scholarly journals The RAW Filter: An Improvement to the Robert–Asselin Filter in Semi-Implicit Integrations

2011 ◽  
Vol 139 (6) ◽  
pp. 1996-2007 ◽  
Author(s):  
Paul D. Williams
Keyword(s):  
Small Time ◽  
Time Stepping ◽  
Phase Errors ◽  
Power Series Expansions ◽  
Analytic Expressions ◽  
Optimal Values ◽  
The Stability ◽  
Stability And Accuracy ◽  
Total Model ◽  
Elastic Pendulum

Abstract Errors caused by discrete time stepping may be an important component of total model error in contemporary atmospheric and oceanic simulations. To reduce time-stepping errors in leapfrog integrations, the Robert–Asselin–Williams (RAW) filter was proposed by the author as a simple improvement to the widely used Robert–Asselin (RA) filter. The present paper examines the behavior of the RAW filter in semi-implicit integrations. First, in a linear theoretical analysis, the stability and accuracy are interrogated by deriving analytic expressions for the amplitude errors and phase errors. Then, power-series expansions are used to interpret the leading-order errors for small time steps and hence to identify optimal values of the filter parameters. Finally, the RAW filter is tested in a realistic nonlinear setting, by applying it to semi-implicit integrations of the elastic pendulum equations. The results suggest that replacing the RA filter with the RAW filter could reduce time-stepping errors in semi-implicit integrations.

Design of Runge-Kutta based split-explicit time integration algorithms for the NEMO ocean model

2021 ◽  
Author(s):  
Nicolas Ducousso ◽  
Florian Lemarié ◽  
Gurvan Madec ◽  
Laurent Debreu
Keyword(s):  
Time Integration ◽  
Internal Gravity Waves ◽  
Positive Definiteness ◽  
Ocean Model ◽  
Splitting Technique ◽  
Time Stepping ◽  
Phase Errors ◽  
Runge Kutta ◽  
Leapfrog Scheme ◽  
Stability And Accuracy

<p>The NEMO ocean model is currently based on the Leapfrog scheme that provides a good combination between simplicity and efficiency for low-resolution global simulations. However, this scheme is subject to difficulties that question its relevance at high-resolution : the necessary damping of its computational mode, e.g. via a Robert-Asselin filter, affect stability and increases amplitude and phase errors of the physical mode ; because it is unconditionally unstable for diffusive processes, monotonicity or positive-definiteness comes at a substantial cost and complication. The evolution toward a 2-level time stepping algorithm based on Runge-Kutta schemes is studied. Special attention is given to how to articulate a mode-splitting technique to handle the fast dynamics associated with the free surface. Linear stability analyses of several Runge-Kutta based, split-explicit algorithms are performed and the most promising ones are identified. They allow a good compromise between robustness, stability and accuracy for integration of internal gravity waves, Coriolis and advection processes. Idealized test-cases illustrate the benefits associated to the revised time-stepping compared to the original Leapfrog.</p>

A FAST AND ACCURATE STEP-BY-STEP SOLUTION PROCEDURE FOR DIRECT INTEGRATION

2011 ◽  
Vol 11 (03) ◽  
pp. 473-493 ◽  
Author(s):  
SHYH-RONG KUO ◽  
J. D. YAU
Keyword(s):  
Time Integration ◽  
Closed Form Solution ◽  
Solution Procedure ◽  
Small Time ◽  
Form Solution ◽  
Dynamic Problems ◽  
Sdof System ◽  
Linear Dynamic ◽  
The Stability ◽  
Stability And Accuracy

Very small time steps are usually needed in numerical computation as conventional time integration methods are used to compute the response of a structure subjected to a dynamic loading with rapid changes or load discontinuity. To overcome this drawback, this study proposed a fast, fourth-order accurate step-by-step time integration (FASSTI) algorithm that is unconditionally stable and allows larger time steps for linear dynamic problems. From the stability and accuracy analysis, it is shown that the FASSTI algorithm retains the features of unconditional stability, accuracy, and fast convergence than the Newmark method. As a first test, a closed-form solution of an excited single degree of freedom (SDOF) system is derived and used to verify the reliability of the present algorithm in solving linear dynamic problems. In the numerical examples, the accuracy and efficiency of the proposed method is demonstrated in the solution of the dynamic response of an SDOF system under a series of impulse-type forces.

scholarly journals Dynamical System Inspired Adaptive Time Stepping Controller for Residual Network Families

2020 ◽  
Vol 34 (04) ◽  
pp. 6648-6655
Author(s):  
Yibo Yang ◽  
Jianlong Wu ◽  
Hongyang Li ◽  
Xia Li ◽  
Tiancheng Shen ◽  
...  
Keyword(s):  
Euler Method ◽  
Time Stepping ◽  
Network Training ◽  
Variable Step ◽  
Adaptive Time ◽  
Good Trade ◽  
And Performance ◽  
The Stability ◽  
Stability And Accuracy ◽  
Adaptive Time Stepping

