Research Topics

Numerical Simulation

A central topic in our research is the development of iterative solvers for sparse linear systems that arise after discretisation of stationary and time-dependent partial differential equations. These solvers are based on preconditioned Krylov subspace iteration, geometric and algebraic multigrid, and domain decomposition.

We also study matrix compression algorithms and solvers for large, dense systems that result from the discretization of integral equations. Here, we focus on oscillatory problems. Part of this research is theoretical and deals with such issues as convergence, complexity and robustness. Another part of this work is highly practical and involves software development and real-life engineering applications.

We are engaged in research projects with other groups, that specialize in such areas as electromagnetics, materials science, acoustics, and bio-engineering.

 

People

• Stefan Vandewalle
• Eveline Rosseel
• Daan Huybrechs
• Sam Corveleyn
• Nico Scheerlinck
• Hendrik Speleers
• Andreas Asheim

Collaboration

• Department of Metallurgy and Materials Engineering, Research team Chemical and Extractive Metallurgy (B. Blanpain)
• Department of Mechanical Engineering, Division of Production engineering, Machine design and Automation (D. Vandepitte)
• Department of Biosystems, Division MeBios (B. Nicolai)
• Center for Plasma-Astrophysics (S. Poedts)
• Subfaculty of Sciences Campus Kortrijk, Research Group Electromagnetic Field Computations (H. De Gersem)

Key publications

• Boonen, T., Van lent, J., Vandewalle, S. (2008). Local Fourier analysis of multigrid for the curl-curl equation. SIAM Journal on Scientific Computing, 30(4), 1730-1755.
• Rosseel, E., Boonen, T., Vandewalle, S. (2008). Algebraic multigrid for stationary and time-dependent partial differential equations with stochastic coefficients. Numerical linear algebra with applications, 15(2-3), 141-163.
• Vanherpe, L., Moelans, N., Blanpain, B., Vandewalle, S. (2007). Bounding box algorithm for three-dimensional phase field simulations of microstructural evolution in polycrystalline materials. Physical Review E, 76(5), 056702-1-056702-11.
• Huybrechs, D., Vandewalle, S. (2007). A sparse discretization for integral equation formulations of high frequency scattering problems. SIAM Journal on Scientific Computing, 29(6), 2305-2328.

Analysis, Control and Optimization of Large-Scale Systems

As in advanced control systems' design computationally aspects move more and more to the forefront, the research focus is shifting towards an integrated approach unifying state-of-the-art research in numerical simulation, numerical optimization, as well as systems and control. This observation motivates this research theme on numerical methods for analysis, control and optimization of large-scale systems. The focus lies on systems described by delay differential equations and partial differential equations. The analysis problems include numerical stability analysis, computation and characterization of stability regions and robustness measures. The corresponding controller synthesis problems include stabilization, the optimization of robustness measures, and optimal control. Special attention is paid to the design of fixed structure controllers for infinite-dimensional systems, which gives rise to large-scale eigenvalue optimization problems. The group also works on PDE constrained optimization and on solving large-scale matrix equations in systems and control, for which efficient approaches have been developed based on solving optimization problems over matrix manifolds.

The developed theoretical results, numerical tools and software are applied to various problems from engineering and the life sciences, in close collaboration with application oriented groups.

 

People

• Dirk Abbeloos
• Zhen Wu
• Suat Gumussoy
• Elias Jarlebring
• Wim Michiels
• Stefan Vandewalle

Collaboration

• M. Diehl, ESAT-SCD, K.U.Leuven
• S.-I. Niculescu, LSS-Supelec
• T. Vyhlidal, P. Zitek, Czech Technical University in Prague
• E.I. Verriest, Georgia Institute of Technology
• E. Fridman, Tel Aviv University
• H. Huijberts, Queen Mary, University of London
• H. Nijmeijer, Eindhoven University of Technology

Key publications

• W. Michiels and S.-I. Niculescu, Stability and stabilization of time-delay systems. An eigenvalue based approach, vol. 12 of Advances in Design and Control, SIAM Publications, Philadelphia, 2007.
• J. Vanbiervliet, K. Verheyden, W. Michiels and S. Vandewalle, A nonsmooth optimization approach for the stabilization of time-delay systems, ESIAM: Control, Optimisation and Calcalus of Variations, Vol.14, No.3, 2009, pp.478-493.
• W. Michiels, T. Vhylidal, H. Huijberts and H. Nijmeijer, Stabilizability and stability robustness of state derivative feedback controllers, SIAM Journal on Control and Optimization. Vol.47, No.6, 2009, pp. 3100-3117.
• J. Vanbiervliet, B. Vandereycken, W. Michiels, S. Vandewalle and M. Diehl, The smoothed spectral abscissa for robust stability optimization, SIAM Journal on Optimization, 2009, accepted. See also Technical Report TW 505.

