24,548 research outputs found
Variational Integrators for the Gravitational N-Body Problem
This paper describes a fourth-order integration algorithm for the
gravitational N-body problem based on discrete Lagrangian mechanics. When used
with shared timesteps, the algorithm is momentum conserving and symplectic. We
generalize the algorithm to handle individual time steps; this introduces
fifth-order errors in angular momentum conservation and symplecticity. We show
that using adaptive block power of two timesteps does not increase the error in
symplecticity. In contrast to other high-order, symplectic, individual
timestep, momentum-preserving algorithms, the algorithm takes only forward
timesteps. We compare a code integrating an N-body system using the algorithm
with a direct-summation force calculation to standard stellar cluster
simulation codes. We find that our algorithm has about 1.5 orders of magnitude
better symplecticity and momentum conservation errors than standard algorithms
for equivalent numbers of force evaluations and equivalent energy conservation
errors.Comment: 31 pages, 8 figures. v2: Revised individual-timestepping description,
expanded comparison with other methods, corrected error in predictor
equation. ApJ, in pres
Aerospace Medicine and Biology: A continuing bibliography with indexes, supplement 199
This bibliography lists 82 reports, articles, and other documents introduced into the NASA scientific and technical information system in October 1979
Wavelet-Based High-Order Adaptive Modeling of Lossy Interconnects
Abstract—This paper presents a numerical-modeling strategy for simulation of fast transients in lossy electrical interconnects. The proposed algorithm makes use of wavelet representations of voltages and currents along the structure, with the aim of reducing the computational complexity of standard time-domain solvers. A special weak procedure for the implementation of possibly dynamic and nonlinear boundary conditions allows to preserve stability as well as a high approximation order, thus leading to very accurate schemes. On the other hand, the wavelet expansion allows the computation of the solution by using few significant coefficients which are automatically determined at each time step. A dynamically refinable mesh is then used to perform a sparse time-stepping. Several numerical results illustrate the high efficiency of the proposed algorithm, which has been tuned and optimized for best performance in fast digital applications typically found on modern PCB structures. Index Terms—Finite difference methods, time-domain analysis, transmission lines, wavelet transforms. I
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