A fast global nodewise mass matrix inversion framework tailored for sparse block-diagonal systems

2022 ◽  
Vol 172 ◽  
pp. 108700
Author(s):  
C.S. Rekatsinas
Keyword(s):  
Mass Matrix ◽  
Matrix Inversion ◽  
Block Diagonal

Closed Form Solutions to the Equation of Motion Avoiding Mass Matrix Inversion and Eigenvectors Decomposition

2001 ◽  
Author(s):  
Karine Reaud ◽  
Claude Vallee ◽  
Danielle Fortune
Keyword(s):  
Closed Form ◽  
Mass Matrix ◽  
Equation Of Motion ◽  
Matrix Inversion ◽  
Matrix Exponential ◽  
Linear Case ◽  
Closed Form Solutions ◽  
Damping Matrix ◽  
Ill Conditioned Matrices ◽  
Damping Systems

Abstract Solutions of the vibrations equations are generally obtained, in the linear case, by methods involving either matrix exponential computation or matrix eigendecomposition. However, these methods lead to a loss of symmetry because of the necessary inversion of the mass matrix. In doing so, one can introduce ill-conditioned matrices and, thus, compute eigenvectors with poor accuracy. In order to avoid these inconveniences, our method, which is an extension of Le Verrier-Souriau algorithm, provides solutions to the vibrations equations without inverting the mass matrix or computing eigenvectors. Moreover, we can solve damping systems even when the damping matrix has no specific properties such as the Basile property.

Application of Parallel Computing to Joint-Disconnected Multibody Systems

2005 ◽  
Author(s):  
James Critchley ◽  
Michael McCullough
Keyword(s):  
Parallel Computing ◽  
Execution Time ◽  
Multibody Systems ◽  
Mass Matrix ◽  
Interaction Forces ◽  
Kinematic Constraints ◽  
Fully Coupled ◽  
Block Diagonal ◽  
Parallel Resources

In some areas of application, large multibody systems are encountered which are not completely coupled by kinematic constraints (joints). For these “joint-disconnected” systems, the generalized mass matrix is block diagonal and the coordinate accelerations associated with each block may be solved with independent dynamic inversions. In the absence of a complex (fully coupled) mass matrix, coupling through interaction forces becomes the dominant issue in parallel multibody solutions. An implementation which addresses these issues is described and evaluated on two current parallel platforms. The results demonstrate that inexpensive parallel resources can significantly improve the execution time.

Parallelizable block diagonal preconditioners for 3D viscous compressible flow calculations

1993 ◽  
Author(s):  
LAURA DUTTO ◽  
WAGDI HABASHI ◽  
MICHEL FORTIN ◽  
MICHEL ROBICHAUD
Keyword(s):  
Compressible Flow ◽  
Viscous Compressible Flow ◽  
Block Diagonal

Autoencoder-Based Latent Block-Diagonal Representation for Subspace Clustering

2020 ◽  
pp. 1-11
Author(s):  
Yesong Xu ◽  
Shuo Chen ◽  
Jun Li ◽  
Zongyan Han ◽  
Jian Yang
Keyword(s):  
Subspace Clustering ◽  
Diagonal Representation ◽  
Block Diagonal
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