Multiple Grid and Multiple Time-Scale (MGMT) Simulations in Continuum Mechanics

2012 ◽  
Author(s):  
Tejas Ruparel ◽  
Azim Eskandarian ◽  
James Lee
Keyword(s):  
Finite Element ◽  
Continuum Mechanics ◽  
Time Scale ◽  
Computational Time ◽  
Discrete Equation ◽  
Integration Scheme ◽  
Multiple Time ◽  
Multiple Time Scale ◽  
Time Step ◽  
Stable Algorithm

The work presented in this paper describes a general formulation for implementation of Multiple Grid and Multiple Time-scale (MGMT) simulations in continuum mechanics. Using this method one can solve problems in structural dynamics in which the domain under consideration can be selectively discretized (spatially and temporally) in critical and remote regions, hence allowing the user to obtain a desired level of accuracy and save computational time. The formulation is based upon the fundamental principles of Domain Decomposition Methods (DDM) used to obtain the semi-discrete equation of motion for coupled sub-domains augmented with interface energy. Lagrange Multipliers, based on Schur’s dual formulation, are used to enforce interface conditions since they not only ensure energy balance but also enforce continuity of kinematic quantities across the interface. The Finite Element Tearing and Interconnecting (FETI) based Multi Time-step (MTS) coupling algorithm proposed by Prakash and Hjelmstad [1] is then used to obtain the evolution of unknown quantities in respective sub-domains using different time-steps and/or different variants of the Newmark Implicit Method. Our work is in the direction of coupling this MTS algorithm with multiple grid discretizations in respective subdomains. We propose using coarse grid discretization to define the mortar space between non-conforming sub-domains and show that this particular choice when combined with the implicit integration scheme yields a stable algorithm for MGMT simulations. The formulation is implemented, comprehensively, using Finite Element Methods and programming in FORTRAN 90. Several scenarios with different mesh densities and time-steps are evaluated to analyze the efficiency of MGMT simulations. The purpose of this paper is to study and evaluate its accuracy and stability by looking at evolution and distribution of quantities across the connecting interface. Results show that the interface coupling for non-conforming sub-domains with distinct integration time-steps can be efficiently modeled using this approach.

scholarly journals A Multiple Step Active Stiffness Integration Scheme to Couple a Stochastic Cross-Bridge Model and Continuum Mechanics for Uses in Both Basic Research and Clinical Applications of Heart Simulation

2021 ◽  
Vol 12 ◽  
Author(s):  
Kazunori Yoneda ◽  
Jun-ichi Okada ◽  
Masahiro Watanabe ◽  
Seiryo Sugiura ◽  
Toshiaki Hisada ◽  
...  
Keyword(s):  
Finite Element ◽  
Continuum Mechanics ◽  
Stiffness Matrix ◽  
Basic Research ◽  
Clinical Applications ◽  
Integration Scheme ◽  
Fe Model ◽  
Active Tension ◽  
Time Step ◽  
Multiple Step

In a multiscale simulation of a beating heart, the very large difference in the time scales between rapid stochastic conformational changes of contractile proteins and deterministic macroscopic outcomes, such as the ventricular pressure and volume, have hampered the implementation of an efficient coupling algorithm for the two scales. Furthermore, the consideration of dynamic changes of muscle stiffness caused by the cross-bridge activity of motor proteins have not been well established in continuum mechanics. To overcome these issues, we propose a multiple time step scheme called the multiple step active stiffness integration scheme (MusAsi) for the coupling of Monte Carlo (MC) multiple steps and an implicit finite element (FE) time integration step. The method focuses on the active tension stiffness matrix, where the active tension derivatives concerning the current displacements in the FE model are correctly integrated into the total stiffness matrix to avoid instability. A sensitivity analysis of the number of samples used in the MC model and the combination of time step sizes confirmed the accuracy and robustness of MusAsi, and we concluded that the combination of a 1.25 ms FE time step and 0.005 ms MC multiple steps using a few hundred motor proteins in each finite element was appropriate in the tradeoff between accuracy and computational time. Furthermore, for a biventricular FE model consisting of 45,000 tetrahedral elements, one heartbeat could be computed within 1.5 h using 320 cores of a conventional parallel computer system. These results support the practicality of MusAsi for uses in both the basic research of the relationship between molecular mechanisms and cardiac outputs, and clinical applications of perioperative prediction.

Decentralized monthly generation scheduling of cascade hydropower plants in multiple time scale markets

2022 ◽  
Vol 135 ◽  
pp. 107420
Author(s):  
Yuhang Ma ◽  
Yuan Huang ◽  
Gang Wu ◽  
Junyong Liu ◽  
Yang Liu ◽  
...  
Keyword(s):  
Time Scale ◽  
Multiple Time ◽  
Multiple Time Scale ◽  
Generation Scheduling ◽  
Hydropower Plants

The plasma transport equations derived by multiple time‐scale expansions. II. An application

1995 ◽  
Vol 2 (4) ◽  
pp. 1206-1216 ◽  
Author(s):  
J. W. Edenstrasser ◽  
M. M. M. Kassab
Keyword(s):  
Time Scale ◽  
Transport Equations ◽  
Plasma Transport ◽  
Multiple Time ◽  
Multiple Time Scale

Predicting the trend of stock index based on feature engineering and CatBoost model

2021 ◽  
pp. 2150027
Author(s):  
Renzhe Xu ◽  
Yudong Chen ◽  
Tenglong Xiao ◽  
Jingli Wang ◽  
Xiong Wang
Keyword(s):  
Time Scale ◽  
Stock Index ◽  
Feature Engineering ◽  
Multiple Time ◽  
Multiple Time Scale ◽  
Back Testing ◽  
Price Series ◽  
Out Of Sample ◽  
Out Of Sample Prediction ◽  
Sharp Ratio

As an important tool to measure the current situation of the whole stock market, the stock index has always been the focus of researchers, especially for its prediction. This paper uses trend types, which are received by clustering price series under multiple time scale, combined with the day-of-the-week effect to construct a categorical feature combination. Based on the historical data of six kinds of Chinese stock indexes, the CatBoost model is used for training and predicting. Experimental results show that the out-of-sample prediction accuracy is 0.55, and the long–short trading strategy can obtain average annualized return of 34.43%, which is a great improvement compared with other classical classification algorithms. Under the rolling back-testing, the model can always obtain stable returns in each period of time from 2012 to 2020. Among them, the SSESC’s long–short strategy has the best performance with an annualized return of 40.85% and a sharp ratio of 1.53. Therefore, the trend information on multiple time-scale features based on feature engineering can be learned by the CatBoost model well, which has a guiding effect on predicting stock index trends.

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