Low-Dimensional Approximations of Multiscale Epitaxial Growth Models for Microstructure Control of Materials

2000 ◽  
Vol 160 (2) ◽  
pp. 564-576 ◽  
Author(s):  
S. Raimondeau ◽  
D.G. Vlachos
Keyword(s):  
Epitaxial Growth ◽  
Growth Models ◽  
Microstructure Control ◽  
Low Dimensional Approximations ◽  
Low Dimensional

Low-Dimensional Approximation for Control of Spatio-Temporal Processes Using Principal Interaction Patterns

2012 ◽  
Vol 591-593 ◽  
pp. 1217-1220
Author(s):  
Xiang Ping Cao ◽  
Zhao Yang Li ◽  
Mei Xing Liu
Keyword(s):  
Galerkin Approximation ◽  
Basis Functions ◽  
Interaction Patterns ◽  
Infinite Dimensional ◽  
Dynamical Behaviors ◽  
Dimensional Approximation ◽  
Spatio Temporal ◽  
Low Dimensional Approximations ◽  
Low Dimensional ◽  
Advanced Model

Although the first-principal models of the spatio-temporal processes can accurately predict nonlinear and distributed dynamical behaviors, their infinite-dimensional nature does not allow their directly use. In this note, low-dimensional approximations for control of spatio-temporal processes using principal interaction patterns are constructed. Advanced model reduction approach based on spatial basis function expansion together with Galerkin method is used to obtain the low-dimensional approximation. Spatial structure called principal interaction patterns are extracted from the system according to a variational principle and used as basis functions in a Galerkin approximation. The simulations of the burgers equations has illustrated that low-dimensional approximation based on principal interaction patterns for spatio-temporal processes has smaller errors than more conventional approaches using Fourier modes or Empirical Eigenfunctions as basis functions.

scholarly journals Global well-posedness and regularity criteria for epitaxial growth models

2017 ◽  
Vol 74 (3) ◽  
pp. 459-465 ◽  
Author(s):  
Jishan Fan ◽  
Ahmed Alsaedi ◽  
Tasawar Hayat ◽  
Yong Zhou
Keyword(s):  
Epitaxial Growth ◽  
Growth Models ◽  
Regularity Criteria ◽  
Well Posedness

Model Reduction by Proper Orthogonal Decomposition Coupled With Centroidal Voronoi Tessellations (Keynote)

2002 ◽  
Author(s):  
Qiang Du ◽  
Max Gunzburger
Keyword(s):  
Complex Systems ◽  
Model Reduction ◽  
Turbulent Flows ◽  
Implementation Strategies ◽  
Practical Implementation ◽  
Voronoi Tessellations ◽  
Centroidal Voronoi Tessellations ◽  
Low Dimensional Approximations ◽  
Low Dimensional ◽  
Proper Orthogonal

Proper orthogonal decompositions (POD) have been used to define reduced bases for low-dimensional approximations of complex systems, including turbulent flows. Centroidal Voronoi tessellations (CVT) have been used in a variety of data compression and clustering settings. We review both strategies in the context of model reduction for complex systems and propose combining the ideas of CVT and POD into a hybrid method that inherets favorable characteristics from both its parents. The usefulness of such an approach and various practical implementation strategies are discussed.

scholarly journals Low-Dimensional Approximations of High-Dimensional Asset Price Models

2021 ◽  
Vol 12 (1) ◽  
pp. 1-28
Author(s):  
Martin Redmann ◽  
Christian Bayer ◽  
Pawan Goyal
Keyword(s):  
Asset Price ◽  
High Dimensional ◽  
Low Dimensional Approximations ◽  
Low Dimensional
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