67 research outputs found
Nodal Discontinuous Galerkin Methods on Graphics Processors
Discontinuous Galerkin (DG) methods for the numerical solution of partial
differential equations have enjoyed considerable success because they are both
flexible and robust: They allow arbitrary unstructured geometries and easy
control of accuracy without compromising simulation stability. Lately, another
property of DG has been growing in importance: The majority of a DG operator is
applied in an element-local way, with weak penalty-based element-to-element
coupling.
The resulting locality in memory access is one of the factors that enables DG
to run on off-the-shelf, massively parallel graphics processors (GPUs). In
addition, DG's high-order nature lets it require fewer data points per
represented wavelength and hence fewer memory accesses, in exchange for higher
arithmetic intensity. Both of these factors work significantly in favor of a
GPU implementation of DG.
Using a single US$400 Nvidia GTX 280 GPU, we accelerate a solver for
Maxwell's equations on a general 3D unstructured grid by a factor of 40 to 60
relative to a serial computation on a current-generation CPU. In many cases,
our algorithms exhibit full use of the device's available memory bandwidth.
Example computations achieve and surpass 200 gigaflops/s of net
application-level floating point work.
In this article, we describe and derive the techniques used to reach this
level of performance. In addition, we present comprehensive data on the
accuracy and runtime behavior of the method.Comment: 33 pages, 12 figures, 4 table
Nodal discontinuous Galerkin methods on graphics processors
Discontinuous Galerkin (DG) methods for the numerical solution of partial differential equations have enjoyed considerable success because they are both flexible and robust: They allow arbitrary unstructured geometries and easy control of accuracy without compromising simulation stability. Lately, another property of DG has been growing in importance: The majority of a DG operator is applied in an element-local way, with weak penalty-based element-to-element coupling. The resulting locality in memory access is one of the factors that enables DG to run on off-the-shelf, massively parallel graphics processors (GPUs). In addition, DG's high-order nature lets it require fewer data points per represented wavelength and hence fewer memory accesses, in exchange for higher arithmetic intensity. Both of these factors work significantly in favor of a GPU implementation of DG. Using a single US$400 Nvidia GTX 280 GPU, we accelerate a solver for Maxwell's equations on a general 3D unstructured grid by a factor of around 50 relative to a serial computation on a current-generation CPU. In many cases, our algorithms exhibit full use of the device's available memory bandwidth. Example computations achieve and surpass 200 gigaflops/s of net application-level floating point work. In this article, we describe and derive the techniques used to reach this level of performance. In addition, we present comprehensive data on the accuracy and runtime behavior of the method. (C) 2009 Elsevier Inc. All rights reserved
Finite Element Integration on GPUs
We present a novel finite element integration method for low order elements
on GPUs. We achieve more than 100GF for element integration on first order
discretizations of both the Laplacian and Elasticity operators.Comment: 16 pages, 3 figure
Heterogeneous Computing on Mixed Unstructured Grids with PyFR
PyFR is an open-source high-order accurate computational fluid dynamics
solver for mixed unstructured grids that can target a range of hardware
platforms from a single codebase. In this paper we demonstrate the ability of
PyFR to perform high-order accurate unsteady simulations of flow on mixed
unstructured grids using heterogeneous multi-node hardware. Specifically, after
benchmarking single-node performance for various platforms, PyFR v0.2.2 is used
to undertake simulations of unsteady flow over a circular cylinder at Reynolds
number 3 900 using a mixed unstructured grid of prismatic and tetrahedral
elements on a desktop workstation containing an Intel Xeon E5-2697 v2 CPU, an
NVIDIA Tesla K40c GPU, and an AMD FirePro W9100 GPU. Both the performance and
accuracy of PyFR are assessed. PyFR v0.2.2 is freely available under a 3-Clause
New Style BSD license (see www.pyfr.org).Comment: 21 pages, 9 figures, 6 table
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