Events

October 2010

• 13 October 2010: Aleksey Kudreyko on Multiscale approaches for the solution of PDEs and integral equations.
  • Speaker: Aleksey Kudreyko, University of Salerno, Italy
  • Date and time: Wednesday, 13 October 2010, 10:30-11:30
  • Abstract:
    Beginning from the 1980's wavelets have been used for the solution of partial differential equations (PDE). For their numerical solution, we employ wavelet schemes based on full space-time variational formulations. Periodic wavelets, which constitute a multiresolution analysis in L_2([0,1]), were applied for the solution of the Burgers and Korteweg-de Vries equations. Analytical estimates of the error are given.
    The application of periodic wavelets for the solution of integral equations (IE) is also considered for integral equations of Fredholm type.
    One of the not well-studied problems in the dynamics of liquid crystals is the problem of relaxation of director's field in twisted nematic cells (TNC). In the present part of the work, we investigate by means of the Haar wavelets the nonlinear mechanism of relaxation of the director field in the form of a traveling wave that arises in a TNC in response to an external electric field.

September 2010

• 17 September 2010: Yves Frederix defends his thesis on Multiscale Methods for the Simulation of Molecular Dynamics and Stochastic Models.
• 9 September 2010: Liesbeth Vanherpe defends her thesis on Acceleration Strategies for Phase Field Simulation of Grain Growth in Polycrystalline Materials.
• 7 September 2010: Seminar of Melina Freitag on Solving matrix nearness problems using the implicit determinant method.
  • Speaker: Melina Freitag, University of Bath, U.K.
  • Date and time: Tuesday, September 7, 2010, 11:00-12:00
  • Place: 200A.05.001, Department of Computer Science, Celestijnenlaan 200A, B-3001 Heverlee
  • Abstract:
    The purpose of this talk is to provide algorithms for the solution of two matrix nearness problems: First, a new fast algorithm for the computation of the distance of a stable matrix to the unstable matrices is provided. The method is based on finding a two-dimensional Jordan block corresponding to a pure imaginary eigenvalue in a certain two-parameter Hamiltonian eigenvalue problem introduced by Byers (SIAM J. Sci. Statist. Comput., 9 (1988), pp. 875-881). Second, a new method for the computation of the distance of a matrix to a nearby defective matrix is presented. The problem is formulated following Alam & Bora (Linear Algebra Appl., 396 (2005), pp. 273-301) and reduces to finding when a parameter-dependent matrix is singular subject to a constraint. The solution is achieved by an extension of the Implicit Determinant Method. Numerical results show the performance of both algorithms for several examples and comparison is made with other methods for the same problem.
• 1 September 2010: Seminar of Oliver Ernst, titled On the Convergence of Generalized Polynomial Chaos Expansions.
  • Speaker: Oliver Ernst, TU Bergakademie Freiberg
  • Date and time: Wednesday, September 1, 2010, 10:30-11:30
  • Place: 200A.05.001, Department of Computer Science, Celestijnenlaan 200A, B-3001 Heverlee
  • Abstract:
    A number of approaches for discretizing partial differential equations with random data are based on generalized polynomial chaos expansions of random variables. These constitute generalizations of the polynomial chaos expansions introduced by Norbert Wiener to expansions in polynomials orthogonal with respect to non-Gaussian probability measures. We present conditions on such measures which imply mean-square convergence of generalized polynomial chaos expansions to the correct limit and complement these with some illustrative examples.

August 2010

• 31 August 2010: Eveline Rosseel defends her thesis on Multigrid Algorithms for Stochastic Finite Element Computations.
• 17 August 2010: Joris Vanbiervliet defends his thesis on Stability Optimization and Robust Control Design for the Class of Time-Delay Systems.

July 2010

• 5-9 July 2010: International Congress on Computational and Applied Mathematics (ICCAM 2010):
  • More information can be found on the ICCAM 2010-website.

June 2010

• 10 June 2010: Seminar of Tim Schulze on Kinetic Monte Carlo Simulation of Dendrites and Quantum Dots.
  • Speaker: Tim Schulze, Associate Professor at the University of Tennessee, USA
  • Date and time: Thursday, June 10, 2010, 10:30-11:30
  • Place: Room 00.39, Department of Department of Metallurgy and Materials Engineering, Kasteelpark Arenberg 44, 3001 Heverlee

