The Reduced Basis Method (RBM) (Rozza et al., Archiv Comput Methods Eng 15:229–275, 2008) generates low-order models for efficient evaluation of parametrized PDEs in many-query and real-time contexts. It can be seen as a parametric model reduction method (Benner et al., SIAM Rev 57(4):483–531, 2015), where greedy selection is combined with a projection space composed of solution snapshots. The approximation quality is certified by using rigorous error estimators. We apply the RBM to systems of Maxwell’s equations arising from electrical circuits. Using microstrip models, the input-output behaviour of the interconnect structures is approximated for a certain frequency range. Typically, an output is given by a linear functional, but in the case of impedance parameters (also called Z-parameters), the output is quadratic. An expanded formulation is used to rewrite the system to compliant form, i.e., a form, where the input and output are identical. This enables fast convergence in the approximation error and thus very low reduced model sizes. A numerical example from the microwave regime shows the advantage of this approach. © Springer International Publishing Switzerland 2016

Output Error Estimates in Reduced Basis Methods for Time-Harmonic Maxwell’s Equations / Hess, Martin Wilfried; Benner, P.. - 112:(2016), pp. 351-358. (Intervento presentato al convegno European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) tenutosi a Middle East Technical University, Ankara, Turkey nel September 14-18, 2015) [10.1007/978-3-319-39929-4].

Output Error Estimates in Reduced Basis Methods for Time-Harmonic Maxwell’s Equations

Hess, Martin Wilfried;
2016-01-01

Abstract

The Reduced Basis Method (RBM) (Rozza et al., Archiv Comput Methods Eng 15:229–275, 2008) generates low-order models for efficient evaluation of parametrized PDEs in many-query and real-time contexts. It can be seen as a parametric model reduction method (Benner et al., SIAM Rev 57(4):483–531, 2015), where greedy selection is combined with a projection space composed of solution snapshots. The approximation quality is certified by using rigorous error estimators. We apply the RBM to systems of Maxwell’s equations arising from electrical circuits. Using microstrip models, the input-output behaviour of the interconnect structures is approximated for a certain frequency range. Typically, an output is given by a linear functional, but in the case of impedance parameters (also called Z-parameters), the output is quadratic. An expanded formulation is used to rewrite the system to compliant form, i.e., a form, where the input and output are identical. This enables fast convergence in the approximation error and thus very low reduced model sizes. A numerical example from the microwave regime shows the advantage of this approach. © Springer International Publishing Switzerland 2016
2016
Numerical Mathematics and Advanced Applications ENUMATH 2015
112
351
358
978-3-319-39927-0
978-3-319-39929-4
https://books.google.it/books?id=I9B5DQAAQBAJ&pg=PR5&lpg=PR5&dq=Numerical+Mathematics+and+Advanced+Applications+ENUMATH+2015&source=bl&ots=GPUh1qNYKH&sig=R_H-WA4ChH9REDMPYmUBQxYTNPc&hl=it&sa=X&ved=0ahUKEwjrht79-oXUAhXKDxoKHaTxATwQ6AEINTAC#v=onepage&q=Numerical%20Mathematics%20and%20Advanced%20Applications%20ENUMATH%202015&f=false
http://link.springer.com/chapter/10.1007/978-3-319-39929-4_33
Springer, Cham
Hess, Martin Wilfried; Benner, P.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/33311
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact