MPI Routines Research Articles

Exploiting underlying crystal lattice for efficient computation of Coulomb matrix elements in multi-million atoms nanostructures

Atomistic modeling of nanostructures often leads to computationally challenging problems involving millions of atoms and tens of thousands of Coulomb matrix elements. In our previous work, we presented a practical solution to this problem, where quasi-linear efficiency, both in time and memory, was obtained by utilizing the fast Fourier transform. Here, we present an updated version of our highly-parallelized computer program, named Coulombo-Lattice, that eliminates the necessity of introducing an auxiliary basis set for the wave-function transfer to the computational grid. Here, we instead exploit the properties of the underlying crystal lattice and run calculations on a regular three-dimensional grid superimposed on the original, lower-symmetry lattice. Due to removal of spurious interactions from other supercells, the resulting Coulomb matrix elements are, up to numerical precision, identical to those obtained by the direct summation O(N2) method, yet our code maintains O(Nlog⁡N) scaling. We illustrate our approach by calculations involving up to 1.7 million integrals, and number of atoms reaching up to 2.8 million, for the problem of dopant charging energy for a single phosphorus dopant embedded in a silicon lattice. Next, to emphasize the broad applicability of our code, we show the results for mixed zinc-blend/wurtzite lattice systems, also known as crystal phase quantum dots. Program summaryProgram Title: Coulombo-LatticeCPC Library link to program files:https://doi.org/10.17632/jwkvh5ycbf.1Licensing provisions: CC BY 4.0Programming language: C++Nature of problem: Computing the Coulomb matrix elements (Coulomb and exchange integrals), while being a demanding computational task, is a necessary step in a range of quantum mechanical calculations. For example, in the field of nanostructures, such as quantum dots and nanowires or novel single dopant devices, this stage of calculation (even after a series of approximations) is at least an O(N2) operation (a summation over all pairs of N atoms or grid points in the analyzed system). Moreover, calculating the full Coulomb matrix usually requires the computation of thousands of such elements, thus presenting a formidable computational challenge.Solution method: We provide a ready-to-use implementation for calculating Coulomb matrix elements for a given set of input wavefunctions in LCAO (linear combination of atomic orbitals) form resulting from tight-binding calculation. This implementation is based on the approach introduced in [1,2], by using a fast Fourier transform. In this work, we further significantly improved the method by eliminating the need to introduce wave-function transfer via auxiliary basis set.Additional comments including Restrictions and Unusual features: The implementation is fully parallelized in a distributed-memory model, using MPI and parallel routines from FFTW [3].

Višekriterijumska aerodinamička optimizacija energetske efikasnosti farme vetrogeneratora koja je zasnovana na genetskim algoritmima

In this paper, the possibilities of using parallel processing algorithms and methodologies were analyzed in order to more efficiently solve the very complex problem of multi-criteria aerodynamic optimization in order to achieve the maximum energy efficiency of the entire wind farm, which is based on genetic optimization algorithms. It has been shown that the best results are obtained by applying the genetic algorithm method of distributive differential evolution. The program algorithm was written using MPI routines for communication between processors and was executed on a computer cluster located at the Faculty of Mechanical Engineering of the University of Belgrade within the SimLab laboratory.

GenASiSBasics: Object-oriented utilitarian functionality for large-scale physics simulations (Version 4)

GenASiSBasics: Object-oriented utilitarian functionality for large-scale physics simulations (Version 4)

Efficient computation of Coulomb and exchange integrals for multi-million atom nanostructures

