2021 Spring Meeting

An online presentation at the 2021 Spring meeting

Friday May 28th, 2021, the Dutch-Flemish Scientific Computing Society organized its annual spring meeting, together with the Technical University in Delft the Netherlands. Last years meeting was cancelled but this years meeting was a fully online version because the situation around COVID-19 had not really changed. A mix of young and senior researcher were invited to present their research, among them the poster winners of the 2019 Woudschoten meeting.

Participation was free of charge and the participants received a zoom link after registration. This year we had 58 participants.

Organization

The spring meeting is organized yearly by the Dutch-Flemish Scientific Computing Society (SCS), this year in cooperation with Technical University Delft.

Organizing comittee: Prof.dr.ir. Kees Vuik (TUD, ) Martine Anholt (CWI, Secretary SCS).

Support for this meeting has been obtained from Centrum Wiskunde & Informatica (CWI) and Technical University Delft. The Scientific Computing Society is very grateful for that support.


Program 2021

09:15-09:30 Log in via Zoom
                    Host: Kees Vuik from TU Delft

09:30-10:10 Kristof Cools (TU Delft)

10:10-10:35 Marieke Kootte (TU Delft)

10:35-11:00 Yuan Hou (University of Antwerp)

11:00-11:10 Break

11:10-11:35 Kelbij Star (Ghent University/SCK CEN)

11:35-12:00 Harshit Bansal (TU Eindhoven)

12:00-13:00 Break

13:00-13:25 Nick Luiken (University of Utrecht)

13:25-13:50 Jorge Aguayo (RUG University of Groningen)

13:50-14:00 Break

14:00-14:25 Pieter Appeltans (KU Leuven)

14:25-15:05 Matthias Schlottbom (University of Twente)

15:05-15:15 Closure

 

Speakers Spring meeting SCS 2021

Kristof Cools: In 2018, Dr. Cools joined the Department of Industrial and Applied Mathematics at TU Delft. His research interests include the spectral properties of the boundary integral operators of electromagnetics, stable and accurate discretization schemes for frequency and time domain boundary element methods, domain decomposition techniques, and on the implementations of algorithms from computational physics for high-performance computing.
Marieke Kootte: received her B.Sc. degree in civil engineering in 2014 at Delft University of Technology, The Netherlands. She then obtained her double degree in applied mathematics at Delft University of Technology and KTH Stockholm, Sweden, in 2017.
Currently she is pursuing her Ph.D. degree at the Numerical Analysis research group of the Delft Institute of Applied Mathematics, Delft University of Technology. Her topic focuses mainly on fast and robust power flow solvers for integrated transmission-distribution networks and partly on defining optimal bid strategies for different electricity markets.
Yuan Hou:

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.

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 Ghent University under the supervision of professor Degroote in October 2017. The PhD about developing reduced order models for fluid dynamics problems is in collaboration with SCK CEN, a nuclear research institution in Belgium. She joined SISSA’s mathLab group in Italy for a research stay during the first half of her second year. In addition, she visited the Scientific Computing group at CWI for a three-month internship program in her third year of the PhD.
Kelbij obtained her PhD in February and will start an advisory/research position in the Netherlands from May 1st 2021.
Harshit Bansal pursued the dual-degree program in Mechanical Engineering at the Indian Institute of Technology, Kharagpur, India. He obtained Bachelor of Technology (Honors) in Mechanical Engineering and Master of Technology in Mechanical Engineering with specialization in Mechanical Systems Design in 2016. After finishing his masters, he started his PhD in September 2016 (under the guidance of Prof. dr. Wil Schilders, Prof. dr. ir. Nathan van de Wouw and Dr. Laura Iapichino) in the Centre for Analysis, Scientific Computing and Applications (CASA) at the Department of Mathematics and Computer Science, Eindhoven University of Technology (TU/e), The Netherlands. He carried out his Ph.D. under the aegis of Shell-NWO/FOM Programme in Computational Sciences for Energy Research, where in the main focus was to develop structure-preserving model order reduction techniques in the scope of drilling automation. He defended his Ph.D. thesis in October 2020 and is currently affiliated as a guest researcher at CASA, Department of Mathematics and Computer Science, TU/e, and mainly focusing on structure-preserving numerics with a drive towards hardware-aware aspects. His research interests include port-Hamiltonian modelling, structure-preserving discretization, and model order reduction of distributed parameter systems (including transport-dominated problems), high-performance computing, hardware-aware numerics, and multiphase flow dynamics.

Nick Luiken studied Applied Mathematics at the University of Twente. During his master he focused on inverse problems. After obtaining his degree, he started as a PhD student at Utrecht University under supervision of Dr. Tristan van Leeuwen and Dr. Eric Verschuur of Delft University of Technology. His research focuses on developing fast algorithms for inverse problems. In the fall of 2021 he will start as a Postdoc at the King Abdullah University of Science and Technology.