Multiscale Methods

To accurately describe and/or simulate macroscopically observable physical phenomena one often needs to take into account processes acting on a much finer scale, the microscopic scale. Modeling the microscopic scale can be done with techniques such as molecular dynamics, particle dynamics, Monte Carlo simulation, lattice Boltzmann methods, and many others. These modeling techniques cannot be used to perform simulations over macroscopic domains since this would be computationally too expensive. Therefore one often makes simplifying assumptions and derives an evolution law for the system on the macroscopic scale. Multiscale methods avoid these ad hoc assumptions by coupling a macroscopic simulation technique with a microscopic model. The unavailable macroscopic data is estimated from short microscopic simulations, resulting in accurate and (relatively) efficient simulations.

Our group has been working on a general framework for this kind of multiscale coupling called equation-free methods. We also collaborate with other research groups to apply these techniques on more complex and realistic problems, such as molecular dynamics simulations, deformation of heterogeneous materials and also permeability of textiles.

 

People

• Giovanni Samaey
• Jerzy Gawad
• Yaidel Reyes Lopez
• Kasra Mohaghegh
• Giacomo Mazzi
• Dirk Roose

Collaboration

• Wim Vanroose, Dept. Wiskunde en Informatica, U. Antwerpen
• Mathias Rousset and Pauline Lafitte, team SIMPAF, INRIA, Lille
• Vincent Legat, CESAME, U.C. Louvain
• B. Tijskens, P. Van Liedekerke, H. Ramon, MeBioS, K.U.Leuven
• P. Van Houtte, S. V. Lomov, N. Moelans, MTM, K.U.Leuven
• M. Griebel, INS, Bonn
• Y. Kevrekidis and C.W. Gear, Princeton University
• Tony Lelievre, CERMICS, ENPC, Paris

Key publications

• P. Van Leemput, W. Vanroose and D. Roose, Mesoscale analysis of the equation-free constrained runs initialization scheme. (SIAM) Multiscale Modeling and Simulation 6 (4), p. 1234-1255, December 2007. Article on the SIAM MMS website. See also Technical Report TW 444, entitled: Initialization of a lattice Boltzmann model with constrained runs.
• P. Ghysels, G. Samaey, B. Tijskens, P. Van Liedekerke, H. Ramon and D. Roose. Multi-scale simulation of plant tissue deformation using a model for individual cell mechanics. Submitted to Physical Biology. See also Technical Report TW 522, entitled: Multi-scale computation of plant tissue deformation using models for individual cell behaviour
• G. Samaey, D. Roose, and I.G. Kevrekidis. The gap-tooth scheme for homogenization problems. SIAM Multiscale Modeling and Simulation, 4(1):278-306, 2005.
• I. G. Kevrekidis and G. Samaey, Equation-free multiscale computation: algorithms and applications, Annual Review in Physical Chemistry 60 (2009), 321-344.

High Performance Computing

The research group has experience in the development of large-scale parallel simulation codes, which run efficiently on modern supercomputers, such as the recently acquired university-wide HPC cluster. The group has contributed extensively to the development of dynamic load-balancing algorithms for distributed memory parallel computers. The dynamic grid repartitioning software library for finite element applications is integrated in industrial software packages.

