Large Parallel Computers Research Articles

An expandable local and parallel two-grid finite element scheme

An expandable local and parallel two-grid finite element scheme based on superposition principle for elliptic problems is proposed and analyzed in this paper by taking example of Poisson equation. Compared with the usual local and parallel finite element schemes, the scheme proposed in this paper can be easily implemented in a large parallel computer system that has a lot of CPUs. Convergence results based on H1 and L2 a priori error estimation of the scheme are obtained, which show that the scheme can reach the optimal convergence orders within |lnH|2 or |lnH| two-grid iterations if the coarse mesh size H and the fine mesh size h are properly configured in 2-D or 3-D case, respectively. Some numerical results are presented at the end of the paper to support our analysis.

Application of a force field algorithm for creating strongly correlated multiscale sphere packings

This work presents a protocol driven force field algorithm, used to create multiscale correlated dense sphere packings. It was developed as part of a tool chain for the reconstruction of realistic multiscale porous rock samples. It overcomes limitations of Monte-Carlo or deposition based approaches, that are quite common in this field and were used previously. The new algorithm can create large, low porosity sphere packings with radius distributions covering two decades. Highly correlated structures that model pore clogging and sedimentation can be generated. To achieve this, an adequate force field and proper termination strategies are necessary. By changing the algorithm parameters in a controlled way during the simulation, a complex protocol driven process can be established. The implementation of the algorithm targets large parallel computer platforms to perform simulations with more than 10 million spheres. This article includes an application of the algorithm used to generate a highly polydisperse sphere packing with roughly 106 spheres and radii from 1 źtoź 100 µm . The continuum description of this packing is discretized at resolutions from 0.25 źtoź 1 µm and investigated using geometric and statistical characterizations and results from Lattice-Boltzmann flow simulations. These resolution dependent results affirm that reliable, predictive calculations for multiscale porous microstructures depend on the availability of large realistic continuum models. To obtain such models the algorithm presented herein can be used as a starting point.

A Comparative Study of Interconnection Network

The topology of interconnection networks the stage a key role in the performance of all general purpose networking applications. Cube-based architectures are one of the most important interconnection networks that focuses upon the evaluation and applications of cube-based networks. Cubebased architectures have received greatly focus over the past decade since they propose a wealthy interconnected structure with a number of attractive properties such as low diameter, high bisection width, smaller complexity and Cost. However, the major drawback of cube-based architectures is the difficulty of its VLSI layout. In Parallel computer, the hypercube network has been broadly used as the interconnection network. However, the number of communication links for each node is a logarithmic function of the total number of nodes in hypercubes. Therefore, the hypercube is not a superior applicant for an interconnection network for a extremely large parallel computer that might contain hundreds of thousands of nodes due to IC technology and port number restrictions. In this paper a variety of interconnection network based on the cube-based networks is brief discussed along with their properties. X-torus topology has better properties in terms of diameter, average latency, throughput, and path diversity. Although some more links are added in xtorus, the number of links is of the same order of magnitude with that of mesh, xmesh, and torus. It also takes advantage of increasing higher levels of VLSI process. The comparative study suggests the methods to overcome the above restrictions besides having attractive properties. General Terms Parallel processing, Interconnection networks, Topological Properties

An upwind least square formulation for free surfaces calculation of viscoplastic steady-state metal forming problems

Despite using very large parallel computers, numerical simulation of some forming processes such as multi-pass rolling, extrusion or wire drawing, need long computation time due to the very large number of time steps required to model the steady regime of the process. The direct calculation of the steady-state, whenever possible, allows reducing by 10–20 the computational effort. However, removing time from the equations introduces another unknown, the steady final shape of the domain. Among possible ways to solve this coupled multi-fields problem, this paper selects a staggered fixed-point algorithm that alternates computation of mechanical fields on a prescribed domain shape with corrections of the domain shape derived from the velocity field and the stationary condition v.n = 0. It focuses on the resolution of the second step in the frame of unstructured 3D meshes, parallel computing with domain partitioning, and complex shapes with strong contact restraints. To insure these constraints a global finite elements formulation is used. The weak formulation based on a Galerkin method of the v.n = 0 equation is found to diverge in severe tests cases. The least squares formulation experiences problems in the presence of contact restraints, upwinding being shown necessary. A new upwind least squares formulation is proposed and evaluated first on analytical solutions. Contact being a key issue in forming processes, and even more with steady formulations, a special emphasis is given to the coupling of contact equations between the two problems of the staggered algorithm, the thermo-mechanical and free surface problems. The new formulation and algorithm is finally applied to two complex actual metal forming problems of rolling. Its accuracy and robustness with respect to the shape initialization of the staggered algorithm is discussed, and its efficiency is compared to non-steady simulations.

