1,086 research outputs found
Highly accelerated simulations of glassy dynamics using GPUs: caveats on limited floating-point precision
Modern graphics processing units (GPUs) provide impressive computing
resources, which can be accessed conveniently through the CUDA programming
interface. We describe how GPUs can be used to considerably speed up molecular
dynamics (MD) simulations for system sizes ranging up to about 1 million
particles. Particular emphasis is put on the numerical long-time stability in
terms of energy and momentum conservation, and caveats on limited
floating-point precision are issued. Strict energy conservation over 10^8 MD
steps is obtained by double-single emulation of the floating-point arithmetic
in accuracy-critical parts of the algorithm. For the slow dynamics of a
supercooled binary Lennard-Jones mixture, we demonstrate that the use of
single-floating point precision may result in quantitatively and even
physically wrong results. For simulations of a Lennard-Jones fluid, the
described implementation shows speedup factors of up to 80 compared to a serial
implementation for the CPU, and a single GPU was found to compare with a
parallelised MD simulation using 64 distributed cores.Comment: 12 pages, 7 figures, to appear in Comp. Phys. Comm., HALMD package
licensed under the GPL, see http://research.colberg.org/projects/halm
Working With Incremental Spatial Data During Parallel (GPU) Computation
Central to many complex systems, spatial actors require an awareness of their local environment to enable behaviours such as communication and navigation. Complex system simulations represent this behaviour with Fixed Radius Near Neighbours (FRNN) search. This algorithm allows actors to store data at spatial locations and then query the data structure to find all data stored within a fixed radius of the search origin.
The work within this thesis answers the question: What techniques can be used for improving the performance of FRNN searches during complex system simulations on Graphics Processing Units (GPUs)?
It is generally agreed that Uniform Spatial Partitioning (USP) is the most suitable data structure for providing FRNN search on GPUs. However, due to the architectural complexities of GPUs, the performance is constrained such that FRNN search remains one of the most expensive common stages between complex systems models.
Existing innovations to USP highlight a need to take advantage of recent GPU advances, reducing the levels of divergence and limiting redundant memory accesses as viable routes to improve the performance of FRNN search. This thesis addresses these with three separate optimisations that can be used simultaneously.
Experiments have assessed the impact of optimisations to the general case of FRNN search found within complex system simulations and demonstrated their impact in practice when applied to full complex system models. Results presented show the performance of the construction and query stages of FRNN search can be improved by over 2x and 1.3x respectively. These improvements allow complex system simulations to be executed faster, enabling increases in scale and model complexity
Cellular Automata Applications in Shortest Path Problem
Cellular Automata (CAs) are computational models that can capture the
essential features of systems in which global behavior emerges from the
collective effect of simple components, which interact locally. During the last
decades, CAs have been extensively used for mimicking several natural processes
and systems to find fine solutions in many complex hard to solve computer
science and engineering problems. Among them, the shortest path problem is one
of the most pronounced and highly studied problems that scientists have been
trying to tackle by using a plethora of methodologies and even unconventional
approaches. The proposed solutions are mainly justified by their ability to
provide a correct solution in a better time complexity than the renowned
Dijkstra's algorithm. Although there is a wide variety regarding the
algorithmic complexity of the algorithms suggested, spanning from simplistic
graph traversal algorithms to complex nature inspired and bio-mimicking
algorithms, in this chapter we focus on the successful application of CAs to
shortest path problem as found in various diverse disciplines like computer
science, swarm robotics, computer networks, decision science and biomimicking
of biological organisms' behaviour. In particular, an introduction on the first
CA-based algorithm tackling the shortest path problem is provided in detail.
After the short presentation of shortest path algorithms arriving from the
relaxization of the CAs principles, the application of the CA-based shortest
path definition on the coordinated motion of swarm robotics is also introduced.
Moreover, the CA based application of shortest path finding in computer
networks is presented in brief. Finally, a CA that models exactly the behavior
of a biological organism, namely the Physarum's behavior, finding the
minimum-length path between two points in a labyrinth is given.Comment: To appear in the book: Adamatzky, A (Ed.) Shortest path solvers. From
software to wetware. Springer, 201
Matrix-free GPU implementation of a preconditioned conjugate gradient solver for anisotropic elliptic PDEs
Many problems in geophysical and atmospheric modelling require the fast
solution of elliptic partial differential equations (PDEs) in "flat" three
dimensional geometries. In particular, an anisotropic elliptic PDE for the
pressure correction has to be solved at every time step in the dynamical core
of many numerical weather prediction models, and equations of a very similar
structure arise in global ocean models, subsurface flow simulations and gas and
oil reservoir modelling. The elliptic solve is often the bottleneck of the
forecast, and an algorithmically optimal method has to be used and implemented
efficiently. Graphics Processing Units have been shown to be highly efficient
for a wide range of applications in scientific computing, and recently
iterative solvers have been parallelised on these architectures. We describe
the GPU implementation and optimisation of a Preconditioned Conjugate Gradient
(PCG) algorithm for the solution of a three dimensional anisotropic elliptic
PDE for the pressure correction in NWP. Our implementation exploits the strong
vertical anisotropy of the elliptic operator in the construction of a suitable
preconditioner. As the algorithm is memory bound, performance can be improved
significantly by reducing the amount of global memory access. We achieve this
by using a matrix-free implementation which does not require explicit storage
of the matrix and instead recalculates the local stencil. Global memory access
can also be reduced by rewriting the algorithm using loop fusion and we show
that this further reduces the runtime on the GPU. We demonstrate the
performance of our matrix-free GPU code by comparing it to a sequential CPU
implementation and to a matrix-explicit GPU code which uses existing libraries.
The absolute performance of the algorithm for different problem sizes is
quantified in terms of floating point throughput and global memory bandwidth.Comment: 18 pages, 7 figure
Graph Algorithms on GPUs
This chapter introduces the topic of graph algorithms on GPUs. It starts by presenting and comparing the main important data structures and techniques applied for representing and analysing graphs on GPUs at the state of the art.It then presents the theory and an updated review of the most efficient implementations of graph algorithms for GPUs. In particular, the chapter focuses on graph traversal algorithms (breadth-first search), single-source shortest path(Djikstra, Bellman-Ford, delta stepping, hybrids), and all-pair shortest path (Floyd-Warshall). By the end of the chapter, load balancing and memory access techniques are discussed through an overview of their main issues and management techniques
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