Variable step size time integration methods for transient eddy current problems

1998 ◽  
Vol 34 (5) ◽  
pp. 3319-3322 ◽  
Author(s):  
F. Cameron ◽  
R. Piche ◽  
K. Forsman
Keyword(s):  
Eddy Current ◽  
Time Integration ◽  
Variable Step Size ◽  
Transient Eddy ◽  
Step Size ◽  
Integration Methods ◽  
Variable Step ◽  
Time Integration Methods ◽  
Transient Eddy Current

scholarly journals Implementation of multirate time integration methods for air pollution modelling

2012 ◽  
Vol 5 (6) ◽  
pp. 1395-1405 ◽  
Author(s):  
M. Schlegel ◽  
O. Knoth ◽  
M. Arnold ◽  
R. Wolke
Keyword(s):  
Time Integration ◽  
Efficient Implementation ◽  
Step Size ◽  
Time Step ◽  
Worst Case ◽  
Integration Methods ◽  
Integration Schemes ◽  
Numerical Effort ◽  
Multirate Time Integration ◽  
Time Integration Methods

Abstract. Explicit time integration methods are characterised by a small numerical effort per time step. In the application to multiscale problems in atmospheric modelling, this benefit is often more than compensated by stability problems and step size restrictions resulting from stiff chemical reaction terms and from a locally varying Courant-Friedrichs-Lewy (CFL) condition for the advection terms. Splitting methods may be applied to efficiently combine implicit and explicit methods (IMEX splitting). Complementarily multirate time integration schemes allow for a local adaptation of the time step size to the grid size. In combination, these approaches lead to schemes which are efficient in terms of evaluations of the right-hand side. Special challenges arise when these methods are to be implemented. For an efficient implementation, it is crucial to locate and exploit redundancies. Furthermore, the more complex programme flow may lead to computational overhead which, in the worst case, more than compensates the theoretical gain in efficiency. We present a general splitting approach which allows both for IMEX splittings and for local time step adaptation. The main focus is on an efficient implementation of this approach for parallel computation on computer clusters.

The Generalized-α Scheme as a Linear Multistep Integrator: Towards a General Mechatronic Simulator

2007 ◽  
Author(s):  
Olivier Bru¨ls ◽  
Martin Arnold
Keyword(s):  
Mass Matrix ◽  
Time Integration ◽  
Theoretical Background ◽  
Integration Scheme ◽  
Variable Step Size ◽  
Step Size ◽  
Mechatronic Systems ◽  
Variable Step ◽  
Time Integration Scheme ◽  
Consistent Formulation

This paper presents a consistent formulation of the generalized-α time integration scheme for mechanical and mechatronic systems. The algorithm can deal with a non-constant mass matrix, controller dynamics, and kinematic constraints. The theoretical background relies on the analogy with linear multistep formulae, which leads to elegant results related with consistency, order conditions for constant and variable step-size methods, as well as global convergence. The algorithm is applied for the simulation of a vehicle semi-active suspension.

Unconditional Stability in Numerical Time Integration Methods

1973 ◽  
Vol 40 (2) ◽  
pp. 417-421 ◽  
Author(s):  
R. D. Krieg
Keyword(s):  
Time Integration ◽  
Step Size ◽  
Time Step ◽  
Central Difference ◽  
Integration Methods ◽  
Time Step Size ◽  
Time Integration Method ◽  
Time Integration Methods ◽  
Numerical Time Integration ◽  
Difference Time

Methods of numerical time integration of the equation M¯q¨ + K¯q = f are examined in this paper. A particular class of explicit time integration methods is defined and this class is searched for an unconditionally stable method. The class is found to contain no such method and, furthermore, is found to contain no method with a larger stable time step size than that characterized by the simple central difference time integration method.

A Variable Step-Size for Sparse Nonlinear Adaptive Filters

2021 ◽  
Author(s):  
Alberto Carini ◽  
Markus V. S. Lima ◽  
Hamed Yazdanpanah ◽  
Simone Orcioni ◽  
Stefania Cecchi
Keyword(s):  
Adaptive Filters ◽  
Variable Step Size ◽  
Step Size ◽  
Variable Step
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