Augmented Time-Stepping by Step Size Adjustment and Extrapolation

2009 ◽  
pp. 99-127
Author(s):  
Christian Studer
Keyword(s):  
Step Size ◽  
Time Stepping ◽  
Size Adjustment

Augmented Time-Stepping by Step-Size Adjustment and Extrapolation

2007 ◽  
Author(s):  
Christian Studer ◽  
Christoph Glocker
Keyword(s):  
Time Evolution ◽  
Integration Method ◽  
Switching Time ◽  
Mechanical Systems ◽  
Unilateral Contact ◽  
Step Size ◽  
Frictional Contacts ◽  
Time Stepping ◽  
Size Adjustment ◽  
Integration Order

Time-stepping schemes are widely used when integrating non-smooth systems. In this paper we discuss an augmented time-stepping scheme which uses step-size adjustment and extrapolation. The time evolution of non-smooth systems can be divided in different smooth parts, which are separated by switching points. We deduce the time-stepping method of Moreau, which is a common order-one integration method for non-smooth systems. We formulate the method using contact inclusions, and show how these inclusions can be solved by a projection. We show how time-steps which contain a switching point can be detected by observing the projection behaviour, and propose a step-size adjustment, which treats these switching time-steps with a minimal step-size Δtmin. Time-steps in smooth parts of the motion are run with a larger step-size, and an extrapolation method, which is based on the time-stepping scheme, is used to increase the integration order. The presented method is suitable for mechanical systems with unilateral and frictional contacts. For simplicity, we deduce the method considering solely mechanical systems with one unilateral contact.

scholarly journals Step size adjustment and extrapolation for time-stepping schemes in non-smooth dynamics

2008 ◽  
Vol 76 (11) ◽  
pp. 1747-1781 ◽  
Author(s):  
C. Studer ◽  
R. I. Leine ◽  
Ch. Glocker
Keyword(s):  
Step Size ◽  
Time Stepping ◽  
Size Adjustment ◽  
Smooth Dynamics

scholarly journals Analysis of a Decoupled Time-Stepping Scheme for Evolutionary Micropolar Fluid Flows

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
S. S. Ravindran
Keyword(s):  
Micropolar Fluid ◽  
Stokes Equations ◽  
Fluid Model ◽  
Navier Stokes ◽  
Optimal Order ◽  
Step Size ◽  
Time Step ◽  
Order Error ◽  
Time Step Size ◽  
Time Stepping

Micropolar fluid model consists of Navier-Stokes equations and microrotational velocity equations describing the dynamics of flows in which microstructure of fluid is important. In this paper, we propose and analyze a decoupled time-stepping algorithm for the evolutionary micropolar flow. The proposed method requires solving only one uncoupled Navier-Stokes and one microrotation subphysics problem per time step. We derive optimal order error estimates in suitable norms without assuming any stability condition or time step size restriction.

scholarly journals Adaptive Cuckoo Search Algorithm for Unconstrained Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Pauline Ong
Keyword(s):  
Marked Improvement ◽  
Search Algorithm ◽  
Cuckoo Search ◽  
Cuckoo Search Algorithm ◽  
Optimal Solutions ◽  
Step Size ◽  
Adjustment Strategy ◽  
Global Optimal ◽  
Adaptive Step ◽  
Size Adjustment

Modification of the intensification and diversification approaches in the recently developed cuckoo search algorithm (CSA) is performed. The alteration involves the implementation of adaptive step size adjustment strategy, and thus enabling faster convergence to the global optimal solutions. The feasibility of the proposed algorithm is validated against benchmark optimization functions, where the obtained results demonstrate a marked improvement over the standard CSA, in all the cases.

A Variable Step Size LMS Based on Sparsity for System Identification

2013 ◽  
Vol 475-476 ◽  
pp. 1060-1066
Author(s):  
X.Q. Chen ◽  
Hua Ju ◽  
Wei Fan ◽  
W.G. Huang ◽  
Z.K. Zhu
Keyword(s):  
Steady State ◽  
System Identification ◽  
Lms Algorithm ◽  
Variable Step Size ◽  
Least Mean Square ◽  
Step Size ◽  
Practical Applications ◽  
Variable Step ◽  
Size Adjustment ◽  
State Error

In many practical applications, the impulse responses of the unknown system are sparse. However, the standard Least Mean Square (LMS) algorithm does not make full use of the sparsity, and the general sparse LMS algorithms increase steady-state error because of giving much large attraction to the small factor. In order to improve the performance of sparse system identification, we propose a new algorithm which introduces a variable step size method into the Reweighted Zero-Attracting LMS (RZALMS) algorithm. The improved algorithm, whose step size adjustment is controlled by the instantaneous error, is called Variable step size RZALMS (V-RZALMS). The variable step size leads to yielding smaller steady-state error on the premise of higher convergent speed. Moreover, the sparser the system is, the better the V-RZALMS performs. Three different experiments are implemented to validate the effectiveness of our new algorithm.

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