2,402 research outputs found
Guidance, flight mechanics and trajectory optimization. Volume 6 - The N-body problem and special perturbation techniques
Analytical formulations and numerical integration methods for many body problem and special perturbative technique
Solving periodic semilinear stiff PDEs in 1D, 2D and 3D with exponential integrators
Dozens of exponential integration formulas have been proposed for the
high-accuracy solution of stiff PDEs such as the Allen-Cahn, Korteweg-de Vries
and Ginzburg-Landau equations. We report the results of extensive comparisons
in MATLAB and Chebfun of such formulas in 1D, 2D and 3D, focusing on fourth and
higher order methods, and periodic semilinear stiff PDEs with constant
coefficients. Our conclusion is that it is hard to do much better than one of
the simplest of these formulas, the ETDRK4 scheme of Cox and Matthews
The application of generalized, cyclic, and modified numerical integration algorithms to problems of satellite orbit computation
Generalized, cyclic, and modified multistep numerical integration methods are developed and evaluated for application to problems of satellite orbit computation. Generalized methods are compared with the presently utilized Cowell methods; new cyclic methods are developed for special second-order differential equations; and several modified methods are developed and applied to orbit computation problems. Special computer programs were written to generate coefficients for these methods, and subroutines were written which allow use of these methods with NASA's GEOSTAR computer program
A 3D MHD model of astrophysical flows: algorithms, tests and parallelisation
In this paper we describe a numerical method designed for modelling different
kinds of astrophysical flows in three dimensions. Our method is a standard
explicit finite difference method employing the local shearing-box technique.
To model the features of astrophysical systems, which are usually
compressible, magnetised and turbulent, it is desirable to have high spatial
resolution and large domain size to model as many features as possible, on
various scales, within a particular system. In addition, the time-scales
involved are usually wide-ranging also requiring significant amounts of CPU
time.
These two limits (resolution and time-scales) enforce huge limits on
computational capabilities. The model we have developed therefore uses parallel
algorithms to increase the performance of standard serial methods. The aim of
this paper is to report the numerical methods we use and the techniques invoked
for parallelising the code. The justification of these methods is given by the
extensive tests presented herein.Comment: 17 pages with 21 GIF figures. Accepted for publication in A&
Stability regions for one-step multiderivative methods
Stability regions are plotted for certain members of a family of one-step multiderivative predictor-corrector methods developed by the authors in an earlier paper.
The methods discussed are tested on a linear system where the matrix of coefficients has constant complex eigenvalues and on a stiff non-linear system arising in reactor kinetics
An intelligent processing environment for real-time simulation
The development of a highly efficient and thus truly intelligent processing environment for real-time general purpose simulation of continuous systems is described. Such an environment can be created by mapping the simulation process directly onto the University of Alamba's OPERA architecture. To facilitate this effort, the field of continuous simulation is explored, highlighting areas in which efficiency can be improved. Areas in which parallel processing can be applied are also identified, and several general OPERA type hardware configurations that support improved simulation are investigated. Three direct execution parallel processing environments are introduced, each of which greatly improves efficiency by exploiting distinct areas of the simulation process. These suggested environments are candidate architectures around which a highly intelligent real-time simulation configuration can be developed
The Improvement of Efficiency in the Numerical Computation of Orbit Trajectories
An analysis, system design, programming, and evaluation of results are described for numerical computation of orbit trajectories. Evaluation of generalized methods, interaction of different formulations for satellite motion, transformation of equations of motion and integrator loads, and development of efficient integrators are also considered
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