Error analysis of generalized- $$\alpha $$ α Lie group time integration methods for constrained mechanical systems

2014 ◽  
Vol 129 (1) ◽  
pp. 149-179 ◽  
Author(s):  
Martin Arnold ◽  
Olivier Brüls ◽  
Alberto Cardona
Keyword(s):  
Error Analysis ◽  
Lie Group ◽  
Time Integration ◽  
Mechanical Systems ◽  
Integration Methods ◽  
Constrained Mechanical Systems ◽  
Group Time ◽  
Time Integration Methods

Accuracy and efficiency of time integration methods for 1D diffusive wave equation

2014 ◽  
Vol 18 (5) ◽  
pp. 697-709 ◽  
Author(s):  
Sylvain Weill ◽  
Raphael di Chiara-Roupert ◽  
Philippe Ackerer
Keyword(s):  
Wave Equation ◽  
Time Integration ◽  
Integration Methods ◽  
Time Integration Methods

Second derivative time integration methods for discontinuous Galerkin solutions of unsteady compressible flows

2017 ◽  
Vol 350 ◽  
pp. 493-517 ◽  
Author(s):  
A. Nigro ◽  
C. De Bartolo ◽  
A. Crivellini ◽  
F. Bassi
Keyword(s):  
Discontinuous Galerkin ◽  
Compressible Flows ◽  
Time Integration ◽  
Second Derivative ◽  
Integration Methods ◽  
Time Integration Methods

scholarly journals Some topics in matrix analysis for time integration methods

2018 ◽  
pp. 1-45
Author(s):  
Mikhail Aleksandrovich Botchev
Keyword(s):  
Time Integration ◽  
Matrix Analysis ◽  
Integration Methods ◽  
Time Integration Methods

scholarly journals Efficient time integration methods for Gross-Pitaevskii equations with rotation term

2019 ◽  
Vol 6 (2) ◽  
pp. 147-169 ◽  
Author(s):  
Philipp Bader ◽  
◽  
Sergio Blanes ◽  
Fernando Casas ◽  
Mechthild Thalhammer ◽  
...  
Keyword(s):  
Time Integration ◽  
Integration Methods ◽  
Time Integration Methods

Singularity-Free Lie Group Integration and Geometrically Consistent Evaluation of Multibody System Models described in terms of Standard Absolute Coordinates

2021 ◽  
Author(s):  
Andreas Mueller
Keyword(s):  
Rigid Body ◽  
Lie Group ◽  
Time Integration ◽  
Integration Methods ◽  
Product Group ◽  
Local Coordinates ◽  
Group Integration ◽  
The Absolute ◽  
Lie Group Integration ◽  
Absolute Coordinates

Abstract A classical approach to the MBS modeling is to use absolute coordinates, i.e. a set of (possibly redundant) coordinates that describe the absolute position and orientation of the individual bodies w.r.t. to an inertial frame (IFR). A well-known problem for the time integration of the equations of motion (EOM) is the lack of a singularity-free parameterization of spatial motions, which is usually tackled by using unit quaternions. Lie group integration methods were proposed as alternative approach to the singularity-free time integration. Lie group integration methods, operating directly on the configuration space Lie group, are incompatible with standard formulations of the EOM, and cannot be implemented in existing MBS simulation codes without a major restructuring. A framework for interfacing Lie group integrators to standard EOM formulations is presented in this paper. It allows describing MBS in terms of various absolute coordinates and at the same using Lie group integration schemes. The direct product group SO(3)xR3; and the semidirect product group SE(3) are use for representing rigid body motions. The key element of this method is the local-global transitions (LGT) transition map, which facilitates the update of (global) absolute coordinates in terms of the (local) coordinates on the Lie group. This LGT map is specific to the absolute coordinates, the local coordinates on the Lie group, and the Lie group used to represent rigid body configurations. This embedding of Lie group integration methods allows for interfacing with standard vector space integration methods.

Monolithic and partitioned time integration methods for real-time heterogeneous simulations

2012 ◽  
Vol 52 (1) ◽  
pp. 99-119 ◽  
Author(s):  
O. S. Bursi ◽  
Z. Wang ◽  
C. Jia ◽  
B. Wu
Keyword(s):  
Real Time ◽  
Time Integration ◽  
Integration Methods ◽  
Time Integration Methods

Development of Differential Quadrature Related Generalized Methods, Discrete Element Analysis Methods and EDQ Based Time Integration Methods

2005 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Time Integration ◽  
Numerical Algorithms ◽  
Discrete Element ◽  
Numerical Results ◽  
Differential Quadrature ◽  
Element Analysis ◽  
Integration Methods ◽  
Analysis Methods ◽  
Time Integration Methods

Development of differential quadrature related generalized methods, discrete element analysis methods and EDQ based time integration methods has been carried out the last few years. The related numerical algorithms are summarized and presented. Numerical results are also presented.

Sign in / Sign up

Export Citation Format

Share Document