminyl-tRNA synthetase (GlnRS) with 540 residues to analyze the performance of our system. The parallel speedups for the Hessian calculation were 6.8 for Gln-tRNA with 24 processors and 11.2 for GlnRS with 54 processors. The parallel speedups for the Newton–Raphson optimization were 6.3 for Gln-tRNA with 30 processors and 12.0 for GlnRS with 62 processors. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1716–1723, 1998     

Parallel and distributed computing in problems of supercomputer simulation of molecular liquids by the Monte Carlo method

An effective strategy of molecular Monte Carlo simulation is proposed. The strategy is based on a combination of two key approaches to parallel computing. The advantage of spatial (domain) decomposition is the high scalability of computing algorithms by splitting “big tasks” into several simultaneously solvable subtasks. However, the domain size in this method can be reduced to a certain limit only. Particle decomposition (division of program loops into portions) is, by contrast, very efficient in the study of small and medium size objects, but is poorly scalable and quickly exhausts the computer system memory with increasing size of the model. The combination of the approaches helps neutralize their limitations and create efficient supercomputing programs for the study of molecular models consisting of hundreds of millions of atoms.     

Replicated data and domain decomposition molecular dynamics techniques for simulation of anisotropic potentials

The implementation of parallel molecular dynamics techniques is discussed in the context of the simulation of single-site anisotropic potentials. We describe the use of both replicated data and domain decomposition approaches to molecular dynamics and present results for systems of up to 65536 Gay-Berne molecules on a range of parallel computers (Transtech i860/XP Paramid, Intel iPSC/860 Hypercube, Cray T3D). We find that excellent parallel speed-ups are possible for both techniques, with the domain decomposition method found to be the most efficient for the largest systems studied. © 1997 by John Wiley & Sons, Inc.     

Computing the electric potential of biomolecules: Application of a new method of molecular surface triangulation

A new method is presented for defining a smooth, triangulated analytic surface for biological molecules. The surface produced by the algorithm is well-suited for use with a recently developed polarizationcharge technique¹ for the computation of the electrostatic potential of solvated molecules, and may also be used for calculations of molecular surface areas and volumes. The new method employs Connolly's definitions of contact, reentrant and saddle surface,² but includes modifications that preclude the presence of self-interesting reentrant surface, and also insure a rigorous decomposition of contact regions into curvilinear finite elements. The triangulation algorithm may be used in conjunction with the electrostatic methods described previously to compute the electric potential of molecules of arbitrary shape in solution. Applications include the estimation of hydration enthalpies, computation of the electrostatic forces associated with solvation, estimation of interactions between separate charged species in solution, and computation of the three-dimensional form of the molecular electric potential. Test calculations are presented for a double-stranded dinucleotide, the polypeptide enkephalin, and the protein ferredoxin.     

Parallel molecular computations of pairwise exclusive-or (XOR) using DNA "string tile" self-assembly

Self-assembling DNA nanostructures are an efficient means of executing parallel molecular computations. However, previous experimental demonstrations of computations by DNA tile self-assembly only allowed for one set of distinct input to be processed at a time. Here, we report the multibit, parallel computation of pairwise exclusive-or (XOR) using DNA "string tile" self-assembly. A set of DNA tiles encoding the truth table for the XOR logical operation was constructed. Parallel tile self-assembly and ligation led to the formation of reporter DNA strands which encoded both the input and the output of the computations. These reporter strands provided a molecular look-up table containing all possible pairwise XOR calculations up to a certain input size. The computation was readout by sequencing the cloned reporter strands. This is the first experimental demonstration of a parallel computation by DNA tile self-assembly in which a large number of distinct input were simultaneously processed.     

Portably parallel construction of a configuration-interaction wave function from a matrix–product state using the Charm++ framework

The construction of configuration-interaction (CI) expansions from a matrix product state (MPS) involves numerous matrix operations and the skillful sampling of important configurations in a large Hilbert space. In this work, we present an efficient procedure for constructing CI expansions from MPS employing the parallel object-oriented Charm++ programming framework, upon which automatic load-balancing and object migrating facilities can be employed. This procedure was employed in the MPS-to-CI utility (Moritz et al., J. Chem. Phys. 2007, 126, 224109), the sampling-reconstructed complete active-space algorithm (SR-CAS, Boguslawski et al., J. Chem. Phys. 2011, 134, 224101), and the entanglement-driven genetic algorithm (EDGA, Luo et al., J. Chem. Theory Comput. 2017, 13, 4699). It enhances productivity and allows the sampling programs to evolve to their population-expansion versions, for example, EDGA with population expansion (PE-EDGA). Further, examples of 1,2-dioxetanone and firefly dioxetanone anion (FDO⁻) molecules demonstrated the following: (a) parallel efficiencies can be persistently improved by simply by increasing the proportions of the asynchronous executions and (b) a sampled CAS-type CI wave function of a bi-radical-state FDO⁻ molecule utilizing the full valence (30e,26o) active space can be constructed within a few hours with using thousands of cores.     

TopoMS: Comprehensive topological exploration for molecular and condensed‐matter systems

We introduce Topo MS, a computational tool enabling detailed topological analysis of molecular and condensed‐matter systems, including the computation of atomic volumes and charges through the quantum theory of atoms in molecules, as well as the complete molecular graph. With roots in techniques from computational topology, and using a shared‐memory parallel approach, Topo MS provides scalable, numerically robust, and topologically consistent analysis. Topo MS can be used as a command‐line tool or with a GUI (graphical user interface), where the latter also enables an interactive exploration of the molecular graph. This paper presents algorithmic details of Topo MS and compares it with state‐of‐the‐art tools: Bader charge analysis v1.0 (Arnaldsson et al., 01/11/17) and molecular graph extraction using Critic2 (Otero‐de‐la‐Roza et al., Comput. Phys. Commun. 2014, 185, 1007). Topo MS not only combines the functionality of these individual codes but also demonstrates up to 4× performance gain on a standard laptop, faster convergence to fine‐grid solution, robustness against lattice bias, and topological consistency. Topo MS is released publicly under BSD License. © 2018 Wiley Periodicals, Inc.     

A smooth‐particle mesh Ewald method for DL_POLY molecular dynamics simulation package on the Fujitsu VPP700

An N⋅ log (N) smooth‐particle mesh Ewald method has been incorporated into the DL_POLY molecular dynamics simulation package. The performance of the new code has been tested on a Fujitsu VPP700 for several DL_POLY‐specific benchmark systems. The new method is highly vectorizable, and makes use of the extremely efficient Fast Fourier Transforms on the Fujitsu vector machine. In calculations of the coulombic forces in periodic systems requiring large reciprocal space vectors, the new code was found to be considerably faster than the conventional Ewald method. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1187–1191, 2000