2020 Springmeeting CANCELLED

Kelbij Star studied Applied Physics at the Delft University of Technology. Her master was mainly focused on transport phenomena and fluid flow. After having worked in the industry for one year, she started a PhD at the University of Ghent under the supervision of professor Degroote in October 2017. The PhD is in collaboration with SCK·CEN, a nuclear research institution in Belgium. She joined the mathLab group of professor Rozza at SISSA in Italy for a research stay during the first half of her second year. Her PhD is about developing reduced order models for fluid dynamics problems.

 Yuan Hou:  obtained  his  BSc  and  MSc  degrees  in  Software  Engineering  from  East  China  Normal  University  in  Shanghai,  China,  in  2014  and  2017  respectively.  Since  October  2017,  he  is  a  PhD  student  in  the  Computational  Mathematics  (CMA)  research  group  at  the  University  of  Antwerp  in  Belgium.  His  research  focuses  on  using state‐of‐art multivariate exponential analysis techniques to tackle challenges in  identified computational science and engineering applications.     

 Kristof Cools:
Low Frequency and Dense Grid Stable Boundary Element Methods for Scattering by Non-Perfectly Conducting Obstacles
For many scattering problems where an electromagnetic wave meets a penetrable target, the internal dynamics can be accurately modelled by enforcing an impedance boundary condition. Examples are the scattering by highly (but not perfectly) conducting objects, the transmission of waves through frequency selective surfaces, and the interaction of waves with layers of graphene. Classic impedance boundary conditions enforce a pointwise proportionality between the electric and magnetic field at the surface of the scatterer. The resulting method unfortunately suffers from numerical instabilities when the frequency tends to zero or when the mesh size is chosen very small. This problems limits our ability to model multi-scale problems. In this contribution, we introduce a novel impedance boundary condition. We will demonstrate that the resulting integral equation methods can be rendered stable in the multi-scale regime and solution times remain bounded.

 Harshit Bansal:
Model order reduction for problems with moving discontinuous features*
Abstract:
The motivation of this work is to enable the use of multi-phase hydraulic models, such as the Drift Flux Model (DFM) [1], in developing automation strategies for real-time down-hole pressure 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 characteristics. 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 or 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 approximation of wave propagation phenomena.
We propose a new model order reduction (MOR) approach to obtain effective reduction for transport-dominated problems or hyperbolic PDEs. The main ingredient is a novel decomposition 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 Orthogonal 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 challenges, Proceedings of the Conference Algoritmy, 2016.
* This is joint work with Stephan Rave (University of Muenster), Laura Iapichino (Eindhoven University of Technology), Wil Schilders (Eindhoven University of Technology) and Nathan van de Wouw (Eindhoven University of Technology and University of Minnesota).

Kelbij Star:
A reduced order model of turbulent buoyant flow of low-Prandtl number fluids
Abstract:
Heat transfer in molten salts and liquid metals, so-called low-Prandtl number fluids, is of interest of many industries, like nuclear and solar. Due to the high thermal diffusivity of these fluids, the influence of buoyancy on the turbulent flow characteristics and heat transfer is large. Therefore, low-Prandtl number fluid flows, and especially their turbulent heat fluxes, require additional or different modeling compared to air or water flows.
Reynolds averaged Navier-Stokes (RANS) simulation is computationally more efficient than the more detailed large eddy simulation and direct numerical simulation and is therefore preferred for this type of turbulent flows. Nevertheless, RANS simulation is often impractical when a large number of simulations need to be performed. This has motivated the development of reduced order models.
My latest work includes the development of a Finite-Volume based POD-Galerkin reduced order modeling strategy for buoyancy-aided turbulent flow. Steady-state simulations are performed of liquid sodium flow over a vertical backward-facing step with a uniform wall heat flux imposed on the wall directly downstream of the step. The reduced order model is tested for different values of the heat flux.
The velocity- and temperature fields predicted by the reduced order model are in good agreement with those computed by the RANS simulations, while the computational cost is reduced by a factor of the order O(105).