May 2010

• 18 May 2010: Seminar of Ben Adcock on Modified Fourier series: from d-variate cubes to expansions in simplices.
  • Speaker: Ben Adcock, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK
  • Date and time: Tuesday, May 18, 2010, 14:00-15:00
  • Place: 200A.00.0144, Department of Computer Science, Celestijnenlaan 200A, 3001 Heverlee
  • Abstract:
    Modified Fourier expansions have been introduced as an adjustment of classical Fourier series for the approximation of nonperiodic functions in bounded domains. Unlike the latter, they converge uniformly throughout the domain, including on the boundary. Moreover, when highly oscillatory quadratures are used to compute expansion coefficients (as opposed to the FFT), tools such as the hyperbolic cross may be easily incorporated, leading to great potential savings in computational cost. The first part of this talk will describe the theory and construction of such expansions in d-variate cubes.
    The modified Fourier basis can be identified with the basis of eigenfunctions of the Laplace operator subject to homogeneous Neumann boundary conditions. This observation facilitates the development of approximations in a variety of non-tensor product domains. In the second part of this talk we detail the construction of modified Fourier expansions in a family of simplices, and discuss a number of their properties.
• 6 May 2010: Seminar of Prof. Michael Hinze on PDE constrained optimization in engineering applications.
  • Speaker: Prof. Michael Hinze, Fachbereich Mathematik, University of Hamburg
  • Date and time: Thursday, May 6, 2010, 11:00-12:00
  • Place: 200A.00.0144, Department of Computer Science, Celestijnenlaan 200A, 3001 Heverlee
  • Abstract:
    Solving optimization problems subject to constraints involving distributed parameter systems is one of the most challenging problems in the context of industrial applications. In particular, here the transition from model-based numerical simulations to model-based design and optimal control is crucial.
    In this talk we address the basic tasks and discuss the basic concepts of PDE constrained optimization for model applications dealing with
    
    • flow control,
    • control of crystal growth, and with
    • semiconductor design.
    Numerical examples are presented which show the scope of PDE constrained optimization in engineering applications.
• 5 May 2010: Seminar of Prof. Michael Hinze on Mathematics of PDE constrained optimization.
  • Speaker: Prof. Michael Hinze, Fachbereich Mathematik, University of Hamburg
  • Date and time: Wednesday, May 5, 2010, 15:00-16:00
  • Place: Room 00.57, ESAT
  • Abstract:
    We discuss control problems with PDEs as subsidiary conditions and take special emphasis on
    
    • the proper functional analytic setting,
    • tailored discrete concepts in the presence of additional pointwise constraints, and on
    • structure exploiting solution algorithms.
    The theoretical results are supported by numerical experiments.
• 5 May 2010: Seminar of Prof. Eric de Sturler on Subspace Recycling for Sequences of Linear Systems.
  • Speaker: Prof. Eric de Sturler, Department of Mathematics, 460 McBryde Hall, Virginia Tech, Blacksburg, VA 24061-0123, USA
  • Date and time: Wednesday, May 5, 2010, 11:00-12:00
  • Place: 200A.05.001, Department of Computer Science, Celestijnenlaan 200A, B-3001 Heverlee
  • Abstract:
    In many computational science and engineering problems, we have to solve a sequence of large, sparse, linear systems, in which the matrix changes slowly from one system to the next or changes in an algebraically structured way. The right hand side can change more drastically, although in many applications this is not the case. We have developed several methods that significantly improve the convergence of iterative solvers by recycling from one system to the next a judiciously selected subspace of the search space, for example an approximate invariant subspace, but other possibilities have proven effective as well.
    We will discuss the underlying mathematics of iterative solvers and for recycling search spaces in iterative solvers, a number of applications and results, and a convergence theory for recycling approximate invariant subspaces. Using the latter we demonstrate that significant convergence improvements can be achieved with very modest accuracy.

April 2010

• 28 April 2010: Seminar of Sheehan Olver on Numerical approximation of Riemann-Hilbert problems: Painlevé II.
  • Speaker: Sheehan Olver, Oxford University
  • Date and time: Wednesday, April 28, 2010, 16:00-17:00
  • Place: 200B.02.18, Department of Mathematics, Celestijnenlaan 200B, B-3001 Heverlee
  • Abstract:
    We describe a new spectral method for solving matrix-valued Riemann-Hilbert problems numerically. We demonstrate the effectiveness of this approach by computing solutions to the homogeneous Painlevé II equation. This can be used to relate initial conditions with asymptotic behaviour. Comparison with known values for the Hastings-McLeod solution shows that the method converges spectrally fast. By applying the approach to the deformed Riemann-Hilbert problem from nonlinear steepest descent, we can compute solutions for large values as well as small.
• 27 April 2010: Seminar of Corentin Briat on LPV systems with stochastic parameters.
  • Speaker: Corentin Briat, Division of Optimization and Systems Theory, Royal Institute of Technology (KTH), Stockholm, Sweden
  • Date and time: Tuesday April 27, 2010, 14.00-15.00
  • Place: 200A.05.001, Department of Computer Science, Celestijnenlaan 200A, B-3001 Heverlee
  • Abstract:
    Quite recently, the approaches based on linear matrix inequalities (LMI) have attracted more and more interest. Indeed, they extend prior approaches based on Riccati equations/inequalities to a wider class of systems, including LPV systems. The interest of LPV systems is mainly due to their ability to approximate complex dynamical systems such as nonlinear systems. Under the assumption that parameters are measured in real-time, this framework allows for the design of gain-scheduled controllers whose gains depend explicitly on the measured parameters. Consequently, these controllers are then able to stabilize a larger set of systems than robust-controllers.
    The objective of the talk is twofold. A first part will be devoted to an introduction on LPV systems. How they are represented, which classes of systems are embedded in the LPV systems class, how stability is studied, what makes them more complex than LTI systems and, finally, how stabilization can be performed. The second part will be devoted to the introduction of a new class of LPV systems whose parameters evolve accordingly to a Markov process. Such systems have not been studied in the literature and seem to be of interest. It will be shown that LMI-based necessary and sufficient conditions for stability and stabilizability can be obtained.