The correspondence between residual networks and dynamical systems motivates researchers to unravel the physics of ResNets with well-developed tools in numeral methods of ODE systems. The Runge-Kutta-Fehlberg method is an adaptive time stepping that renders a good trade-off between the stability and efficiency. Can we also have an adaptive time stepping for ResNets to ensure both stability and performance? In this study, we analyze the effects of time stepping on the Euler method and ResNets. We establish a stability condition for ResNets with step sizes and weight parameters, and point out the effects of step sizes on the stability and performance. Inspired by our analyses, we develop an adaptive time stepping controller that is dependent on the parameters of the current step, and aware of previous steps. The controller is jointly optimized with the network training so that variable step sizes and evolution time can be adaptively adjusted. We conduct experiments on ImageNet and CIFAR to demonstrate the effectiveness. It is shown that our proposed method is able to improve both stability and accuracy without introducing additional overhead in inference phase.

scholarly journals Underground Microseismic Event Monitoring and Localization within Sensor Networks

Sensors ◽  
2021 ◽  
Vol 21 (8) ◽  
pp. 2830
Author(s):  
Sili Wang ◽  
Mark P. Panning ◽  
Steven D. Vance ◽  
Wenzhan Song
Keyword(s):  
Sensor Networks ◽  
Real Time ◽  
Information Needs ◽  
Localization Algorithm ◽  
Distributed Sensors ◽  
Distributed Sensor ◽  
Microseismic Events ◽  
The Stability ◽  
Stability And Accuracy

Locating underground microseismic events is important for monitoring subsurface activity and understanding the planetary subsurface evolution. Due to bandwidth limitations, especially in applications involving planetarily-distributed sensor networks, networks should be designed to perform the localization algorithm in-situ, so that only the source location information needs to be sent out, not the raw data. In this paper, we propose a decentralized Gaussian beam time-reverse imaging (GB-TRI) algorithm that can be incorporated to the distributed sensors to detect and locate underground microseismic events with reduced usage of computational resources and communication bandwidth of the network. After the in-situ distributed computation, the final real-time location result is generated and delivered. We used a real-time simulation platform to test the performance of the system. We also evaluated the stability and accuracy of our proposed GB-TRI localization algorithm using extensive experiments and tests.

scholarly journals Explicit parallel co-simulation approach: analysis and improved coupling method based on H-infinity synthesis

2021 ◽  
Author(s):  
Weitao Chen ◽  
Shenhai Ran ◽  
Canhui Wu ◽  
Bengt Jacobson
Keyword(s):  
Frequency Domain ◽  
Wide Frequency Range ◽  
Coupling Method ◽  
Sampled Data ◽  
H Infinity ◽  
First Case ◽  
Communication Step ◽  
Coupling Variables ◽  
The Stability ◽  
Stability And Accuracy

AbstractCo-simulation is widely used in the industry for the simulation of multidomain systems. Because the coupling variables cannot be communicated continuously, the co-simulation results can be unstable and inaccurate, especially when an explicit parallel approach is applied. To address this issue, new coupling methods to improve the stability and accuracy have been developed in recent years. However, the assessment of their performance is sometimes not straightforward or is even impossible owing to the case-dependent effect. The selection of the coupling method and its tuning cannot be performed before running the co-simulation, especially with a time-varying system.In this work, the co-simulation system is analyzed in the frequency domain as a sampled-data interconnection. Then a new coupling method based on the H-infinity synthesis is developed. The method intends to reconstruct the coupling variable by adding a compensator and smoother at the interface and to minimize the error from the sample-hold process. A convergence analysis in the frequency domain shows that the coupling error can be reduced in a wide frequency range, which implies good robustness. The new method is verified using two co-simulation cases. The first case is a dual mass–spring–damper system with random parameters and the second case is a co-simulation of a multibody dynamic (MBD) vehicle model and an electric power-assisted steering (EPAS) system model. Experimental results show that the method can improve the stability and accuracy, which enables a larger communication step to speed up the explicit parallel co-simulation.

scholarly journals A Digital Framework to Predict the Sunshine Requirements of Landscape Plants

2021 ◽  
Vol 11 (5) ◽  
pp. 2098
Author(s):  
Heyi Wei ◽  
Wenhua Jiang ◽  
Xuejun Liu ◽  
Bo Huang
Keyword(s):  
Solar Radiation ◽  
Plant Species ◽  
Large Scale ◽  
Normal Growth ◽  
Adaptive Selection ◽  
Landscape Plant ◽  
Landscape Plants ◽  
The Stability ◽  
Stability And Accuracy ◽  
The City

