279,500 research outputs found
Adaptive Iterative Splitting Methods for Convection-Diffusion-Reaction Equations
[EN] This article proposes adaptive iterative splitting methods to solve Multiphysics problems, which are related to convection-diffusion-reaction equations. The splitting techniques are based on iterative splitting approaches with adaptive ideas. Based on shifting the time-steps with additional adaptive time-ranges, we could embedded the adaptive techniques into the splitting approach. The numerical analysis of the adapted iterative splitting schemes is considered and we develop the underlying error estimates for the application of the adaptive schemes. The performance of the method with respect to the accuracy and the acceleration is evaluated in different numerical experiments. We test the benefits of the adaptive splitting approach on highly nonlinear Burgers' and Maxwell-Stefan diffusion equations.This research was funded by German Academic Exchange Service grant number 91588469.
We acknowledge support by the DFG Open Access Publication Funds of the Ruhr-Universität of
Bochum, Germany and by Ministerio de EconomĂa y Competitividad, Spain, under grant PGC2018-095896-B-C21-C22.Geiser, J.; Hueso, JL.; MartĂnez Molada, E. (2020). Adaptive Iterative Splitting Methods for Convection-Diffusion-Reaction Equations. Mathematics. 8(3):1-22. https://doi.org/10.3390/math8030302S12283Auzinger, W., & Herfort, W. (2014). Local error structures and order conditions in terms of Lie elements for exponential splitting schemes. Opuscula Mathematica, 34(2), 243. doi:10.7494/opmath.2014.34.2.243Auzinger, W., Koch, O., & Quell, M. (2016). Adaptive high-order splitting methods for systems of nonlinear evolution equations with periodic boundary conditions. Numerical Algorithms, 75(1), 261-283. doi:10.1007/s11075-016-0206-8Descombes, S., & Massot, M. (2004). Operator splitting for nonlinear reaction-diffusion systems with an entropic structure : singular perturbation and order reduction. Numerische Mathematik, 97(4), 667-698. doi:10.1007/s00211-003-0496-3Descombes, S., Dumont, T., Louvet, V., & Massot, M. (2007). On the local and global errors of splitting approximations of reaction–diffusion equations with high spatial gradients. International Journal of Computer Mathematics, 84(6), 749-765. doi:10.1080/00207160701458716McLachlan, R. I., & Quispel, G. R. W. (2002). Splitting methods. Acta Numerica, 11, 341-434. doi:10.1017/s0962492902000053Trotter, H. F. (1959). On the product of semi-groups of operators. Proceedings of the American Mathematical Society, 10(4), 545-545. doi:10.1090/s0002-9939-1959-0108732-6Strang, G. (1968). On the Construction and Comparison of Difference Schemes. SIAM Journal on Numerical Analysis, 5(3), 506-517. doi:10.1137/0705041Jahnke, T., & Lubich, C. (2000). Bit Numerical Mathematics, 40(4), 735-744. doi:10.1023/a:1022396519656Nevanlinna, O. (1989). Remarks on Picard-Lindelöf iteration. BIT, 29(2), 328-346. doi:10.1007/bf01952687Farago, I., & Geiser, J. (2007). Iterative operator-splitting methods for linear problems. International Journal of Computational Science and Engineering, 3(4), 255. doi:10.1504/ijcse.2007.018264DESCOMBES, S., DUARTE, M., DUMONT, T., LOUVET, V., & MASSOT, M. (2011). ADAPTIVE TIME SPLITTING METHOD FOR MULTI-SCALE EVOLUTIONARY PARTIAL DIFFERENTIAL EQUATIONS. Confluentes Mathematici, 03(03), 413-443. doi:10.1142/s1793744211000412Geiser, J. (2008). Iterative operator-splitting methods with higher-order time integration methods and applications for parabolic partial differential equations. Journal of Computational and Applied Mathematics, 217(1), 227-242. doi:10.1016/j.cam.2007.06.028Dimov, I., Farago, I., Havasi, A., & Zlatev, Z. (2008). Different splitting techniques with application to air pollution models. International Journal of Environment and Pollution, 32(2), 174. doi:10.1504/ijep.2008.017102Karlsen, K. H., Lie, K.