scholarly journals Abstract Level Parallelization of Finite Difference Methods

1997 ◽  
Vol 6 (4) ◽  
pp. 331-344 ◽  
Author(s):  
Edwin Vollebregt
Keyword(s):  
Finite Difference ◽  
Message Passing ◽  
Finite Difference Methods ◽  
Parallel Computers ◽  
Parallel Programs ◽  
Programming Paradigm ◽  
Index Sets ◽  
Process Channel ◽  
Abstract Level

A formalism is proposed for describing finite difference calculations in an abstract way. The formalism consists of index sets and stencils, for characterizing the structure of sets of data items and interactions between data items (“neighbouring relations”). The formalism provides a means for lifting programming to a more abstract level. This simplifies the tasks of performance analysis and verification of correctness, and opens the way for automaticcode generation. The notation is particularly useful in parallelization, for the systematic construction of parallel programs in a process/channel programming paradigm (e.g., message passing). This is important because message passing, unfortunately, still is the only approach that leads to acceptable performance for many more unstructured or irregular problems on parallel computers that have non-uniform memory access times. It will be shown that the use of index sets and stencils greatly simplifies the determination of which data must be exchanged between different computing processes.

scholarly journals The Semi-Automatic Parallelisation of Scientific Application Codes Using a Computer Aided Parallelisation Toolkit

2001 ◽  
Vol 9 (2-3) ◽  
pp. 163-173 ◽  
Author(s):  
C.S. Ierotheou ◽  
S.P. Johnson ◽  
P.F. Leggett ◽  
M. Cross ◽  
E.W. Evans ◽  
...  
Keyword(s):  
Shared Memory ◽  
Message Passing ◽  
Programming Model ◽  
Parallel Computers ◽  
Parallel Programs ◽  
Scientific Application ◽  
Real World Application ◽  
Interprocedural Analysis ◽  
Computer Aided ◽  
Application Codes

The shared-memory programming model can be an effective way to achieve parallelism on shared memory parallel computers. Historically however, the lack of a programming standard using directives and the limited scalability have affected its take-up. Recent advances in hardware and software technologies have resulted in improvements to both the performance of parallel programs with compiler directives and the issue of portability with the introduction of OpenMP. In this study, the Computer Aided Parallelisation Toolkit has been extended to automatically generate OpenMP-based parallel programs with nominal user assistance. We categorize the different loop types and show how efficient directives can be placed using the toolkit's in-depth interprocedural analysis. Examples are taken from the NAS parallel benchmarks and a number of real-world application codes. This demonstrates the great potential of using the toolkit to quickly parallelise serial programs as well as the good performance achievable on up to 300 processors for hybrid message passing-directive parallelisations.

scholarly journals Mathematical Model of Uniform Cereal Crops Seeding Using a Double-Disk Coulter

2020 ◽  
Vol 23 (4) ◽  
pp. 195-200
Author(s):  
Dmytro Derevjanko ◽  
Ivan Holovach ◽  
Volodymyr Bulgakov ◽  
Yevhen Ihnatiev ◽  
Ladislav Nozdrovický
Keyword(s):  
Mathematical Model ◽  
Finite Difference ◽  
Finite Difference Methods ◽  
Computer Software ◽  
Bottom Surface ◽  
Software Packages ◽  
The Cauchy Problem ◽  
Linear Differential ◽  
Distribution Plate

AbstractThe paper provided presents a new design of two-disk wide-row coulter that ensures uniform distribution of seeds to an even bed at the furrow bottom, as well as preserving of optimal distances between the seeds. Seeds fall from the seed tube of coil sowing apparatus onto a metal distribution plate with staggeringly arranged metal pins, which distribute the seeds to furrow bottom surface in a form of separate strips. To substantiate the kinematic and constructive parameters of proposed coulter design, a mathematical model for transport of seeds along the surface of a distribution plate was developed and the Cauchy problem for a system of the second-order quasi-linear differential equations was solved by the finite difference methods using embedded software procedures in mathematical software packages (Mathcad, Maple, etc.). The finite-difference method implementation was carried out using computer software allowing the determination of coordinates of seeds and, if necessary, changing of direction of their movement by adjusting the coulter operation to improve the distribution of seeds to soil in order to reduce the injury to them, which ultimately can contribute to an increased yield. Coverage of the plate surface and distribution pins with a rubber material can also contribute to a significant reduction in seed injury during sowing.