Jorge Aguayo Jorge Aguayo received his B.Sc Dregree in Mathematical Engineering in 2014 in University professional title of Matematical Engineer in 2016, both in University of Concepción, Chile. Since 2018, he is studying in the Ph.D. Applied Mathematics double degree program of the University of Chile and University of Groningen, The Netherlands. His research interests including Numerical Analysis of PDE, Inverse Problems and applications to Biomedicine.
Pieter Appeltans
Matthias Schlottbom Matthias Schlottbom obtained a PhD in mathematics (Dr. rer. nat.) at the RWTH Aachen in 2011.
After that he was PostDoc at the technical universities in Munich and Darmstadt and at the WWU Münster. In 2016 he joined the Department of Applied Mathematics at the University of Twente where he is an Associate Professor now. His research focuses on the development and analysis of numerical methods for partial differential equations and inverse problems. Areas of applications range from medical imaging and biology to photonic crystals.

 

2021 Abstracts

Kristof Cools:

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.

Marieke Kootte:

Numerical Assessment of Integrated Transmission-Distribution Electricity Networks

Integrated electricity network models are necessary to represent the power flow within modern electricity systems accurately. Conventional models are designed to work on separated transmission and distribution networks only, but 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 model the influence that the networks have on each other.

In this talk, we share several methods to create integrated network models. Furthermore, we compare and assess the numerical performance of the methods, which are convergence rate and CPU-time, on several test networks ranging from 50 to 25000 unknowns. We show the effect of the amount of imbalance at distribution level on transmission networks, that is evoked by highly variable resources and loads installed along the distribution network.

Yuan Hou:

Applications and analysis of exponential models

Based on the latest development in exponential analysis, we present a new method that can extract high resolution information from noisy 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 of the number of spectral peaks. 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.

We apply the proposed method to real world applications. In imaging, we explore the method for texture classification and defect detection. In 3-dimensional space, we extract the location information of scattering centers from inverse synthetic aperture radar (ISAR) noisy data.

Kelbij Star:

Reduced order modeling for computational fluid dynamics problems with parametric boundary conditions

Complex fluid dynamics problems are usually solved numerically using discretization methods such as the finite volume method. Boundary conditions are essential for defining these numerical problems. However, boundary condition values can be uncertain if they come from measurements and/or they depend on certain parameters. In that case, the sensitivity to the boundary conditions needs to be analyzed. Currently, computational fluid dynamics simulations are often unfeasible for applications requiring testing of a large number of different system configurations, such as for sensitivity analysis. This has stimulated the development of modeling techniques that reduce the number of degrees of freedom of the high fidelity fluid flow models. Mathematical techniques are used to extract “features” of the high fidelity model and to replace the latter by a model with a lower number of degrees of freedom. In that way, the required computational time and computer memory usage is reduced. In this talk, I will present and discuss some reduced order modeling methods that I have developed for incompressible flows. In addition, I will focus on the challenge of imposing parametric boundary conditions at the reduced order level.

Harshit Bansal:

Towards mixed-precision, fast and accurate, structure-preserving numerics

Floating-point errors are the characteristic feature of floating-point computations. With petascale and exascale computing systems becoming a reality, floating-point errors can become a serious concern for computational scientists. The problem of the cumulative effect of floating-point errors in a very large number of arithmetical calculations has been rigorously addressed in [1], a bible book by James Wilkinson, and has appeared in several papers since then. Despite some continued efforts, the role/effect of floating-point errors on the numerical solution of practical high-dimensional problems of interest has become a somewhat neglected practice nowadays.

Furthermore, until recently, most of the computing platforms employed single or double-precision arithmetic for floating-point computations. With the evolution of computing hardware, half-precision arithmetical calculations can now be performed. It is also well-known that some mathematical problems, for instance, computation of eigenpairs of a standardized or a generalized eigenvalue problem, maybe ill-conditional at a lower precision and, hence, one may need to employ higher precision, e.g., quadruple precision, for accurate computations. On the one hand, the floating-point operations at lower precision are attractive since they are fast and require less computational resources, but these may be inaccurate. On the other hand, the computations at higher precision are attractive because of their accuracy, but these are slow and require extensive computational resources. In view of obtaining both fast and accurate scientific results, it is worthwhile to develop computational frameworks that employ mixed-precision computations.

With these aspects in mind, in this talk, I will put the need of controlling floating-point errors during numerical computations into perspective by showcasing the numerical results in the context of (port-Hamiltonian-based) structure-preserving discretization of multi-phase flow models and eigenvalue computation of large-scale assembled skew-symmetric matrices. Subsequently, in the scope of the aforementioned numerical examples, I will delve into the floating-point error analysis and present a (block-structured) mixed-precision framework, including related numerical results.