-A., Natvig, J. ., Nordhaug, H. ., & Dahle, H. . (2001). Operator Splitting Methods for Systems of Convection–Diffusion Equations: Nonlinear Error Mechanisms and Correction Strategies. Journal of Computational Physics, 173(2), 636-663. doi:10.1006/jcph.2001.6901Geiser, J. (2010). Iterative operator-splitting methods for nonlinear differential equations and applications. Numerical Methods for Partial Differential Equations, 27(5), 1026-1054. doi:10.1002/num.20568Geiser, J., & Wu, Y. H. (2015). Iterative solvers for the Maxwell–Stefan diffusion equations: Methods and applications in plasma and particle transport. Cogent Mathematics, 2(1), 1092913. doi:10.1080/23311835.2015.1092913Geiser, J., Hueso, J. L., & MartĂnez, E. (2017). New versions of iterative splitting methods for the momentum equation. Journal of Computational and Applied Mathematics, 309, 359-370. doi:10.1016/j.cam.2016.06.002Boudin, L., Grec, B., & Salvarani, F. (2012). A mathematical and numerical analysis of the Maxwell-Stefan diffusion equations. Discrete & Continuous Dynamical Systems - B, 17(5), 1427-1440. doi:10.3934/dcdsb.2012.17.1427Duncan, J. B., & Toor, H. L. (1962). An experimental study of three component gas diffusion. AIChE Journal, 8(1), 38-41. doi:10.1002/aic.69008011
An Adaptive Design Methodology for Reduction of Product Development Risk
Embedded systems interaction with environment inherently complicates
understanding of requirements and their correct implementation. However,
product uncertainty is highest during early stages of development. Design
verification is an essential step in the development of any system, especially
for Embedded System. This paper introduces a novel adaptive design methodology,
which incorporates step-wise prototyping and verification. With each adaptive
step product-realization level is enhanced while decreasing the level of
product uncertainty, thereby reducing the overall costs. The back-bone of this
frame-work is the development of Domain Specific Operational (DOP) Model and
the associated Verification Instrumentation for Test and Evaluation, developed
based on the DOP model. Together they generate functionally valid test-sequence
for carrying out prototype evaluation. With the help of a case study 'Multimode
Detection Subsystem' the application of this method is sketched. The design
methodologies can be compared by defining and computing a generic performance
criterion like Average design-cycle Risk. For the case study, by computing
Average design-cycle Risk, it is shown that the adaptive method reduces the
product development risk for a small increase in the total design cycle time.Comment: 21 pages, 9 figure
Fast YOLO: A Fast You Only Look Once System for Real-time Embedded Object Detection in Video
Object detection is considered one of the most challenging problems in this
field of computer vision, as it involves the combination of object
classification and object localization within a scene. Recently, deep neural
networks (DNNs) have been demonstrated to achieve superior object detection
performance compared to other approaches, with YOLOv2 (an improved You Only
Look Once model) being one of the state-of-the-art in DNN-based object
detection methods in terms of both speed and accuracy. Although YOLOv2 can
achieve real-time performance on a powerful GPU, it still remains very
challenging for leveraging this approach for real-time object detection in
video on embedded computing devices with limited computational power and
limited memory. In this paper, we propose a new framework called Fast YOLO, a
fast You Only Look Once framework which accelerates YOLOv2 to be able to
perform object detection in video on embedded devices in a real-time manner.
First, we leverage the evolutionary deep intelligence framework to evolve the
YOLOv2 network architecture and produce an optimized architecture (referred to
as O-YOLOv2 here) that has 2.8X fewer parameters with just a ~2% IOU drop. To
further reduce power consumption on embedded devices while maintaining
performance, a motion-adaptive inference method is introduced into the proposed
Fast YOLO framework to reduce the frequency of deep inference with O-YOLOv2
based on temporal motion characteristics. Experimental results show that the
proposed Fast YOLO framework can reduce the number of deep inferences by an
average of 38.13%, and an average speedup of ~3.3X for objection detection in
video compared to the original YOLOv2, leading Fast YOLO to run an average of
~18FPS on a Nvidia Jetson TX1 embedded system
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