13,496 research outputs found
Solution of partial differential equations on vector and parallel computers
The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed
A bibliography on parallel and vector numerical algorithms
This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also
GAMER: a GPU-Accelerated Adaptive Mesh Refinement Code for Astrophysics
We present the newly developed code, GAMER (GPU-accelerated Adaptive MEsh
Refinement code), which has adopted a novel approach to improve the performance
of adaptive mesh refinement (AMR) astrophysical simulations by a large factor
with the use of the graphic processing unit (GPU). The AMR implementation is
based on a hierarchy of grid patches with an oct-tree data structure. We adopt
a three-dimensional relaxing TVD scheme for the hydrodynamic solver, and a
multi-level relaxation scheme for the Poisson solver. Both solvers have been
implemented in GPU, by which hundreds of patches can be advanced in parallel.
The computational overhead associated with the data transfer between CPU and
GPU is carefully reduced by utilizing the capability of asynchronous memory
copies in GPU, and the computing time of the ghost-zone values for each patch
is made to diminish by overlapping it with the GPU computations. We demonstrate
the accuracy of the code by performing several standard test problems in
astrophysics. GAMER is a parallel code that can be run in a multi-GPU cluster
system. We measure the performance of the code by performing purely-baryonic
cosmological simulations in different hardware implementations, in which
detailed timing analyses provide comparison between the computations with and
without GPU(s) acceleration. Maximum speed-up factors of 12.19 and 10.47 are
demonstrated using 1 GPU with 4096^3 effective resolution and 16 GPUs with
8192^3 effective resolution, respectively.Comment: 60 pages, 22 figures, 3 tables. More accuracy tests are included.
Accepted for publication in ApJ
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