Page 368 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 368
TIONAL APPROXIMATION FOR DATA-DRIVEN MODELING AND COMPLEXITY
REDUCTION OF LINEAR AND NONLINEAR DYNAMICAL SYSTEMS (MS-69)
Physics-based reduced basis methods for CAD in time-harmonic
Maxwell’s equations
Valentin de la Rubia, valentin.delarubia@upm.es
Universidad Politecnica de Madrid, Spain
Coauthor: Alvaro Martin-Cortinas
Electromagnetics today underpins all modern information and communication technologies.
Increasing deployment of telecommunication services is urging RF industry to carry out better
and better electrical designs, where a single device is no longer conceived to perform a single
functionality, but rather multiple tasks at the same time.
Unfortunately, much electrical design activity is still based on brute-force computational
simulations to predict the actual physical behavior of electromagnetic devices. These time-
consuming simulations are repeated, changing the device characteristics until satisfying stricter
specifications of emerging information and communications technologies (5G and IoT).
In our work we use computational electromagnetics as an actual design tool, rather than just
an analysis one. This can be achieved by shriking computational electromagnetics into a simple
parameterized equivalent circuit form, from which an electrical engineer can get actionable
design insights.
Our efforts stand upon model order reduction techniques, such as the reduced-basis method
[1, 2, 3]. However, a new physics-based strategy is carried out to provide further physical
insight of the electromagnetic device under analysis and, ultimately, extremely valuable design
information.
References
[1] V. de la Rubia, U. Razafison and Y. Maday. Reliable fast frequency sweep for microwave
devices via the reduced-basis method. IEEE Trans. Microwave Theory Tech., 57(12), 292–
2937, 2009.
[2] A. Monje-Real and V. de la Rubia. Electric field integral equation fast frequency sweep for
scattering of nonpenetrable objects via the reduced-basis method. IEEE Trans. Antennas
Propag., 68(8), 6232–6244, 2020.
[3] V. de la Rubia and M. Mrozowski. A compact basis for reliable fast frequency sweep
via the reduced-basis method. IEEE Trans. Microwave Theory Tech., 66(10), 4367–4382,
2018.
Numerical aspects of the Koopman and the dynamic mode decomposition
for model reduction
Zlatko Drmacˇ, drmac@math.hr
University of Zagreb, Faculty of Science, Croatia
Coauthors: Ryan Mohr, Igor Mezic´
The Dynamic Mode Decomposition (DMD) is a tool of trade in computational data driven
analysis of complex dynamical systems, e.g. fluid flows, where it can be used to decompose
the flow field into component fluid structures, called DMD modes, that describe the evolution
of the flow. The DMD is deeply connected with the analysis of nonlinear dynamical systems in
366
REDUCTION OF LINEAR AND NONLINEAR DYNAMICAL SYSTEMS (MS-69)
Physics-based reduced basis methods for CAD in time-harmonic
Maxwell’s equations
Valentin de la Rubia, valentin.delarubia@upm.es
Universidad Politecnica de Madrid, Spain
Coauthor: Alvaro Martin-Cortinas
Electromagnetics today underpins all modern information and communication technologies.
Increasing deployment of telecommunication services is urging RF industry to carry out better
and better electrical designs, where a single device is no longer conceived to perform a single
functionality, but rather multiple tasks at the same time.
Unfortunately, much electrical design activity is still based on brute-force computational
simulations to predict the actual physical behavior of electromagnetic devices. These time-
consuming simulations are repeated, changing the device characteristics until satisfying stricter
specifications of emerging information and communications technologies (5G and IoT).
In our work we use computational electromagnetics as an actual design tool, rather than just
an analysis one. This can be achieved by shriking computational electromagnetics into a simple
parameterized equivalent circuit form, from which an electrical engineer can get actionable
design insights.
Our efforts stand upon model order reduction techniques, such as the reduced-basis method
[1, 2, 3]. However, a new physics-based strategy is carried out to provide further physical
insight of the electromagnetic device under analysis and, ultimately, extremely valuable design
information.
References
[1] V. de la Rubia, U. Razafison and Y. Maday. Reliable fast frequency sweep for microwave
devices via the reduced-basis method. IEEE Trans. Microwave Theory Tech., 57(12), 292–
2937, 2009.
[2] A. Monje-Real and V. de la Rubia. Electric field integral equation fast frequency sweep for
scattering of nonpenetrable objects via the reduced-basis method. IEEE Trans. Antennas
Propag., 68(8), 6232–6244, 2020.
[3] V. de la Rubia and M. Mrozowski. A compact basis for reliable fast frequency sweep
via the reduced-basis method. IEEE Trans. Microwave Theory Tech., 66(10), 4367–4382,
2018.
Numerical aspects of the Koopman and the dynamic mode decomposition
for model reduction
Zlatko Drmacˇ, drmac@math.hr
University of Zagreb, Faculty of Science, Croatia
Coauthors: Ryan Mohr, Igor Mezic´
The Dynamic Mode Decomposition (DMD) is a tool of trade in computational data driven
analysis of complex dynamical systems, e.g. fluid flows, where it can be used to decompose
the flow field into component fluid structures, called DMD modes, that describe the evolution
of the flow. The DMD is deeply connected with the analysis of nonlinear dynamical systems in
366
