scholarly journals Solving Parameter-Dependent Lyapunov Equations Using the Reduced Basis Method with Application to Parametric Model Order Reduction

2017 ◽  
Vol 38 (2) ◽  
pp. 478-504 ◽  
Author(s):  
Nguyen Thanh Son ◽  
Tatjana Stykel
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Parametric Model ◽  
Reduced Basis Method ◽  
Lyapunov Equations ◽  
Reduced Basis ◽  
Model Order ◽  
Parametric Model Order Reduction ◽  
Basis Method ◽  
Parameter Dependent

scholarly journals Localized Reduced Basis Methods for Time Harmonic Maxwell’s Equations

2018 ◽  
Author(s):  
Andreas Buhr ◽  
Mario Ohlberger ◽  
Stephan Rave
Keyword(s):  
Electromagnetic Fields ◽  
Model Order Reduction ◽  
Maxwell's Equations ◽  
Order Reduction ◽  
Reduced Basis Method ◽  
Galerkin Projection ◽  
Reduced Basis ◽  
Model Order ◽  
Time Harmonic ◽  
Basis Method

Localized model order reduction methods have attracted significant attention during the last years. They have favorable parallelization properties and promise to perform well on cloud architectures, which become more and more commonplace. We introduced ArbiLoMod, a localized reduced basis method targeted at the important use case of changing problem definition, wherein the changes are of local nature. This is a common situation in simulation software used by engineers optimizing a CAD model. An especially interesting application is the simulation of electromagnetic fields in printed circuit boards, which is necessary to design high frequency electronics. The simulation of the electromagnetic fields can be done by solving the time-harmonic Maxwell’s equations, which results in a parameterized, inf-sup stable problem which has to be solved for many parameters. In this multi-query setting, the reduced basis method can perform well. Experiments have shown two dimensional time-harmonic Maxwell’s to be amenable to localized model reduction. However, Galerkin projection of an inf-sup stable problem is not guaranteed to be stable. Existing stabilization methods for the reduced basis method involve global computations and are thus not applicable in a localized setting. Replacing the Galerkin projection with the minimization of a localized a posteriori error estimator provides a stable reduction for inf-sup stable projects which retains all the advantageous properties of localized model order reduction. It allows for an offline-online decomposition and requires no global computations in the unreduced space.

scholarly journals A Local Basis Approximation Approach for Nonlinear Parametric Model Order Reduction Paper Draft

2021 ◽  
pp. 116055
Author(s):  
Konstantinos Vlachas ◽  
Konstantinos Tatsis ◽  
Konstantinos Agathos ◽  
Adam R. Brink ◽  
Eleni Chatzi
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Parametric Model ◽  
Model Order ◽  
Approximation Approach ◽  
Parametric Model Order Reduction ◽  
Local Basis
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