Page 366 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 366
TIONAL APPROXIMATION FOR DATA-DRIVEN MODELING AND COMPLEXITY
REDUCTION OF LINEAR AND NONLINEAR DYNAMICAL SYSTEMS (MS-69)
The Loewner Framework: An overview and recent results
Athanasios C. Antoulas, aca@rice.edu
Rice University, United States
In this talk we will present an overview of the Loewner framework for the reduction of dynam-
ical systems both linear and nonlinear. Both time-domain and frequency-domain methods will
be discussed, followed by sevarl numerical examples.
Model order reduction approach for problems with moving discontinuous
features
Harshit Bansal, bansalharshitiit@gmail.com
Department of Mathematics and Computer Science, Eindhoven University of Technology,
Netherlands
Coauthors: Stephan Rave, Laura Iapichino, Wil Schilders, Nathan van de Wouw
The motivation of this work is to enable the usage of multi-phase hydraulic models, such as the
Drift Flux Model (DFM) [1], in developing automation strategies for real-time down-hole pres-
sure management in drilling systems. The DFM is a system of multi-scale non-linear hyperbolic
Partial Differential Equations (PDEs) and its response is dominated by wave propagation char-
acteristics. The central aim of this work is to accurately capture wave-front propagation (and
wave interaction) phenomena (induced by slow or fast transients) in a reduced-order modeling
framework.
Moving discontinuities (shock-fronts) are representative features of the models governed
by hyperbolic PDEs. Such features pose a major hindrance to obtain effective reduced-order
model representations [2]. This motivates us to investigate and propose efficient, advanced, and
automated approaches to obtain reduced models, while still guaranteeing the accurate approxi-
mation of wave propagation phenomena.
We propose a new model order reduction (MOR) approach to obtain an effective reduction
for transport-dominated problems or hyperbolic PDEs. The main ingredient is a novel decom-
position of the solution into a function that tracks the evolving discontinuity and a residual part
that is devoid of shock features. This decomposition ansatz is then combined with Proper Or-
thogonal Decomposition applied to the residual part only to develop an efficient reduced-order
model representation for problems with multiple moving and possibly merging discontinuous
features. Numerical case studies show the potential of the approach in terms of computational
accuracy compared with standard MOR techniques.
References
[1] S. Evje and K. K. Fjelde. Hybrid Flux-Splitting Schemes for a Two-Phase Flow Model.
Journal of Computational Physics, 175(2):674–701, 2002.
[2] M. Ohlberger and S. Rave, Reduced basis methods: Success, limitations and future chal-
lenges, Proceedings of the Conference Algoritmy, 2016.
364
REDUCTION OF LINEAR AND NONLINEAR DYNAMICAL SYSTEMS (MS-69)
The Loewner Framework: An overview and recent results
Athanasios C. Antoulas, aca@rice.edu
Rice University, United States
In this talk we will present an overview of the Loewner framework for the reduction of dynam-
ical systems both linear and nonlinear. Both time-domain and frequency-domain methods will
be discussed, followed by sevarl numerical examples.
Model order reduction approach for problems with moving discontinuous
features
Harshit Bansal, bansalharshitiit@gmail.com
Department of Mathematics and Computer Science, Eindhoven University of Technology,
Netherlands
Coauthors: Stephan Rave, Laura Iapichino, Wil Schilders, Nathan van de Wouw
The motivation of this work is to enable the usage of multi-phase hydraulic models, such as the
Drift Flux Model (DFM) [1], in developing automation strategies for real-time down-hole pres-
sure management in drilling systems. The DFM is a system of multi-scale non-linear hyperbolic
Partial Differential Equations (PDEs) and its response is dominated by wave propagation char-
acteristics. The central aim of this work is to accurately capture wave-front propagation (and
wave interaction) phenomena (induced by slow or fast transients) in a reduced-order modeling
framework.
Moving discontinuities (shock-fronts) are representative features of the models governed
by hyperbolic PDEs. Such features pose a major hindrance to obtain effective reduced-order
model representations [2]. This motivates us to investigate and propose efficient, advanced, and
automated approaches to obtain reduced models, while still guaranteeing the accurate approxi-
mation of wave propagation phenomena.
We propose a new model order reduction (MOR) approach to obtain an effective reduction
for transport-dominated problems or hyperbolic PDEs. The main ingredient is a novel decom-
position of the solution into a function that tracks the evolving discontinuity and a residual part
that is devoid of shock features. This decomposition ansatz is then combined with Proper Or-
thogonal Decomposition applied to the residual part only to develop an efficient reduced-order
model representation for problems with multiple moving and possibly merging discontinuous
features. Numerical case studies show the potential of the approach in terms of computational
accuracy compared with standard MOR techniques.
References
[1] S. Evje and K. K. Fjelde. Hybrid Flux-Splitting Schemes for a Two-Phase Flow Model.
Journal of Computational Physics, 175(2):674–701, 2002.
[2] M. Ohlberger and S. Rave, Reduced basis methods: Success, limitations and future chal-
lenges, Proceedings of the Conference Algoritmy, 2016.
364
