HPC Benchmarking: Problem Size Matters

2016 ◽  
Author(s):  
Vladimir Marjanovic ◽  
Jose Gracia ◽  
Colin W. Glass
Keyword(s):  
Problem Size

Circles on lattices and Hadamard matrices

2019 ◽  
pp. 2-9 ◽  
Author(s):  
N. A. Balonin ◽  
M. B. Sergeev ◽  
J. Seberry ◽  
O. I. Sinitsyna
Keyword(s):  
Hadamard Matrices ◽  
Lattice Points ◽  
Practical Significance ◽  
Upper And Lower Bounds ◽  
Problem Size ◽  
Orthogonal Matrices ◽  
Video Information ◽  
Scientific Schools ◽  
Gauss Theorem ◽  
Triangular Numbers

Introduction: The Hadamard conjecture about the existence of Hadamard matrices in all orders multiple of 4, and the Gauss problem about the number of points in a circle are among the most important turning points in the development of mathematics. They both stimulated the development of scientific schools around the world with an immense amount of works. There are substantiations that these scientific problems are deeply connected. The number of Gaussian points (Z3 lattice points) on a spheroid, cone, paraboloid or parabola, along with their location, determines the number and types of Hadamard matrices.Purpose: Specification of the upper and lower bounds for the number of Gaussian points (with odd coordinates) on a spheroid depending on the problem size, in order to specify the Gauss theorem (about the solvability of quadratic problems in triangular numbers by projections onto the Liouville plane) with estimates for the case of Hadamard matrices. Methods: The authors, in addition to their previous ideas about proving the Hadamard conjecture on the base of a one-to-one correspondence between orthogonal matrices and Gaussian points, propose one more way, using the properties of generalized circles on Z3 .Results: It is proved that for a spheroid, the lower bound of all Gaussian points with odd coordinates is equal to the equator radius R, the upper limit of the points located above the equator is equal to the length of this equator L=2πR, and the total number of points is limited to 2L. Due to the spheroid symmetry in the sector with positive coordinates (octant), this gives the values of R/8 and L/4. Thus, the number of Gaussian points with odd coordinates does not exceed the border perimeter and is no less than the relative share of the sector in the total volume of the figure.Practical significance: Hadamard matrices associated with lattice points have a direct practical significance for noise-resistant coding, compression and masking of video information.

3D simulation of emulsion flow using the boundary element method on the heterogeneous computational systems

2012 ◽  
Vol 9 (1) ◽  
pp. 142-146
Author(s):  
O.A. Solnyshkina
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Problem Size ◽  
Low Reynolds Numbers ◽  
Infinite Domains ◽  
The Matrix ◽  
Computational Systems ◽  
Element Method

In this work the 3D dynamics of two immiscible liquids in unbounded domain at low Reynolds numbers is considered. The numerical method is based on the boundary element method, which is very efficient for simulation of the three-dimensional problems in infinite domains. To accelerate calculations and increase the problem size, a heterogeneous approach to parallelization of the computations on the central (CPU) and graphics (GPU) processors is applied. To accelerate the iterative solver (GMRES) and overcome the limitations associated with the size of the memory of the computation system, the software component of the matrix-vector product

scholarly journals Efficient Multi-Objective CFD-Based Optimization Method for a Scroll Distributor

Energies ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 377
Author(s):  
Damian Obidowski ◽  
Mateusz Stajuda ◽  
Krzysztof Sobczak
Keyword(s):  
Energy Savings ◽  
Axisymmetric Flow ◽  
Geometry Optimization ◽  
Optimization Method ◽  
Problem Size ◽  
Computational Point ◽  
Multi Objective ◽  
Flow Problems ◽  
Multi Objective Genetic Algorithm ◽  
Separation Zones

An efficient approach to the geometry optimization problem of a non-axisymmetric flow channel is discussed. The method combines geometrical transformation with a computational fluid dynamics solver, a multi-objective genetic algorithm, and a response surface. This approach, through geometrical modifications and simplifications allows transforming a non-axisymmetric problem into the axisymmetric one in some specific devices i.e., a scroll distributor or a volute. It results in a significant decrease in the problem size, as only the flow in a quasi-2D section of the channel is solved. A significantly broader design space is covered in a much shorter time than in the standard method, and the optimization of large flow problems is feasible with desktop-class computers. One computational point is obtained approximately eight times faster than in full geometry computations. The method was applied to a scroll distributor. For the case under analysis, it was possible to increase flow uniformity, eradicate separation zones, and increase the overall efficiency, which was followed by energy savings of 16% for the scroll. The results indicate that this method can be successfully applied for the optimization of similar problems.

