19 research outputs found
Numerical integration scheme using singular perturbation method
Some multi degree-of-freedom dynamical systems exhibit a response that contain fast and slow variables. An example of such systems is a multibody system with rigid and deformable bodies. Standard numerical integration of the resultant equations of motion must adjust the time step according to the frequency of the fastest variable. As a result, the computation time is sacrificed. The singular perturbation method is an analysis technique to deal with the interaction of slow and fast variables. In this study, a numerical integration scheme using the singular perturbation method is discussed, its absolute stability condition is derived, and its order of accuracy is investigated. Copyright © 2013 by ASME
A Volume-Agglomeration Multirate Time Advancing Approach
International audienceA frequent configuration in computational fluid mechanics combines an explicit time advancing scheme for accuracy purposes and a computational grid with a very small portion of much smaller elements than in the remaining mesh. Examples of such situations are the traveling of a discontinuity followed by a moving mesh, and the large eddy simulation of high Reynolds number flows around bluff bodies where together very thin boundary layers and vortices of much more important size need to be captured. For such configurations, explicit time advancing schemes with global time stepping are very costly. In order to overcome this problem, the multirate time stepping approach represents an interesting improvement. The objective of such schemes, which allow to use different time steps in the computational domain, is to avoid penalizing the computational cost of the time advancement of unsteady solutions which can become large due to the use of small global time steps imposed by the smallest elements such as those constituting the boundary layers. In the present work, a new multirate scheme based on control volume agglomeration is proposed for the solution of the compressible Navier-Stokes equations possibly equipped with turbulence models. The method relies on a prediction step where large time steps are performed with an evaluation of the fluxes on macro-cells for the smaller elements for stability purpose, and on a correction step in which small time steps are employed only for the smaller elements. The efficiency of the proposed method is evaluated on several benchmarks flows: the problem of a moving contact discontinuity (inviscid flow), the computation with hybrid turbulence model of flows around bluff bodies like a tandem cylinders at Reynolds number , a circular cylinder at Reynolds number , and a flow around a space probe model at Reynolds number
Multirate Training of Neural Networks
We propose multirate training of neural networks: partitioning neural network
parameters into "fast" and "slow" parts which are trained simultaneously using
different learning rates. By choosing appropriate partitionings we can obtain
large computational speed-ups for transfer learning tasks. We show that for
various transfer learning applications in vision and NLP we can fine-tune deep
neural networks in almost half the time, without reducing the generalization
performance of the resulting model. We also discuss other splitting choices for
the neural network parameters which are beneficial in enhancing generalization
performance in settings where neural networks are trained from scratch.
Finally, we propose an additional multirate technique which can learn different
features present in the data by training the full network on different time
scales simultaneously. The benefits of using this approach are illustrated for
ResNet architectures on image data. Our paper unlocks the potential of using
multirate techniques for neural network training and provides many starting
points for future work in this area
On the Effect of Multirate Co-simulation Techniques in the Efficiency and Accuracy of Multibody System Dynamics
This is a post-peer-review, pre-copyedit version of an article published in Multibody System Dynamics.
This version of the article has been accepted for publication, after peer review and is subject to Springer
Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements,
or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/
s11044-010-9234-7.[Abstract] Dynamic simulation of complex mechatronic systems can be carried out in an efficient and
modular way making use of weakly coupled co-simulation setups. When using this approach,
multirate methods are often needed to improve the efficiency, since the physical components of
the system usually have different frequencies and time scales. However, most multirate methods
have been designed for strongly coupled setups, and their application in weakly coupled cosimulation
is not straightforward due to the limitations enforced by commercial simulation tools
used in mechatronics design. This work describes a weakly coupled multirate method intended to
be a generic multirate interface between block diagram software and multibody dynamics
simulators, arranged in a co-simulation setup. Its main advantage is that it does not enforce
equidistant or synchronized communication time-grids, and therefore it can be easily applied to
set up weakly-coupled co-simulations using off-the-shelf commercial block diagram simulators
while giving the user a great flexibility for selecting the integration scheme for each subsystem.
The method is first tested on a simple, purely mechanical system with known analytical
solution and variable frequency ratio (FR) of the coupled subsystems. Several synchronization
schemes (fastest-first and slowest-first) and interpolation/extrapolation methods (polynomials of
different orders and smoothing) have been implemented and tested. Next, the effect of the
interface on accuracy and efficiency is assessed making use of a real-life co-simulation setting
that links an MBS model of a kart to a thermal engine modelled in Simulink. Results show that
the proposed weakly coupled multirate method can achieve considerable reductions in the
execution times of the simulations without degrading the numerical solution of the proble
Multirate timestepping methods for hyperbolic conservation laws
This paper constructs multirate time discretizations for hyperbolic conservation laws that allow different time-steps to be used in different parts of the spatial domain. The discretization is second order accurate in time and preserves the conservation and stability properties under local CFL conditions. Multirate timestepping avoids the necessity to take small global time-steps (restricted by the largest value of the Courant number on the grid) and therefore results in more efficient algorithms