February 2010

• 5 February 2010: Seminar of Mehfooz ur Rehman on Iterative solution techniques for the incompressible Navier-Stokes equations.
  • Speaker: Mehfooz ur Rehman, T.U. Delft
  • Date and time: Friday, February 5, 2010, 15:00-15:45
  • Place: 200A.05.001, Department of Computer Science, Celestijnenlaan 200A, B-3001 Heverlee
  • Abstract:
    In this talk I will discuss iterative methods based on preconditioning techniques for the steady incompressible Navier-Stokes equation. The steady incompressible Navier-Stokes equations are discretized by the FEM. This gives rise to a saddle point problem having large number of zeroes on the main diagonal. The resulting systems of equations are solved by preconditioned Krylov subspace methods. Some new preconditioning strategies, both algebraic and problem-dependent will be discussed. In case of algebraic preconditioner, ILU preconditioner based on renumbering of the grid point and unknowns is used. We see that such a renumbering enhance convergence of Krylov methods.
    In case of problem depedent approach, we emphasize on the approximation of the Schur complement as used in SIMPLE-type preconditioners. In the usual formulation, the Schur complement matrix and updates uses scaling with the diagonal of the convection diffusion matrix. We propose a variant of the SIMPLER preconditioner. Instead of using the diagonal of the convection diffusion matrix, we scale the Schur complement and updates with the diagonal of the velocity mass matrix. This variant is called MSIMPLER (Modified SIMPLER). With the new approximation, we observe a drastic improvement in convergence for large problems.
    In second part of presentation, I will discuss block preconditioners for the Stokes problem. We employ block traingular preconditioner and Schur method to solve the Stokes problem with various viscosity configurations. Both schemes use scaled pressure mass matrix as an approximation for the Schur complement matrix. We observe that the approximation based on the pressure mass matrix give h-independent convergence, for both constant and variable viscosity.
    

January 2010

• 29 January 2010: Seminar of Sam Corveleyn on On a new approach to solve fuzzy elliptic PDEs based on polynomial chaos, and of Koen Delaere on Webtools and Webinterface for Fuzzy Finite Element Analysis.
  • Date and time: Friday, January 29, 2010, 14:00-15:00
  • Room: 200A.05.001, Department of Computer Science, Celestijnenlaan 200A
  1. • Speaker: Sam Corveleyn
     • Title: On a new approach to solve fuzzy elliptic PDEs based on polynomial chaos
     • Abstract:
       We will discuss a new approach to solve fuzzy partial differential equations. Fuzzy calculations typically come down to a global optimization over the uncertainty domain. In case of differential equations this might get very expensive. Therefore we'll use a response surface over the uncertainty domain to approximate the exact solution of the differential equation. It is cheaper to evaluate and is also convenient for post-processing steps in the analysis of the results. Currently, some black-box approaches to construct a response surface have already been applied and explored to solve fuzzy differential equations. We propose to use methods from stochastic PDE theory, based on polynomial chaos. For certain types of PDEs these response surfaces converge exponentially in the maximum norm to the exact solution, which is exactly what we need for fuzzy calculations.
  2. • Speaker: Koen Delaere
     • Title: Webtools and Webinterface for Fuzzy Finite Element Analysis
     • Abstract:
       An interactive website enables project partners to explore theory and practice of using fuzzy numbers to represent uncertainty. A fuzzy calculator and plot window allow the beginning user to experiment with fuzzy arithmetic and visualize membership functions. On a second level (fuzzy modeling) a set of pre-defined ODE en PDE (BVP and IVP) is offered where some parameters or initial conditions are fuzzy numbers. A third level offers pre-defined engineering problems where the deterministic core computation is performed analytically or using commercial finite element (FE) software such as Nastran and SCIA Engineer, e.g. the computation of a fuzzy tip-to-tip FRF.
       Apart from problem selection, the user selects the method of fuzzy optimization as well as other parameters relevant to the uncertainty. The method of fuzzy optimization is a plug-in toolbox provided by any partner, i.c. new methods of fuzzy optimization under development. New methods can readily be tested and calibrated for performance on all pre-defined problems, or new benchmark problems supplied by the partner.
       The website interfaces Python, Java, C/C++ and Matlab Mex compilation (using a Matlab engine from within C/C++ code). Next there is the additional interface with commercial finite element software, and an ssh link. Because SCIA Engineer runs only on WindowsXP, an SSH link was introduced to link the webserver with remote clients; the machine where jobs run also becomes a parameter. If the client is a cluster, a large set of jobs is queued at the same time. For a given FE problem, mesh size can vary (coarse, normal, fine) by making the filename a parameter. Component by component, the entire website structure becomes more and more modular and parametric, and every setting, value, filename, hostname, ... becomes a parameter to be parsed on some level.