Yuan Hou:
Exponential analysis in Inverse Synthetic Aperture Radar (ISAR)
Abstract:
Inverse  synthetic  aperture  radar  (ISAR)  imaging  is  a  system  consisting  of  a  real‐aperture radar, emitting a sequence of high frequency bursts, tracking a moving  target in the far field of the radar. When the target is hit by an electromagnetic wave,  a  limited  number  of  locations  on  the  object,  such  as  edges  and  surface  discontinuities,  scatter  the  energy  back  toward  the  observation  point.  The  locations  of these concentrated sources of scattering energy are called scattering centers, each  of  which  can  be  described  by  a  multivariate  complex  exponential.  ISAR  plays  an  important  role  in  target  identification,  commercial  aircraft  classification,  military  surveillance and the like.    Based on the latest development in exponential analysis, we present a new method  that  can  extract  high  resolution  information  from  noisy  ISAR  data.  In  comparison  to  other methods, our method offers a range of advantages. The method neither suffers  the curse of dimensionality nor requires a prior estimate on the number of scattering  centers.  It  can  work  with  sub‐Nyquist  sampled  data  and  offers  a  validation  step,  which  is  very  useful  in  low  SNR  conditions.  A  favourable  computation  cost  results  from  the  fact  that  several  independent  smaller  systems  are  solved  instead  of  one  large system incorporating all measurements simultaneously.   

 Lars Corbijn van Willemswaard
A Discontinuous Galerkin discretization for the periodic Maxwell eigenvalue problem
Abstract:
Photonic crystal are nanostructures where the optical properties periodically vary on same size as the wave length. These crystals can by careful design exhibit a bandgap, a range of frequency where light propagation is forbidden. By intentional deviation from such a design one can control the propagation of the light and slow it down or let it hop between points. The design of these crystals requires the prediction of these effects by numerical means, which requires solving a Maxwell eigenvalue problem on a periodic domain.
The sharp material interfaces in photonic crystals can lead to solutions with discontinuities in the solution across these interfaces. The Discontinuous Galerkin method can naturally handle such discontinuities and is therefore a suitable choice for such problem. In this talk we will present the latest progress on our Discontinous Galerkin solver for analysing the properties of photonic crystals.

 Jeremias Garay
Determining the quality of 4D flow MRI
Abstract:
3D time resolved Phase-Contrast MRI or 4D flow is gaining space into clinical practice for measuring blood flow velocity in large vessels. Due to the long acquisition times, 4D flow is susceptible to several image artifacts due to noise and aliasing, respiration, large accelerations and turbulence. However, to the authors best knowledge, there is no mean to quantitatively and locally assess the quality of the data which may help in interpreting the quality of the results.The purpose of this work is to develop a metric to determine the quality of 4D flow MRI in view on how the measurements fulfill the Navier-Stokes equations.

 Marieke Kootte
Solving the power flow problem on integrated networks
Abstract:
Power flow simulations form an essential tool for electricity network analysis but conventional power flow solvers are designed to work on a separated transmission or distribution networks only. The continuing growth of electricity consumption, demand side participation, and renewable resources makes the electricity networks co-dependent. Integrated models incorporate the coupling of the networks and interaction that they have on each other, representing the power flow within this changing environment accurately.
During this talk I will compare several numerical methods that are available to solve the power flow problem on integrated network models. I reviewed and assessed these methods by running simulations on small test networks and comparing the outcome on accuracy, computational time, and convergence.

Koen Ruymbeek:
Tensor-Krylov method for parametrized eigenvalue problems
Abstract:
In applications of linear algebra, there is a need to deal with uncertainty in the matrices. We focus on matrices that depend on a set of parameters. In this talk, we want to calculate a particular eigenvalue for a large set of parameter samples. As eigenvalues and corresponding eigenvectors of neighboring parameter values are close to each other, one can use the common information to speed up the computations. In this talk we extend Krylov methods to the case the matrices depend on parameters. We discuss the convergence of the method and give numerical examples where the matrices are taken from applications in time-delay systems and PDEs.

Matthias Schlottbom:
On classical numerical methods for radiative transfer in a unified variational framework.
Abstract:
High-frequency electromagnetic radiation is at the heart of several high-tech applications, including medical imaging, tumor treatment, gas and oil reservoir exploration, climate simulations, and in the energy efficient generation of white light. The extremely high complexity of the scattering media in terms of number, geometry and position of scattering objects does not allow to directly simulate Maxwell’s equations in such applications. Instead, the radiative transfer equation (RTE) has been established as a sound physical model by a rigorous derivation from Maxwell’s equations, and important physical observables, such as the electromagnetic energy, can be recovered from the solution of the RTE.
Due to the wide range of applications for the RTE, several techniques for its numerical solution have been developed, and many techniques that are nowadays well-established in various fields can originally be associated to the RTE, such as the Monte-Carlo method or discontinuous Galerkin methods. In this talk we review classical deterministic approximations of the RTE, including truncated spherical harmonics approximations and discrete ordinates methods, and give an interpretation in a unified variational framework. We also briefly discuss the efficient numerical solution by iterative methods.