Atomistic modeling of nanostructures such as quantum dots or nanowires often involves numbers of atoms reaching and even exceeding well beyond 1 million. Such a large quantity of atoms presents a very complex computational challenge especially at a stage of many-body calculation where numerous Coulomb matrix elements need to be calculated. Here we present a practical solution to this problem by performing calculations in the momentum space and utilizing fast Fourier transform combined with a memory-efficient way to compute the convolution that overcomes the problem of spurious interactions with quasi-charges from other super-cells. Finally, calculation of multiple integrals is optimized by reducing the problem to finding a minimum vertex cover of a graph. All these algorithms are implemented and presented here in a self-contained and highly parallelized computer program named Coulombo. Coulombo demonstrates quasi-linear scaling of computational time of Coulomb matrix elements with respect to the number of points in the computational box and, at the same time, significantly reduced memory demand. The proposed solution can have potential applications not only in the realm of nano-physics, but could be applied to other mesoscopic simulations or large-scale quantum chemistry problems. Program summaryProgram Title: CoulomboProgram Files doi:http://dx.doi.org/10.17632/98bhm5zbrd.1Licensing provisions: CC BY 4.0Programming language: C++Nature of problem: Computing the Coulomb matrix elements (Coulomb and exchange integrals), while being a demanding computational task, is a necessary step in a range of quantum mechanical calculations. For example, in the field of nanostructures, such as quantum dots and nanowires, this stage of calculation even after numerous approximations is at least an O(N2) operation (a summation over all pairs of N atoms or grid points in the analyzed system). Moreover, calculating the full Coulomb matrix usually requires computation of thousands of such elements, thus presenting a formidable computational challenge.Solution method: We provide a ready-to-use implementation for calculating Coulomb matrix elements for a given set of input wavefunctions. This implementation is based on the approach introduced in [1], by using a fast Fourier transform to compute the convolution. In this work we further significantly improved the method by eliminating the need to extend the computational domain with padding, thus reducing the memory consumption by a factor of 8. The optimal computational plan for each run is prepared by calculating a minimum vertex cover on a graph representing the subset of requested Coulomb matrix elements.Additional comments including restrictions and unusual features: The implementation is fully parallelized in a distributed-memory model, using MPI and parallel routines from FFTW [2]. A minimum vertex cover is computed by our greedy approximation algorithm, which we found to perform significantly better than the standard text-book heuristic.

A Case for Embedded FPGA-based SoCs in Energy-Efficient Acceleration of Graph Problems

Sparse graph problems are notoriously hard to accelerate on conventional platforms due to irregular memory access patterns resulting in underutilization of memory bandwidth. These bottlenecks on traditional x86-based systems mean that sparse graph problems scale very poorly, both in terms of performance and power efficiency. A cluster of embedded SoCs systems-on-chip with closely-coupled FPGA accelerators can support distributed memory access with better matched low-power processing. We first conduct preliminary experiments across a range of COTS commercial off-the-shelf embedded SoCs to establish promise for energy-efficiency acceleration of sparse problems. We select the Xilinx Zynq SoC with FPGA accelerators to construct a prototype 32 node Beowulf cluster. We develop specialized MPI routines and memory DMA offload engines to support irregular communication efficiently. In this setup, we use the ARM processor as a data marshaller for local DMA traffic as well as remote MPI traffic while the FPGA may be used as a programmable accelerator. Across a set of benchmark graphs, we show that 32-node embedded SoC cluster can exceed the energy efficiency of an Intel E5-2407 by as much as 1.7 at a total graph processing capacity of 91-95 MTEPS for graphs as large as 32 million nodes and edges.

Towards Automatic Load Balancing for Programming Parallel Fuzzy Expert Systems in Heterogeneous Clusters

FuzzyCLIPS is a rule-based language designed especially for developing fuzzy expert systems. A FuzzyCLIPS programmer has no need to write an algorithm to solve a problem. Instead, he only needs to list the rules for dealing with various conditions. However, due to the characteristics of rule-based languages, the execution of an expert system is always more time-consuming than any one of the conventional algorithmic languages. To cope with this problem, we propose to execute a FuzzyCLIPS application in parallel on the emerging heterogeneous cluster system. Furthermore, to maximize the speedup of the parallel execution and to minimize the burden of programmers, we have implemented built-in selfscheduling schemes in the FuzzyCLIPS interpreter for better load balancing. Programmers only need to use our proposed directives to specify where the parallelisms are, no explicit and complicated send and receive routines have to be invoked in their parallel programs. According to the specified directives, the master process will automatically assign the tasks and transmit the required data to slave processes by calling MPI routines. Experimental results show that the built-in load balancing schemes can improve the system performance significantly.

