scholarly journals Low-Frequency Model-Order Reduction of Electromagnetic Fields Without Matrix Factorization

2004 ◽  
Vol 52 (9) ◽  
pp. 2298-2304 ◽  
Author(s):  
R.F. Remis
Keyword(s):  
Electromagnetic Fields ◽  
Matrix Factorization ◽  
Model Order Reduction ◽  
Low Frequency ◽  
Order Reduction ◽  
Frequency Model ◽  
Model Order

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 Design of Low Frequency Suitable Fractional Order Differintegrators

2019 ◽  
Vol 8 (2) ◽  
pp. 3251-3255
Keyword(s):  
Fractional Order ◽  
Model Order Reduction ◽  
Continued Fraction ◽  
Low Frequency ◽  
Order Reduction ◽  
The Novel ◽  
Continued Fraction Expansion ◽  
Reduction Procedure ◽  
Model Order ◽  
First Order

Design of low frequency applicable fractional order digital differentiators and integrators using direct discretization is the main objective of this paper. Model order reduction procedure is used to obtain the novel first order s-to-z transform. Continued fraction expansion (CFE) technique is used to discretize that transform. The design of one-half digital differintegrators based on proposed transforms will be compared with the well known existing first order transforms namely, Bilinear and Al-Alaoui transforms. The efficacy of the designed methods presented interms of normalized magnitude error (NME). The designed fractional order digital filter coefficients are tabulated and all simulation results are carried out by using MATLAB software.

THE NEW ALGORITHM OF SOLVING HARMONIC BALANCE EQUATIONS

2019 ◽  
Author(s):  
Vladimir Lantsov ◽  
A. Papulina
Keyword(s):  
Harmonic Balance ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Balance Equations ◽  
Model Order ◽  
Cad Systems ◽  
Computational Costs ◽  
Reduction Methods ◽  
Model Equations

The new algorithm of solving harmonic balance equations which used in electronic CAD systems is presented. The new algorithm is based on implementation to harmonic balance equations the ideas of model order reduction methods. This algorithm allows significantly reduce the size of memory for storing of model equations and reduce of computational costs.

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