A Priori Model Reduction Method for Thermo-mechanical Simulations

2002 ◽  
Vol 5 (2-3-4) ◽  
pp. 477-491
Author(s):  
David Ryckelynck
Keyword(s):  
Model Reduction ◽  
Reduction Method ◽  
A Priori

scholarly journals Cross-Gramian-based dominant subspaces

2019 ◽  
Vol 45 (5-6) ◽  
pp. 2533-2553 ◽  
Author(s):  
Peter Benner ◽  
Christian Himpe
Keyword(s):  
Model Reduction ◽  
Reduction Method ◽  
A Priori ◽  
Balanced Truncation ◽  
Efficient Computation ◽  
Projection Model ◽  
Numerical Examples ◽  
Error Indicator ◽  
System Properties ◽  
Controllability And Observability

AbstractA standard approach for model reduction of linear input-output systems is balanced truncation, which is based on the controllability and observability properties of the underlying system. The related dominant subspaces projection model reduction method similarly utilizes these system properties, yet instead of balancing, the associated subspaces are directly conjoined. In this work, we extend the dominant subspace approach by computation via the cross Gramian for linear systems, and describe an a-priori error indicator for this method. Furthermore, efficient computation is discussed alongside numerical examples illustrating these findings.

Multidimensional Hyper-Reduction of Large Mechanical Models Involving Internal Variables

2012 ◽  
Author(s):  
David Ryckelynck
Keyword(s):  
Model Reduction ◽  
Reduction Method ◽  
A Priori ◽  
Functional Space ◽  
Weak Form ◽  
Point Of View ◽  
Internal Variables ◽  
Equilibrium Equations ◽  
Mechanical Models ◽  
Reduced Integration Domain

We propose to incorporate a Response Surface (RS) approximation of variables over a parametric domain into a weak form of parametric Partial Differential Equations (PDEs). Hence a multidimensional model-reduction can be achieved. We propose a multidimensional a priori model reduction method to generate or to enrich RSs. It is coined multidimensional because the fields to forecast are defined over an augmented domain in term of dimension. They are functions of both space variables and parameters that simultaneously evolve in time. This changes the functional space related to the weak form of the PDEs and the definition of the reduced bases. It has a significant impact on the proposed model reduction method. In particular, a new point of view on interpolation of variables has to be addressed. A Multidimensional Reduced Integration Domain (MRID) is proposed to reduce the complexity of the reduced formulation. A multidimensional Hyper-Reduction method extract from the MRID truncated equilibrium equations, truncated residuals and a truncated error indicator.

A Model Reduction Method for the Control of Rigid Mechanisms

2006 ◽  
Vol 15 (3) ◽  
pp. 213-227 ◽  
Author(s):  
O. Brüls ◽  
P. Duysinx ◽  
J.-C. Golinval
Keyword(s):  
Model Reduction ◽  
Reduction Method
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