A Duality between Forward and Adjoint MPI Communication Routines

In this article, we explore a natural duality that exist between MPI communication routines in parallel programs, and show the ease of its adjoint implementation via pointers.

Parallel Programming: Techniques and Applications Using Networked Workstations and Parallel Computers

I. BASIC TECHNIQUES. 1. Parallel Computers. 2. Message-Passing Computing. 3. Embarrassingly Parallel Computations. 4. Partitioning and Divide-and-Conquer Strategies. 5. Pipelined Computations. 6. Synchronous Computations. 7. Load Balancing and Termination Detection. 8. Programming with Shared Memory. 9. Distributed Shared Memory Systems and Programming. II. ALGORITHMS AND APPLICATIONS. 10. Sorting Algorithms. 11. Numerical Algorithms. 12. Image Processing. 13. Searching and Optimization. Appendix A: Basic MPI Routines. Appendix B: Basic Pthread Routines. Appendix C: OpenMP Directives, Library Functions, and Environment Variables Index.

A Spectral Global Gyrokinetic Approach to Plasma Linear Microinstability Analysis

With the term microinstabilities, we indicate a class of plasma drift waves such as the ion temperature gradient (ITG) mode, the trapped electron mode (TEM), and the electromagnetic Alfvénic ion temperature gradient (AITG) mode. They are usually driven by spatial gradients in the plasma and they are held responsible for anomalous transport and enhanced heat flux in tokamaks. Their understanding is therefore crucial for the development of magnetically confined plasma fusion devices. Our approach is based on the gyrokinetic model (Hahm 1988) for particle dynamics. The gyrokinetic nonlinear Vlasov equation, in the presence of an electromagnetic perturbation (Brizard 1989, 1995), is derived using Lie perturbation theory (Cary and Littlejohn 1983) to average out the fast particle motion around the gyrocenter. We have linearized the gyrokinetic Vlasov equation and added the quasi‐neutrality equation and Ampère's law, providing closure to the system. A temporal spectral formulation is used, ensuring the absence of numerical instabilities due to high frequency modes. The equations are simplified with a large aspect ratio approximation for an axisymmetric toroidal configuration. The fields are expanded in a Fourier series in the three spatial directions (radial, poloidal, and toroidal) reducing the problem in a matrix form. The code EM‐GLOGYSTO (Brunner et al. 1998; Falchetto et al. 2003; Joint Varenna‐Lausanne International Workshop 2002) has been developed to look at its solutions. Recently, we have included in the model an electrostatic equilibrium potential in order to provide E×B sheared flow. The code has been optimized for running in a parallel environment using MPI routines, and it allows us to study frequencies, growth rates, and mode structures of electromagnetic microinstabilities. Results on an AITG mode are shown to illustrate these features.

MPI‐CHECK: a tool for checking Fortran 90 MPI programs

AbstractMPI is commonly used to write parallel programs for distributed memory parallel computers. MPI‐CHECK is a tool developed to aid in the debugging of MPI programs that are written in free or fixed format Fortran 90 and Fortran 77. MPI‐CHECK provides automatic compile‐time and run‐time checking of MPI programs. MPI‐CHECK automatically detects the following problems in the use of MPI routines: (i) mismatch in argument type, kind, rank or number; (ii) messages which exceed the bounds of the source/destination array; (iii) negative message lengths; (iv) illegal MPI calls before MPI_INIT or after MPI_FINALIZE; (v) inconsistencies between the declared type of a message and its associated DATATYPE argument; and (vi) actual arguments which violate the INTENT attribute. Copyright © 2003 John Wiley & Sons, Ltd.