6,512 research outputs found
Multigrid Waveform Relaxation on Spatial Finite Element Meshes: The Discrete-Time Case
The efficiency of numerically solving time-dependent partial differential equations on parallel computers can be greatly improved by computing the solution on many time levels simultaneously. The theoretical properties of one such method, namely the discrete-time multigrid waveform relaxation method, are investigated for systems of ordinary differential equations obtained by spatial finite-element discretisation of linear parabolic initial-boundary value problems. The results are compared to the corresponding continuous-time results. The theory is illustrated for a one-dimensional and a two-dimensional model problem and checked against results obtained by numerical experiments
Parallel Factorizations in Numerical Analysis
In this paper we review the parallel solution of sparse linear systems,
usually deriving by the discretization of ODE-IVPs or ODE-BVPs. The approach is
based on the concept of parallel factorization of a (block) tridiagonal matrix.
This allows to obtain efficient parallel extensions of many known matrix
factorizations, and to derive, as a by-product, a unifying approach to the
parallel solution of ODEs.Comment: 15 pages, 5 figure
Parallelization of a treecode
I describe here the performance of a parallel treecode with individual
particle timesteps. The code is based on the Barnes-Hut algorithm and runs
cosmological N-body simulations on parallel machines with a distributed memory
architecture using the MPI message-passing library. For a configuration with a
constant number of particles per processor the scalability of the code was
tested up to P=128 processors on an IBM SP4 machine. In the large limit the
average CPU time per processor necessary for solving the gravitational
interactions is higher than that expected from the ideal scaling
relation. The processor domains are determined every large timestep according
to a recursive orthogonal bisection, using a weighting scheme which takes into
account the total particle computational load within the timestep. The results
of the numerical tests show that the load balancing efficiency of the code
is high () up to P=32, and decreases to when P=128. In the
latter case it is found that some aspects of the code performance are affected
by machine hardware, while the proposed weighting scheme can achieve a load
balance as high as even in the large limit.Comment: 30 pages, 3 tables, 9 figures, accepted for publication in New
Astronom
Fast and stable method for simulating quantum electron dynamics
A fast and stable method is formulated to compute the time evolution of a
wavefunction by numerically solving the time-dependent Schr{\"o}dinger
equation. This method is a real space/real time evolution method implemented by
several computational techniques such as Suzuki's exponential product, Cayley's
form, the finite differential method and an operator named adhesive operator.
This method conserves the norm of the wavefunction, manages periodic conditions
and adaptive mesh refinement technique, and is suitable for vector- and
parallel-type supercomputers. Applying this method to some simple electron
dynamics, we confirmed the efficiency and accuracy of the method for simulating
fast time-dependent quantum phenomena.Comment: 10 pages, 35 eps figure
Conservation Laws in Smooth Particle Hydrodynamics: the DEVA Code
We describe DEVA, a multistep AP3M-like-SPH code particularly designed to
study galaxy formation and evolution in connection with the global cosmological
model. This code uses a formulation of SPH equations which ensures both energy
and entropy conservation by including the so-called \bn h terms. Particular
attention has also been paid to angular momentum conservation and to the
accuracy of our code. We find that, in order to avoid unphysical solutions, our
code requires that cooling processes must be implemented in a non-multistep
way.
We detail various cosmological simulations which have been performed to test
our code and also to study the influence of the \bn h terms. Our results
indicate that such correction terms have a non-negligible effect on some
cosmological simulations, especially on high density regions associated either
to shock fronts or central cores of collapsed objects. Moreover, they suggest
that codes paying a particular attention to the implementation of conservation
laws of physics at the scales of interest, can attain good accuracy levels in
conservation laws with limited computational resources.Comment: 36 pages, 10 figures. Accepted for publication in The Astrophysical
Journa
QTM: computational package using MPI protocol for quantum trajectories method
The Quantum Trajectories Method (QTM) is one of {the} frequently used methods
for studying open quantum systems. { The main idea of this method is {the}
evolution of wave functions which {describe the system (as functions of time).
Then,} so-called quantum jumps are applied at {a} randomly selected point in
time. {The} obtained system state is called as a trajectory. After averaging
many single trajectories{,} we obtain the approximation of the behavior of {a}
quantum system.} {This fact also allows} us to use parallel computation
methods. In the article{,} we discuss the QTM package which is supported by the
MPI technology. Using MPI allowed {utilizing} the parallel computing for
calculating the trajectories and averaging them -- as the effect of these
actions{,} the time {taken by} calculations is shorter. In spite of using the
C++ programming language, the presented solution is easy to utilize and does
not need any advanced programming techniques. At the same time{,} it offers a
higher performance than other packages realizing the QTM. It is especially
important in the case of harder computational tasks{,} and the use of MPI
allows {improving the} performance of particular problems which can be solved
in the field of open quantum systems.Comment: 28 pages, 9 figure
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