1,330 research outputs found
Efficient and accurate three dimensional Poisson solver for surface problems
We present a method that gives highly accurate electrostatic potentials for
systems where we have periodic boundary conditions in two spatial directions
but free boundary conditions in the third direction. These boundary conditions
are needed for all kind of surface problems. Our method has an O(N log N)
computational cost, where N is the number of grid points, with a very small
prefactor. This Poisson solver is primarily intended for real space methods
where the charge density and the potential are given on a uniform grid.Comment: 6 pages, 2 figure
Direct Integration of the Collisionless Boltzmann Equation in Six-dimensional Phase Space: Self-gravitating Systems
We present a scheme for numerical simulations of collisionless
self-gravitating systems which directly integrates the Vlasov--Poisson
equations in six-dimensional phase space. By the results from a suite of
large-scale numerical simulations, we demonstrate that the present scheme can
simulate collisionless self-gravitating systems properly. The integration
scheme is based on the positive flux conservation method recently developed in
plasma physics. We test the accuracy of our code by performing several test
calculations including the stability of King spheres, the gravitational
instability and the Landau damping. We show that the mass and the energy are
accurately conserved for all the test cases we study. The results are in good
agreement with linear theory predictions and/or analytic solutions. The
distribution function keeps the property of positivity and remains
non-oscillatory. The largest simulations are run on 64^6 grids. The computation
speed scales well with the number of processors, and thus our code performs
efficiently on massively parallel supercomputers.Comment: 35 pages, 19 figures. Submitted to the Astrophysical Journa
COSMOS: A Hybrid N-Body/Hydrodynamics Code for Cosmological Problems
We describe a new hybrid N-body/hydrodynamical code based on the
particle-mesh (PM) method and the piecewise-parabolic method (PPM) for use in
solving problems related to the evolution of large-scale structure, galaxy
clusters, and individual galaxies. The code, named COSMOS, possesses several
new features which distinguish it from other PM-PPM codes. In particular, to
solve the Poisson equation we have written a new multigrid solver which can
determine the gravitational potential of isolated matter distributions and
which properly takes into account the finite-volume discretization required by
PPM. All components of the code are constructed to work with a nonuniform mesh,
preserving second-order spatial differences. The PPM code uses vacuum boundary
conditions for isolated problems, preventing inflows when appropriate. The PM
code uses a second-order variable-timestep time integration scheme. Radiative
cooling and cosmological expansion terms are included. COSMOS has been
implemented for parallel computers using the Parallel Virtual Machine (PVM)
library, and it features a modular design which simplifies the addition of new
physics and the configuration of the code for different types of problems. We
discuss the equations solved by COSMOS and describe the algorithms used, with
emphasis on these features. We also discuss the results of tests we have
performed to establish that COSMOS works and to determine its range of
validity.Comment: 43 pages, 14 figures, submitted to ApJS and revised according to
referee's comment
A Parallel Adaptive P3M code with Hierarchical Particle Reordering
We discuss the design and implementation of HYDRA_OMP a parallel
implementation of the Smoothed Particle Hydrodynamics-Adaptive P3M (SPH-AP3M)
code HYDRA. The code is designed primarily for conducting cosmological
hydrodynamic simulations and is written in Fortran77+OpenMP. A number of
optimizations for RISC processors and SMP-NUMA architectures have been
implemented, the most important optimization being hierarchical reordering of
particles within chaining cells, which greatly improves data locality thereby
removing the cache misses typically associated with linked lists. Parallel
scaling is good, with a minimum parallel scaling of 73% achieved on 32 nodes
for a variety of modern SMP architectures. We give performance data in terms of
the number of particle updates per second, which is a more useful performance
metric than raw MFlops. A basic version of the code will be made available to
the community in the near future.Comment: 34 pages, 12 figures, accepted for publication in Computer Physics
Communication
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
A Direct Multigrid Poisson Solver for Oct-Tree Adaptive Meshes
We describe a finite-volume method for solving the Poisson equation on
oct-tree adaptive meshes using direct solvers for individual mesh blocks. The
method is a modified version of the method presented by Huang and Greengard
(2000), which works with finite-difference meshes and does not allow for shared
boundaries between refined patches. Our algorithm is implemented within the
FLASH code framework and makes use of the PARAMESH library, permitting
efficient use of parallel computers. We describe the algorithm and present test
results that demonstrate its accuracy.Comment: 10 pages, 6 figures, accepted by the Astrophysical Journal; minor
revisions in response to referee's comments; added char
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