A reduced basis method for microwave semiconductor devices with geometric variations

2014 ◽  
Vol 33 (4) ◽  
pp. 1071-1081 ◽  
Author(s):  
Martin W. Hess ◽  
Peter Benner
Keyword(s):  
Model Reduction ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Semiconductor Devices ◽  
Reduced Basis Method ◽  
Reduced Basis ◽  
Content Type ◽  
Guaranteed Error Bounds ◽  
Basis Method ◽  
Microwave Semiconductor Devices

Purpose – The Reduced Basis Method (RBM) generates low-order models of parametrized PDEs to allow for efficient evaluation of parametrized models in many-query and real-time contexts. The purpose of this paper is to investigate the performance of the RBM in microwave semiconductor devices, governed by Maxwell's equations. Design/methodology/approach – The paper shows the theoretical framework in which the RBM is applied to Maxwell's equations and present numerical results for model reduction under geometry variation. Findings – The RBM reduces model order by a factor of $1,000 and more with guaranteed error bounds. Originality/value – Exponential convergence speed can be observed by numerical experiments, which makes the RBM a suitable method for parametric model reduction (PMOR).

Reduced basis method for Maxwell's equations with resonance phenomena

2015 ◽  
Author(s):  
Martin Hammerschmidt ◽  
Sven Herrmann ◽  
Jan Pomplun ◽  
Lin Zschiedrich ◽  
Sven Burger ◽  
...  
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Reduced Basis Method ◽  
Reduced Basis ◽  
Resonance Phenomena ◽  
Basis Method

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.

Reduced basis method for real-time inverse scatterometry

2011 ◽  
Author(s):  
Jan Pomplun ◽  
Sven Burger ◽  
Lin Zschiedrich ◽  
Frank Schmidt
Keyword(s):  
Real Time ◽  
Reduced Basis Method ◽  
Reduced Basis ◽  
Basis Method
Sign in / Sign up

Export Citation Format

Share Document