Section Based Hex-Cell Routing ALGORITHM (SBHCR)

A Hex-Cell network topology can be constructed using units of hexagon cells. It has been introduced in the literature as interconnection network suitable for large parallel computers, which can connect large number of nodes with three links per node. Although this topology exhibits attractive characteristics such as embeddability, symmetry, regularity, strong resilience, and simple routing, the previously suggested routing algorithms suffer from the high number of logical operations and the need for readdressing of nodes every time a new level is add to the network. This negatively impacts the performance of the network as it increases the execution time of these algorithms. In this paper we propose an improved optimal point to point routing algorithm for Hex-Cell network. The algorithm is based on dividing the Hex-Cell topology into six divisions, hence the name Section Based Hex-Cell Routing (SBHCR). The SBHCR algorithm is simple and preserves the advantage of the addressing scheme proposed for the Hex-Cell network. It does not depend on the depth of the network topology which leads to overcome the issue of readdressing of nodes every time a new level is added. Evaluation against two previously suggested routing algorithms has shown the superiority of SBHCR in term of less logical operations.

A parallel space-time domain decomposition method for unsteady source inversion problems

In this paper, we propose a parallel space-time domain decomposition method for solving an unsteady source identification problem governed by the linear convection-diffusion equation. Traditional approaches require to solve repeatedly a forward parabolic system, an adjoint system and a system with respect to the unknowns. The three systems have to be solved one after another. These sequential steps are not desirable for large scale parallel computing. A space-time restrictive additive Schwarz method is proposed for a fully implicit space-time coupled discretization scheme to recover the time-dependent pollutant source intensity functions. We show with numerical experiments that the scheme works well with noise in the observation data. More importantly it is demonstrated that the parallel space-time Schwarz preconditioner is scalable on a supercomputer with over $10^3$ processors, thus promising for large scale applications.

Node-to-set disjoint paths routing in a metacube

The metacube interconnection network was designed for large parallel computers in 2002. Compared with a hypercube of the same size, a metacube has a degree significantly lower while retaining a similar diameter. For example, a metacube having only six links per node has the capacity to connect 2

Analysis of the second order accurate uniform equilibrium flux method and its graphics processing unit acceleration

The extension of the Uniform Equilibrium Flux Method (UEFM) to second order accuracy in space is presented. This extension is made possible through the recasting of the original UEFM flux expressions from a volumetric flux to a surface flux, allowing for reconstruction through a Taylor series expansion of the resulting split surface fluxes at the cell interfaces. By doing so, we avoid the difficulties associated with integration of the gradient terms over velocity and physical space as required by the original UEFM fluxes. Analysis of the dissipative qualities of the renewed direction split UEFM flux expressions demonstrate that the numerical dissipation is a function of Mach number, with increasing amounts of dissipation present with increasing Mach numbers. Following this analysis, the higher order UEFM fluxes are applied to large scale parallel computation using Graphics Processing Units, or GPUs, through the use of CUDA. The vector split nature of the UEFM fluxes are well suited to GPU computation due to the high degree of locality. This parallelization is performed using a cell-based parallel paradigm through the creation of several key CUDA kernels for the calculation of split fluxes, gradient of split fluxes and state related computations. The algorithm is executed entirely on the GPU device, with the host remaining idle during the computation stage. The GPU accelerated UEFM algorithm is then applied to the solution of several two dimensional benchmark problems. Speedup of approximately 200 and 171 times for first order accuracy and second order accuracy respectively is demonstrated when using an Nvidia Tesla C2075 computing GPU compared to that of a single core of an Intel Xeon E5-2760 CPU.

Toward large scale parallel computer simulation of viscoelastic fluid flow: A study of benchmark flow problems

Followed by our previous study, an OpenFOAM-based viscoelastic flow solver has been further validated through simulation of viscoelastic flow past a cylinder. The drag coefficients calculated by the Oldroyd-B model under the creeping flow in a range of Weissenberg (Wi) number are in good agreements with those reported in the literature. Using the linear Phan-Thien Tanner (L-PTT) model, time-dependent two-dimensional simulations of flow past cylinder have been carried out in a range of Wi number and Reynolds (Re) number, and revealed interesting cooperative effects of inertia and elasticity on the structural evolution of the wake behind the cylinder. The details of parallel computing strategy are analysed and discussed. The codes are evaluated for large scale parallel simulation of two-dimensional and three-dimensional contraction flow as well as two-dimensional flow past a cylinder. The key bottlenecks, which affect the scalability of parallel computing, are discussed.