Knowledge of the sunshine requirements of landscape plants is important information for the adaptive selection and configuration of plants for urban greening, and is also a basic attribute of plant databases. In the existing studies, the light compensation point (LCP) and light saturation point (LSP) have been commonly used to indicate the shade tolerance for a specific plant; however, these values are difficult to adopt in practice because the landscape architect does not always know what range of solar radiation is the best for maintaining plant health, i.e., normal growth and reproduction. In this paper, to bridge the gap, we present a novel digital framework to predict the sunshine requirements of landscape plants. First, the research introduces the proposed framework, which is composed of a black-box model, solar radiation simulation, and a health standard system for plants. Then, the data fitting between solar radiation and plant growth response is used to obtain the value of solar radiation at different health levels. Finally, we adopt the LI-6400XT Portable Photosynthetic System (Li-Cor Inc., Lincoln, NE, USA) to verify the stability and accuracy of the digital framework through 15 landscape plant species of a residential area in the city of Wuhan, China, and also compared and analyzed the results of other researchers on the same plant species. The results show that the digital framework can robustly obtain the values of the healthy, sub-healthy, and unhealthy levels for the 15 landscape plant species. The purpose of this study is to provide an efficient forecasting tool for large-scale surveys of plant sunshine requirements. The proposed framework will be beneficial for the adaptive selection and configuration of urban plants and will facilitate the construction of landscape plant databases in future studies.

scholarly journals Modelling of the Power Interface of the Digital-Physical Hybrid Simulation System of a VSC-HVDC Based on Virtual Resistance Compensation

Electronics ◽  
2018 ◽  
Vol 7 (11) ◽  
pp. 333
Author(s):  
Jian Le ◽  
Hao Zhang ◽  
Cao Wang ◽  
Xingrui Li ◽  
Jiangfeng Zhu
Keyword(s):  
Current Source ◽  
Hybrid Simulation ◽  
Simulation System ◽  
System Stability ◽  
Interface Model ◽  
Simulation Accuracy ◽  
Hvdc System ◽  
High Voltage Direct Current ◽  
The Stability ◽  
Stability And Accuracy

To enhance the stability and accuracy of the digital-physical hybrid simulation system of a modular multilevel converter-based high voltage direct current (MMC-HVDC) system, this paper presents an improved power interface modeling algorithm based on ideal transformer method (ITM). By analyzing the stability condition of a hybrid simulation system based on the ITM model, the current of a so-called virtual resistance is added to the control signal of the controlled current source in the digital subsystem, and the stability of the hybrid simulation system with the improved power interface model is analyzed. The value of the virtual resistance is optimized by comprehensively considering system stability and simulation precision. A two-terminal bipolar MMC-HVDC simulation system based on the proposed power interface model is established. The comparisons of the simulation results verify that the proposed method can effectively improve the stability of the hybrid simulation system, and at the same time has the advantages of high simulation accuracy and easy implementation.

Solving Vlasov-Poisson-Fokker-Planck Equations using NRxx method

2017 ◽  
Vol 21 (3) ◽  
pp. 782-807 ◽  
Author(s):  
Yanli Wang ◽  
Shudao Zhang
Keyword(s):  
Splitting Method ◽  
Linear Convergence ◽  
Mass Conservation ◽  
System A ◽  
Spectral Convergence ◽  
The Stability ◽  
The Moment ◽  
Stability And Accuracy ◽  
Fokker Planck Equations ◽  
Fokker Planck

AbstractWe present a numerical method to solve the Vlasov-Poisson-Fokker-Planck (VPFP) system using the NRxx method proposed in [4, 7, 9]. A globally hyperbolic moment system similar to that in [23] is derived. In this system, the Fokker-Planck (FP) operator term is reduced into the linear combination of the moment coefficients, which can be solved analytically under proper truncation. The non-splitting method, which can keep mass conservation and the balance law of the total momentum, is used to solve the whole system. A numerical problem for the VPFP system with an analytic solution is presented to indicate the spectral convergence with the moment number and the linear convergence with the grid size. Two more numerical experiments are tested to demonstrate the stability and accuracy of the NRxx method when applied to the VPFP system.

scholarly journals SPECTRA OF THERMOSTIMULATED DEPOLARIZATION OF BIOCOMPOSITES WITH FILLERS OF BIOLOGICAL ORIGIN

2021 ◽  
Vol 5 (1(82)) ◽  
pp. 45-49
Author(s):  
E. Gojayev ◽  
V. Salimova ◽  
Sh. Alieva
Keyword(s):  
Surface Density ◽  
Fish Bone ◽  
Fish Scales ◽  
Biological Origin ◽  
Space Charges ◽  
High Pressure Polyethylene ◽  
Optimal Values ◽  
The Stability ◽  
Thermally Stimulated Depolarization ◽  
Volumetric Content

The paper presents the results of studying the spectra of thermally stimulated depolarization of high-pressure polyethylene modified with fillers of biocomposites with fillers of biological origin - fish bone and fish scales. It was revealed that the stability and surface density of space charges can be controlled by varying the volumetric content of biological fillers. The optimal values of bio-fillers that contribute to the stability of the surface density of the studied biocomposites have been determined.

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