scholarly journals Multirate Time Integration for ODEs and DAEs Final Report

2019 ◽  
Author(s):  
C S Woodward ◽  
L Loffeld ◽  
D J Gardner
Keyword(s):  
Time Integration ◽  
Final Report ◽  
Multirate Time Integration

scholarly journals Multirate linearly-implicit GARK schemes

2021 ◽  
Author(s):  
Michael Günther ◽  
Adrian Sandu
Keyword(s):  
Numerical Stability ◽  
Initial Value Problems ◽  
Time Integration ◽  
Order Conditions ◽  
Systems Of Equations ◽  
Implicit Methods ◽  
Initial Value ◽  
Multirate Time Integration ◽  
Efficient Coupling ◽  
Linear Systems Of Equations

AbstractMany complex applications require the solution of initial-value problems where some components change fast, while others vary slowly. Multirate schemes apply different step sizes to resolve different components of the system, according to their dynamics, in order to achieve increased computational efficiency. The stiff components of the system, fast or slow, are best discretized with implicit base methods in order to ensure numerical stability. To this end, linearly implicit methods are particularly attractive as they solve only linear systems of equations at each step. This paper develops the Multirate GARK-ROS/ROW (MR-GARK-ROS/ROW) framework for linearly-implicit multirate time integration. The order conditions theory considers both exact and approximative Jacobians. The effectiveness of implicit multirate methods depends on the coupling between the slow and fast computations; an array of efficient coupling strategies and the resulting numerical schemes are analyzed. Multirate infinitesimal step linearly-implicit methods, that allow arbitrarily small micro-steps and offer extreme computational flexibility, are constructed. The new unifying framework includes existing multirate Rosenbrock(-W) methods as particular cases, and opens the possibility to develop new classes of highly effective linearly implicit multirate integrators.

scholarly journals Terminal Current Interpolation for Multirate Time Integration of Hierarchical IC Models

2010 ◽  
pp. 333-339
Author(s):  
A. Verhoeven ◽  
E. J. W. ter Maten ◽  
J. J. Dohmen ◽  
B. Tasić ◽  
R. M. M. Mattheij
Keyword(s):  
Time Integration ◽  
Multirate Time Integration

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.

A Cosimulation Framework for Multirate Time Integration of Field/Circuit Coupled Problems

2010 ◽  
Vol 46 (8) ◽  
pp. 3233-3236 ◽  
Author(s):  
Sebastian Schops ◽  
Herbert De Gersem ◽  
Andreas Bartel
Keyword(s):  
Time Integration ◽  
Coupled Problems ◽  
Multirate Time Integration
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