 

 

People

• Stefan Vandewalle
• Dirk Roose
• Bart Verleye

Collaboration

• S. Poedts, Center for Plasma-Astrophysics, K.U.Leuven

Key publications

• Kimpe, D., Ross, R., Vandewalle, S., Poedts, S. (2007). Transparant log-based data storage in MPI-IO applications. Lecture notes in computer science, 4757, 233-241.
• Gander, M., Vandewalle, S. (2007). Analysis of the parareal time-parallel time-integration method. SIAM journal on scientific computing, 29(2), 556-578.
• B. Maerten, D. Roose, A. Basermann, J. Fingberg, and G. Lonsdale, DRAMA: A library for parallel dynamic load balancing of finite element applications, Euro-Par'99 Parallel Processing (Amestoy, P., ed.), vol 1685, Lecture Notes in Computer Science, pp. 313-316, 1999

Dynamical Systems

Physical systems usually depend on one or more parameters. When these parameters are varied, qualitative changes may occur in the behavior of the system. Mathematically, these changes are called bifurcation phenomena; they are typically associated with a change in the stability of the physical system. Examples are the onset of periodic oscillations (e.g. flutter of an airfoil), spatiotemporal pattern formation (e.g. flame fronts in combustion processes) and chaotic behavior (e.g. turbulence). The research group develops numerical methods for the bifurcation analysis of large-scale dynamical systems, with the emphasis on systems modeled by partial differential equations and delay differential equations. We further develop robust methods for solving large-scale eigenvalue problems, arising in the stability analysis of such systems, and numerical methods for parameter estimation.

 

People

• Giovanni Samaey
• Wim Michiels
• Dirk Roose

Collaboration

• R. Szalai, University of Bristol
• T. Luzyanina, Institute of Mathematical Problems in Biology, Pushchino, Russia
• G. Bocharov, Institute of Numerical Mathematics, RAS, Moscow, Russia

Key publications

• T. Luzyanina, D. Roose, T. Schenkel, M. Sester, S. Ehl, A. Meyerhans, and G. Bocharov, Numerical modelling of label-structured cell population growth using CFSE distribution data, Theoretical Biology and Medical Modelling, Vol. 4, 2007, pp. 26-39.
• D. Roose, and R. Szalai, Continuation and bifurcation analysis of delay differential equations. In B. Krauskopf, H.M. Osinga, and J. Galan-Vioque, Eds., Numerical Continuation Methods for Dynamical Systems. Path following and boundary value problems, Springer Verlag, 2007, pp.359-399.
• W. Michiels, S.-I. Niculescu, Stability analysis of a fluid flow model for TCP like behavior. International Journal of Bifurcation and Chaos, Vol.15, No.7, 2005, pp.2277-2282.
• D. Roose, T. Luzyanina, K. Engelborghs and W. Michiels, Software for stability and bifurcation analysis of delay differential equations and applications to stabilization. In S.-I. Niculescu and K. Gu, Eds., Advances in Time-Delay Systems, Lecture Notes in Control and Information Sciences, vol. 38, Springer Verlag, 2004, pp. 167-182.
• K. Engelborghs, T. Luzyanina and G. Samaey, DDE-BIFTOOL v. 2.00: a Matlab package for bifurcation analysis of delay differential equations, Technical Report TW330, October, 2001.

Point Cloud Processing

In the industry, CAD models are indispensable to the manufacturing process. Such models represent the geometry of industrial parts and are useful for the design, re-design, inspection, production and visualisation of those parts. In reverse engineering a CAD model is created by scanning a physical 3D object, resulting in a point cloud, i.e. an unordered collection of points. In order to create a valid CAD model from such a point cloud, efficient and robust algorithms for processing point cloud data are required. In our research we develop such algorithms, e.g. methods for segmentation, feature line extraction, meshing, meshless parameterizations and smoothing.

 

People

• Dirk Roose

Collaboration

• Metris

Key publications

• T. Volodine, D. Roose, and D. Vanderstraeten. Efficient triangulation of point clouds using Floater parameterization. In Proc. of the Eighth SIAM Conference on Geometric Design and Computing, pages 523-536. Nashboro Press, 2003.
• T. Volodine, D. Vanderstraeten, and D. Roose. Smoothing of meshes and point clouds using weighted geometry-aware bases. In Proceedings of Geometric Modeling and Processing, pages 687-693, 2006.
• K. Demarsin, D. Vanderstraeten, T. Volodine, and D. Roose. Detection of closed sharp edges in point clouds using normal estimation and graph theory. Computer-Aided Design, 39(4):276-283, 2007.
• K. Demarsin, D. Vanderstraeten, and D. Roose. Meshless extraction of closed feature lines using histogram thresholding. Computer-Aided Design and Applications, 5(5):589-600, 2008.