High performance computing for flood simulation using Telemac based on hybrid MPI/OpenMP parallel programming

Usually simulations on environment flood issues will face the scalability problem of large scale parallel computing. The plain parallel technique based on pure MPI is difficult to have a good scalability due to the large number of domain partitioning. Therefore, the hybrid programming using MPI and OpenMP is introduced to deal with the issue of scalability. This kind of parallel technique can give a full play to the strengths of MPI and OpenMP. During the parallel computing, OpenMP is employed by its efficient fine grain parallel computing and MPI is used to perform the coarse grain parallel domain partitioning for data communications. Through the tests, the hybrid MPI/OpenMP parallel programming was used to renovate the finite element solvers in the BIEF library of Telemac. It was found that the hybrid programming is able to provide helps for Telemac to deal with the scalability issue.

Large Data Visualization Analysis and Application in Scientific Computing

With the rapid development of computer hardware, software and network technology, the size of data is growing exponentially. Recently, large scientific computing data visualization becomes one of the important researches in scientific computing. This paper introduces the definition of big data, visualization analysis field and the significance of scientific computing for large data visualization. In the following part, we analyze and discuss the traditional scientific visualization methods, and introduce the algorithms in classification according to different types of datasets. We analyze the weak points of traditional methods in visualization of scientific computing, and then introduce the method of large data parallel computing and rendering based on GPU. Finally, combining the research of our group on scientific computing theory and application, we point out the direction for future work of scientific computing visualization with large data development.

Impact of mesh partitioning methods in CFD for large scale parallel computing

It was well known that high performance computing depends on load balance and mesh cell distributions. A well balanced load can improve efficiency of parallel computing and minimizing the number of cells with remote neighbors can reduce the time spent on the data communication among processors. Mesh partitioning methods were able to optimize the mesh cell distributions for large scale parallel computing. In this paper, the open source mesh partitioning software packages, such as Metis, ParMetis, Scotch, PT-Scotch and Zoltan, were ported into Code_Saturne, which is an open source CFD software package, for realizing the optimization on large scale CFD applications. Through the studies, it was found that the mesh partitioning methods strongly affect the CFD code on high performance computing especially for large scale parallel computing.

The parallelization of the Keller box method on heterogeneous cluster of workstations

High performance computing is the branch of parallel computing dealing with very large problems and large parallel computers that can solve those problems in a reasonable amount of time. This paper will describe the parallelization of the Keller-box method using the high performance computing on heterogeneous cluster of workstations. The problem statement is based on the equation of boundary-layer flow due to a moving flat plate. The objective is to develop the parallel algorithm of the Keller-box method in purpose to solve a large size of matrix. The parallelization is based on the domain decomposition, where the upper and lower matrices will be splitting into a number of blocks, which then will be compute concurrently on the parallel computers. The experiment was run using 200, 2000, and 20000 size of matrices and using 10 number of processors. The comparison was made from the results obtained from that various size of matrices by doing the analysis based on the performance measurement in terms of time execution, speedup, and effectiveness.

EON: software for long time simulations of atomic scale systems

The EON software is designed for simulations of the state-to-state evolution of atomic scale systems over timescales greatly exceeding that of direct classical dynamics. States are defined as collections of atomic configurations from which a minimization of the potential energy gives the same inherent structure. The time evolution is assumed to be governed by rare events, where transitions between states are uncorrelated and infrequent compared with the timescale of atomic vibrations. Several methods for calculating the state-to-state evolution have been implemented in EON, including parallel replica dynamics, hyperdynamics and adaptive kinetic Monte Carlo. Global optimization methods, including simulated annealing, basin hopping and minima hopping are also implemented. The software has a client/server architecture where the computationally intensive evaluations of the interatomic interactions are calculated on the client-side and the state-to-state evolution is managed by the server. The client supports optimization for different computer architectures to maximize computational efficiency. The server is written in Python so that developers have access to the high-level functionality without delving into the computationally intensive components. Communication between the server and clients is abstracted so that calculations can be deployed on a single machine, clusters using a queuing system, large parallel computers using a message passing interface, or within a distributed computing environment. A generic interface to the evaluation of the interatomic interactions is defined so that empirical potentials, such as in LAMMPS, and density functional theory as implemented in VASP and GPAW can be used interchangeably. Examples are given to demonstrate the range of systems that can be modeled, including surface diffusion and island ripening of adsorbed atoms on metal surfaces, molecular diffusion on the surface of ice and global structural optimization of nanoparticles.

