Optimizing the computation of a parallel 3D finite difference algorithm for graphics processing units

2014 ◽  
Vol 27 (6) ◽  
pp. 1591-1602 ◽  
Author(s):  
J. Porter-Sobieraj ◽  
S. Cygert ◽  
D. Kikoła ◽  
J. Sikorski ◽  
M. Słodkowski
Keyword(s):  
Finite Difference ◽  
Graphics Processing Units ◽  
Graphics Processing

Solving finite-difference equations for diffractive optics problems using graphics processing units

2013 ◽  
Vol 52 (9) ◽  
pp. 091719 ◽  
Author(s):  
Dimitry Lvovich Golovashkin ◽  
Daria G. Vorotnokova ◽  
Alexander V. Kochurov ◽  
Svetlana A. Malysheva
Keyword(s):  
Finite Difference ◽  
Difference Equations ◽  
Graphics Processing Units ◽  
Diffractive Optics ◽  
Finite Difference Equations ◽  
Graphics Processing

An Implicit Harmonic Balance Method in Graphics Processing Units for Vibrating Blades

2015 ◽  
Author(s):  
Javier Crespo ◽  
Roque Corral ◽  
Jesus Pueblas
Keyword(s):  
Finite Difference ◽  
Harmonic Balance ◽  
Graphics Processing Units ◽  
Stokes Equations ◽  
Computational Cost ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Transonic Compressor ◽  
Speed Up ◽  
Graphics Processing

An implicit harmonic balance method for modeling the unsteady non-linear periodic flow about vibrating airfoils in turbomachinery is presented. As departing point, an implicit edge-based three-dimensional Reynolds Averaged Navier-Stokes equations solver for unstructured grids that runs both on central processing units (CPUs) and graphics processing units (GPUs) is used. The harmonic balance method performs a spectral discretization of the time derivatives and marches in pseudo-time a new system of equations where the unknowns are the variables at different time samples. The application of the method to vibrating airfoils is discussed. It is shown that a time spectral scheme may achieve the same temporal accuracy at a much lower computational cost than a Backward Finite Difference method at the expense of using more memory. The performance of the implicit solver has been assessed with several application examples. A speed-up factor of 10 is obtained between the spectral and finite difference version of the code whereas and an additional speed-up factor of 10 is obtained when the code is ported to GPUs, totalizing a speed factor of 100. The performance of the solver in GPUs has been assessed using the 10th standard aeroelastic configuration and a transonic compressor.

An Implicit Harmonic Balance Method in Graphics Processing Units for Oscillating Blades

2015 ◽  
Vol 138 (3) ◽  
Author(s):  
Javier Crespo ◽  
Roque Corral ◽  
Jesus Pueblas
Keyword(s):  
Finite Difference ◽  
Harmonic Balance ◽  
Graphics Processing Units ◽  
Stokes Equations ◽  
Computational Cost ◽  
Harmonic Balance Method ◽  
Transonic Compressor ◽  
Central Processing ◽  
Speed Up ◽  
Graphics Processing

An implicit harmonic balance (HB) method for modeling the unsteady nonlinear periodic flow about vibrating airfoils in turbomachinery is presented. An implicit edge-based three-dimensional Reynolds-averaged Navier–Stokes equations (RANS) solver for unstructured grids, which runs both on central processing units (CPUs) and graphics processing units (GPUs), is used. The HB method performs a spectral discretization of the time derivatives and marches in pseudotime, a new system of equations where the unknowns are the variables at different time samples. The application of the method to vibrating airfoils is discussed. It is shown that a time-spectral scheme may achieve the same temporal accuracy at a much lower computational cost than a backward finite-difference method at the expense of using more memory. The performance of the implicit solver has been assessed with several application examples. A speed-up factor of 10 is obtained between the spectral and finite-difference version of the code, whereas an additional speed-up factor of 10 is obtained when the code is ported to GPUs, totalizing a speed factor of 100. The performance of the solver in GPUs has been assessed using the tenth standard aeroelastic configuration and a transonic compressor.

Industry-scale finite-difference elastic wave modeling on graphics processing units using the out-of-core technique

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. T35-T43 ◽  
Author(s):  
Jon Marius Venstad
Keyword(s):  
Finite Difference ◽  
Graphics Processing Units ◽  
Finite Difference Methods ◽  
Main Memory ◽  
Multicore Architectures ◽  
Wave Modeling ◽  
Central Processing ◽  
Computational Overhead ◽  
The Difference ◽  
Graphics Processing

The difference in computational power between the few- and multicore architectures represented by central processing units (CPUs) and graphics processing units (GPUs) is significant today, and this difference is likely to increase in the years ahead. GPUs are, therefore, ever more popular for applications in computational physics, such as wave modeling. Finite-difference methods are popular for wave modeling and are well suited for the GPU architecture, but developing an efficient and capable GPU implementation is hindered by the limited size of the GPU memory. I revealed how the out-of-core technique can be used to circumvent the memory limit on the GPU, increasing the available memory to that of the CPU (the main memory) instead, with no significant computational overhead. This approach has several advantages over a parallel scheme in terms of applicability, flexibility, and hardware requirements. Choices in the numerical scheme — the numerical differentiators in particular — also greatly affect computational efficiency. These factors are considered explicitly for GPU implementations of wave modeling because GPUs are special purpose with a visible architecture.

scholarly journals Finite-Difference Micromagnetic Solvers With the Object-Oriented Micromagnetic Framework on Graphics Processing Units

2016 ◽  
Vol 52 (4) ◽  
pp. 1-9 ◽  
Author(s):  
Sidi Fu ◽  
Weilong Cui ◽  
Matthew Hu ◽  
Ruinan Chang ◽  
Michael J. Donahue ◽  
...  
Keyword(s):  
Finite Difference ◽  
Graphics Processing Units ◽  
Object Oriented ◽  
Graphics Processing
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