2,718 research outputs found
Parallel N
During the last decades, Multigrid methods have been extensively used for solving large sparse linear systems. Considering their efficiency and the convergence behavior, Multigrid methods are used in many scientific fields as solvers or preconditioners. Herewith, we propose two hybrid parallel algorithms for N-Body simulations using the Particle Mesh method and the Particle Particle Particle Mesh method, respectively, based on the V-Cycle Multigrid method in conjunction with Generic Approximate Sparse Inverses. The N-Body problem resides in a three-dimensional torus space, and the bodies are subject only to gravitational forces. In each time step of the above methods, a large sparse linear system is solved to compute the gravity potential at each nodal point in order to interpolate the solution to each body. Then the Velocity Verlet method is used to compute the new position and velocity from the acceleration of each respective body. Moreover, a parallel Multigrid algorithm, with a truncated approach in the levels computed in parallel, is proposed for solving large linear systems. Furthermore, parallel results are provided indicating the efficiency of the proposed Multigrid N-Body scheme. Theoretical estimates for the complexity of the proposed simulation schemes are provided
Afivo: a framework for quadtree/octree AMR with shared-memory parallelization and geometric multigrid methods
Afivo is a framework for simulations with adaptive mesh refinement (AMR) on
quadtree (2D) and octree (3D) grids. The framework comes with a geometric
multigrid solver, shared-memory (OpenMP) parallelism and it supports output in
Silo and VTK file formats. Afivo can be used to efficiently simulate AMR
problems with up to about unknowns on desktops, workstations or single
compute nodes. For larger problems, existing distributed-memory frameworks are
better suited. The framework has no built-in functionality for specific physics
applications, so users have to implement their own numerical methods. The
included multigrid solver can be used to efficiently solve elliptic partial
differential equations such as Poisson's equation. Afivo's design was kept
simple, which in combination with the shared-memory parallelism facilitates
modification and experimentation with AMR algorithms. The framework was already
used to perform 3D simulations of streamer discharges, which required tens of
millions of cells
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
Particle-Particle, Particle-Scaling function (P3S) algorithm for electrostatic problems in free boundary conditions
An algorithm for fast calculation of the Coulombic forces and energies of
point particles with free boundary conditions is proposed. Its calculation time
scales as N log N for N particles. This novel method has lower crossover point
with the full O(N^2) direct summation than the Fast Multipole Method. The
forces obtained by our algorithm are analytical derivatives of the energy which
guarantees energy conservation during a molecular dynamics simulation. Our
algorithm is very simple. An MPI parallelised version of the code can be
downloaded under the GNU General Public License from the website of our group.Comment: 19 pages, 11 figures, submitted to: Journal of Chemical Physic
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