Accurate and ScalableO(N)Algorithm for First-Principles Molecular-Dynamics Computations on Large Parallel Computers

We present the first truly scalable first-principles molecular dynamics algorithm with O(N) complexity and controllable accuracy, capable of simulating systems with finite band gaps of sizes that were previously impossible with this degree of accuracy. By avoiding global communications, we provide a practical computational scheme capable of extreme scalability. Accuracy is controlled by the mesh spacing of the finite difference discretization, the size of the localization regions in which the electronic wave functions are confined, and a cutoff beyond which the components of the overlap matrix can be omitted when computing selected elements of its inverse. We demonstrate the algorithm's excellent parallel scaling for up to 101,952 atoms on 23,328 processors, with a wall-clock time of the order of 1 min per molecular dynamics time step and numerical error on the forces of less than 7×10(-4) Ha/Bohr.

A Parallel Domain Decomposition Method for 3D Unsteady Incompressible Flows at High Reynolds Number

Numerical simulation of three-dimensional incompressible flows at high Reynolds number using the unsteady Navier---Stokes equations is challenging. In order to obtain accurate simulations, very fine meshes are necessary, and such simulations are increasingly important for modern engineering practices, such as understanding the flow behavior around high speed trains, which is the target application of this research. To avoid the time step size constraint imposed by the CFL number and the fine spacial mesh size, we investigate some fully implicit methods, and focus on how to solve the large nonlinear system of equations at each time step on large scale parallel computers. In most of the existing implicit Navier---Stokes solvers, segregated velocity and pressure treatment is employed. In this paper, we focus on the Newton---Krylov---Schwarz method for solving the monolithic nonlinear system arising from the fully coupled finite element discretization of the Navier---Stokes equations on unstructured meshes. In the subdomain, LU or point-block ILU is used as the local solver. We test the algorithm for some three-dimensional complex unsteady flows, including flows passing a high speed train, on a supercomputer with thousands of processors. Numerical experiments show that the algorithm has superlinear scalability with over three thousand processors for problems with tens of millions of unknowns.

A parallel finite element simulator for ion transport through three‐dimensional ion channel systems

A parallel finite element simulator, ichannel, is developed for ion transport through three-dimensional ion channel systems that consist of protein and membrane. The coordinates of heavy atoms of the protein are taken from the Protein Data Bank and the membrane is represented as a slab. The simulator contains two components: a parallel adaptive finite element solver for a set of Poisson-Nernst-Planck (PNP) equations that describe the electrodiffusion process of ion transport, and a mesh generation tool chain for ion channel systems, which is an essential component for the finite element computations. The finite element method has advantages in modeling irregular geometries and complex boundary conditions. We have built a tool chain to get the surface and volume mesh for ion channel systems, which consists of a set of mesh generation tools. The adaptive finite element solver in our simulator is implemented using the parallel adaptive finite element package Parallel Hierarchical Grid (PHG) developed by one of the authors, which provides the capability of doing large scale parallel computations with high parallel efficiency and the flexibility of choosing high order elements to achieve high order accuracy. The simulator is applied to a real transmembrane protein, the gramicidin A (gA) channel protein, to calculate the electrostatic potential, ion concentrations and I - V curve, with which both primitive and transformed PNP equations are studied and their numerical performances are compared. To further validate the method, we also apply the simulator to two other ion channel systems, the voltage dependent anion channel (VDAC) and α-Hemolysin (α-HL). The simulation results agree well with Brownian dynamics (BD) simulation results and experimental results. Moreover, because ionic finite size effects can be included in PNP model now, we also perform simulations using a size-modified PNP (SMPNP) model on VDAC and α-HL. It is shown that the size effects in SMPNP can effectively lead to reduced current in the channel, and the results are closer to BD simulation results.

209 大規模並列計算による球状火炎伝播の直接数値計算

209 大規模並列計算による球状火炎伝播の直接数値計算

Development of Strong Ground Motion and Structure Seismic Response Simulation Method using Large Scale Parallel Computer

Development of Strong Ground Motion and Structure Seismic Response Simulation Method using Large Scale Parallel Computer

Performance Analysis and Optimization of PalaBos on Petascale Sunway BlueLight MPP Supercomputer

We present some results conceming the computational performances of the open source general purpose CFD code PalaBos, in terms of scalability and efficiency, on the petascale Sunway BlueLight MPP system. Based on the numerical simulated program of 3D cavity lid driven flow, the optimization methods in I/O, communication, memory access, etc, are applied in debugging and optimization of the parallel MPI program. Experimental results of large scalar parallel computing of 3D cavity lid driven flow show that, the parallel strategy and optimization methods are correct and efficient. The parallel implementation scheme is very useful and can shorten the computing time explicitly.