Biharmonic navigation using radial basis functions

Robotica ◽  
2021 ◽  
pp. 1-12
Author(s):  
Xu-Qian Fan ◽  
Wenyong Gong
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Radial Basis Functions ◽  
Real World ◽  
Biharmonic Equation ◽  
Finite Difference Methods ◽  
Basis Functions ◽  
Large Size ◽  
Radial Basis ◽  
Difference Methods

Abstract Path planning has been widely investigated by many researchers and engineers for its extensive applications in the real world. In this paper, a biharmonic radial basis potential function (BRBPF) representation is proposed to construct navigation fields in 2D maps with obstacles, and it therefore can guide and design a path joining given start and goal positions with obstacle avoidance. We construct BRBPF by solving a biharmonic equation associated with distance-related boundary conditions using radial basis functions (RBFs). In this way, invalid gradients calculated by finite difference methods in large size grids can be preventable. Furthermore, paths constructed by BRBPF are smoother than paths constructed by harmonic potential functions and other methods, and plenty of experimental results demonstrate that the proposed method is valid and effective.

scholarly journals Reliable Efficient Difference Methods for Random Heterogeneous Diffusion Reaction Models with a Finite Degree of Randomness

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 206
Author(s):  
María Consuelo Casabán ◽  
Rafael Company ◽  
Lucas Jódar
Keyword(s):  
Stochastic Process ◽  
Finite Difference ◽  
Coming Out ◽  
Finite Difference Methods ◽  
Diffusion Reaction ◽  
Finite Difference Schemes ◽  
Finite Degree ◽  
Mean Square Stability ◽  
Reaction Models ◽  
Difference Methods

This paper deals with the search for reliable efficient finite difference methods for the numerical solution of random heterogeneous diffusion reaction models with a finite degree of randomness. Efficiency appeals to the computational challenge in the random framework that requires not only the approximating stochastic process solution but also its expectation and variance. After studying positivity and conditional random mean square stability, the computation of the expectation and variance of the approximating stochastic process is not performed directly but through using a set of sampling finite difference schemes coming out by taking realizations of the random scheme and using Monte Carlo technique. Thus, the storage accumulation of symbolic expressions collapsing the approach is avoided keeping reliability. Results are simulated and a procedure for the numerical computation is given.

scholarly journals A Laplace transform finite difference scheme for the Fisher-KPP equation

2021 ◽  
Vol 15 ◽  
pp. 174830262199958
Author(s):  
Colin L Defreitas ◽  
Steve J Kane
Keyword(s):  
Finite Difference ◽  
Laplace Transform ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Finite Difference Methods ◽  
Reaction Diffusion ◽  
Numerical Approach ◽  
Travelling Wave ◽  
Reaction Diffusion Equation ◽  
Kpp Equation

This paper proposes a numerical approach to the solution of the Fisher-KPP reaction-diffusion equation in which the space variable is developed using a purely finite difference scheme and the time development is obtained using a hybrid Laplace Transform Finite Difference Method (LTFDM). The travelling wave solutions usually associated with the Fisher-KPP equation are, in general, not deemed suitable for treatment using Fourier or Laplace transform numerical methods. However, we were able to obtain accurate results when some degree of time discretisation is inbuilt into the process. While this means that the advantage of using the Laplace transform to obtain solutions for any time t is not fully exploited, the method does allow for considerably larger time steps than is otherwise possible for finite-difference methods.

Protocol-based verification of message-passing parallel programs

2015 ◽  
Vol 50 (10) ◽  
pp. 280-298 ◽  
Author(s):  
Hugo A. López ◽  
Eduardo R. B. Marques ◽  
Francisco Martins ◽  
Nicholas Ng ◽  
César Santos ◽  
...  
Keyword(s):  
Message Passing ◽  
Parallel Programs
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