Strategies for Solving Large Location-Allocation Problems by Heuristic Methods

1992 ◽  
Vol 24 (2) ◽  
pp. 289-304 ◽  
Author(s):  
P J Densham ◽  
G Rushton
Keyword(s):  
Spatial Structure ◽  
Heuristic Methods ◽  
Problem Size ◽  
Interpoint Distance ◽  
Allocation Algorithm ◽  
Complexity Of Algorithms ◽  
Location Allocation ◽  
Network Problems ◽  
Allocation Problems ◽  
Distance Data

Solution techniques for location-allocation problems usually are not a part of microcomputer-based geoprocessing systems because of the large volumes of data to process and store and the complexity of algorithms. In this paper, it is shown that processing costs for the most accurate, heuristic, location-allocation algorithm can be drastically reduced by exploiting the spatial structure of location-allocation problems. The strategies used, preprocessing interpoint distance data as both candidate and demand strings, and use of them to update an allocation table, allow the solution of large problems (3000 nodes) in a microcomputer-based, interactive decisionmaking environment. Moreover, these strategies yield solution times which increase approximately linearly with problem size. Tests on four network problems validate these claims.

scholarly journals Beyond spatial scalability limitations with a massively parallel method for linear oscillatory problems

2017 ◽  
Vol 32 (6) ◽  
pp. 913-933 ◽  
Author(s):  
Martin Schreiber ◽  
Pedro S Peixoto ◽  
Terry Haut ◽  
Beth Wingate
Keyword(s):  
High Performance ◽  
Large Scale ◽  
Weather Prediction ◽  
Finite Difference Methods ◽  
Scaling Limit ◽  
Performance Model ◽  
Massively Parallel ◽  
Large Set ◽  
Problem Size ◽  
Single Node

This paper presents, discusses and analyses a massively parallel-in-time solver for linear oscillatory partial differential equations, which is a key numerical component for evolving weather, ocean, climate and seismic models. The time parallelization in this solver allows us to significantly exceed the computing resources used by parallelization-in-space methods and results in a correspondingly significantly reduced wall-clock time. One of the major difficulties of achieving Exascale performance for weather prediction is that the strong scaling limit – the parallel performance for a fixed problem size with an increasing number of processors – saturates. A main avenue to circumvent this problem is to introduce new numerical techniques that take advantage of time parallelism. In this paper, we use a time-parallel approximation that retains the frequency information of oscillatory problems. This approximation is based on (a) reformulating the original problem into a large set of independent terms and (b) solving each of these terms independently of each other which can now be accomplished on a large number of high-performance computing resources. Our results are conducted on up to 3586 cores for problem sizes with the parallelization-in-space scalability limited already on a single node. We gain significant reductions in the time-to-solution of 118.3× for spectral methods and 1503.0× for finite-difference methods with the parallelization-in-time approach. A developed and calibrated performance model gives the scalability limitations a priori for this new approach and allows us to extrapolate the performance of the method towards large-scale systems. This work has the potential to contribute as a basic building block of parallelization-in-time approaches, with possible major implications in applied areas modelling oscillatory dominated problems.

Study and Analysis of GA-Based Heuristic Applied to Assembly Line Balancing Problem

2014 ◽  
Vol 13 (02) ◽  
pp. 113-131 ◽  
Author(s):  
P. Sivasankaran ◽  
P. Shahabudeen
Keyword(s):  
Cycle Time ◽  
Assembly Line ◽  
Assembly Line Balancing ◽  
Optimal Solution ◽  
Vital Role ◽  
Line Balancing ◽  
Problem Size ◽  
Minimum Number ◽  
Assembly Line Balancing Problem ◽  
Balancing Efficiency

Balancing assembly line in a mass production system plays a vital role to improve the productivity of a manufacturing system. In this paper, a single model assembly line balancing problem (SMALBP) is considered. The objective of this problem is to group the tasks in the assembly network into a minimum number of workstations for a given cycle time such that the balancing efficiency is maximized. This problem comes under combinatorial category. So, it is essential to develop efficient heuristic to find the near optimal solution of the problem in less time. In this paper, an attempt has been made to design four different genetic algorithm (GA)-based heuristics, and analyze them to select the best amongst them. The analysis has been carried out using a complete factorial experiment with three factors, viz. problem size, cycle time, and algorithm, and the results are reported.

scholarly journals A language extension set to generate adaptive versions automatically

2018 ◽  
Vol 73 ◽  
pp. 52 ◽  
Author(s):  
Maxime Schmitt ◽  
Cédric Bastoul ◽  
Philippe Helluy
Keyword(s):  
Second Step ◽  
Development Effort ◽  
Approximate Computing ◽  
Problem Size ◽  
Actual Problem ◽  
Language Extension ◽  
Time Space ◽  
Syntactic Information ◽  
Compiler Infrastructure ◽  
The Impact

A large part of the development effort of compute-intensive applications is devoted to optimization, i.e., achieving the computation within a finite budget of time, space or energy. Given the complexity of modern architectures, writing simulation applications is often a two-step workflow. Firstly, developers design a sequential program for algorithmic tuning and debugging purposes. Secondly, experts optimize and exploit possible approximations of the original program to scale to the actual problem size. This second step is a tedious, time-consuming and error-prone task. In this paper we investigate language extensions and compiler tools to achieve that task semi-automatically in the context of approximate computing. We identified the semantic and syntactic information necessary for a compiler to automatically handle approximation and adaptive techniques for a particular class of programs. We propose a set of language extensions generic enough to provide the compiler with the useful semantic information when approximation is beneficial. We implemented the compiler infrastructure to exploit these extensions and to automatically generate the adaptively approximated version of a program. We provide an experimental study of the impact and expressiveness of our language extension set on various applications.

Sign in / Sign up

Export Citation Format

Share Document