[1] J. H. Wilkinson, Rounding Errors in Algebraic Processes, Courier Corporation, Jan. 1994.(This is joint work with Prof. Wil Schilders)

Nick Luiken:

We consider regularized linear least-squares problems with a sparsity promoting regularizer, of the form minx ½||Ax – b||22 + l||Lx||1. Recently, Zheng et al. [1] proposed an algorithm called Sparse Relaxed Regularized Regression (SR3) that employs a splitting strategy by introducing an auxiliary variable y and solves minx,y ½ ∥Ax − b∥22 + k/2∥Lx − y∥22 + R(y). By minimizing out the variable x we obtain an equivalent system miny ½ ∥Fκy−gκ∥22+R(y). In our work we view the SR3 method as a way to approximately solve the regularized problem. We analyze the conditioning of the relaxed problem in general and give an expression for the SVD of Fκ as a function of κ. Furthermore, we relate the Pareto curve of the original problem to the relaxed problem and we quantify the error incurred by relaxation in terms of κ. Finally, we propose an efficient iterative method for solving the relaxed problem with inexact inner iterations. Numerical examples illustrate the approach.

[1] P. Zheng, T. Askham, S. L. Brunton, J. N. Kutz, and A. Y. Aravkin, A Unified Framework for Sparse Relaxed Regularized Regression: SR3, IEEE Access, 7 (2019), pp. 1404–1423,

Jorge Aguayo:

An inverse problem in Fluid Mechanics applied in Biomedicine

One of the main causes of problems in the human cardiovascular system is malformations in the aortic valve. There exists exploratory techniques to verify the status of an aortic valve, but these procedures are invasive or are not able to detect valve geometry. The aim is to define and study an inverse problem such that, based on measurements of the velocity field of the blood passing through a valve, an estimate of the valve geometry is given in response. Although it is possible to consider this problem as one of obstacle shape optimization, the disadvantage of this technique would be the need of modifying the discretization of the domain at every iteration of the identification procedure. In contrast, the proposed distributed resistance term here allows us to work in a fixed domain to solve the valve shape identification problem adding a penalization term.
This research includes a justification for using fictitious domains to study obstacles immersed in incompressible viscous fluids through a simplified version of Brinkham’s law in porous media applied in Navier-Stokes equations, the formulation and analysis of an identification of parameters problem associated to this inverse problem and numerical experiments in FEniCS and dolfin-adjoint illustrating the applicability of this method.
 

Pieter Appeltans

A structure preserving Arnoldi method for Hamiltonian eigenvalue problems with delays

Hamiltonian eigenvalue problems have a much richer structure than traditional (delay) eigenvalue problems, such as symmetry with respect to both the real and imaginary axis. These Hamiltonian eigenvalue problems arise in several control problems, such as the computation of the H-infinity norm of input-output systems. For these applications, it is often important that certain properties of the Hamiltonian eigenvalue problem, such as eigenvalues on the imaginary axis, are preserved in the numerical method for solving them. On the other hand, for large scale eigenvalue problems one often has to resort to iterative methods such as the Arnoldi method, that allow to compute a small number of eigenvalues around a given target. For traditional, finite dimensional Hamiltonian eigenvalue problems, the structure preserving shift-invert Arnoldi method allows to address both these aspects. A special shift-invert transformation makes sure that the Hamiltonian structure is preserved, while a slightly modified Arnoldi iteration makes the method applicable to large eigenvalue problems. This talk will discuss the generalization of the structure preserving shift-invert Arnoldi method from finite dimensional Hamiltonian eigenvalue problems to characteristic functions that contain delay terms.

Matthias Schlottbom

We study the efficient numerical solution of linear inverse problems with operator valued data which arise, e.g., in seismic exploration, inverse scattering, or tomographic imaging. The high-dimensionality of the data space implies extremely high computational cost already for the evaluation of the forward operator, which makes a numerical solution of the inverse problem, e.g., by iterative regularization methods, practically infeasible. To overcome this obstacle, we develop a novel model reduction approach that takes advantage of the underlying tensor product structure of the problem and which allows to obtain low-dimensional certified reduced order models of quasi-optimal rank. A complete analysis of the proposed model reduction approach is given in a functional analytic setting and the efficient numerical construction of the reduced order models as well as of their application for the numerical solution of the inverse problem is discussed. In summary, the setup of a low-rank approximation can be achieved in an offline stage at essentially the same cost as a single evaluation of the forward operator, while the actual solution of the inverse problem in the online phase can be done with extremely high efficiency. The theoretical results are illustrated by application to a typical model problem in fluorescence optical tomography.