December 2009

• 15 december 2009: Seminar of Alfredo Deaño On asymptotic-numerical solvers for oscillatory ODEs, and of Andreas Asheim on Numerical steepest descent with path approximations.
  • Date and time: Tuesday, December 15, 2009, 10:30-11:30
  • Room: 200A.05.001, Department of Computer Science, Celestijnenlaan 200A
  1. • Speaker: Alfredo Deaño (Universidad Carlos III de Madrid); Joint work (in progress) with M. Condon (Dublin) and A. Iserles (Cambridge)
     • Title: On asymptotic-numerical solvers for oscillatory ODEs
     • Abstract:
       In this talk we propose a new approach to compute efficiently solutions of systems of differential equations that present highly oscillatory forcing terms. The method is based on asymptotic expansions in inverse powers of the oscillatory parameter together with modulated Fourier series for each of the coefficients in the expansion. We will discuss stability and implementation aspects of the method, and give some examples and possible directions of future research.
  2. • Speaker: Andreas Asheim (Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim, Norway)
     • Title: Numerical steepest descent with path approximations
     • Abstract:
       Combining the classical asymptotic method of steepest descent with Gaussian quadrature yields excellent quadrature methods for oscillatory integrals. In particular, they give high asymptotic accuracy, higher than comparable truncated classical asymptotic expansions. One difficulty with these methods, when applied to certain integrals, is the computation of the paths of steepest descent. These paths are defined through non-linear equations.
       In this talk we shall see that a simple truncated power series expansions of the paths, which would not be allowed in classical asymptotic theory, can be used as approximations to the true paths. The asymptotic analysis of the resulting method is rather non-trivial and give some quite unexpected results.
• 10 December 2009: Seminar of Kristian Debrabant on Runge-Kutta and Taylor methods for stochastic differential equations.
  • Speaker: Dr. Kristian Debrabant, Technische Universität Darmstadt, FB Mathematik, Numerik und wissenschaftliches Rechnen, Dolivostr. 15, D-64293 Darmstadt
  • Date and time: Thursday, 10 December 2009, 15h00-16h00
  • Place: 200A.00.114, Department of Computer Science, Celestijnenlaan 200A
  • Abstract:
    In the modeling of many applications, e.g. in chemical reaction systems, taking stochastic effects into account often leads to stochastic differential equations (SDEs). Important classes of approximation methods for solutions of SDEs are stochastic Runge-Kutta (SRK) and stochastic Taylor (ST) methods.
    In this talk we give an introduction to SDEs, SRK and ST methods. We develop an efficient third order SRK method for the weak approximation of SDEs with additive noise and consider the order of iterated SRK and ST methods.
    The content of this talk is joined work with Anne Kvaerno.
• 3 December 2009: Seminar of Tatiana Voitovich-Firiulina on On the construction of second order finite volume upwind schemes for quasilinear convection-diffusion equations with smooth solutions.
  • Speaker: Prof. Tatiana Voitovich-Firiulina, Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingenería, Universidad Católica de Temuco, Chili
  • Date and time: Thursday, 3 December 2009, 14h00-15h00
  • Place: 200A.05.001, Department of Computer Science, Celestijnenlaan 200A
  • Abstract:
    In this contribution, we consider construction of second-order upwind schemes for quasilinear convection-diffusion equations with smooth solutions. For the development of element-based upwind schemes, we introduce the following design principle: to approximate the convection flux as a product of the value of the solution related to the middle of the corresponding element of the dual mesh multiplied by the mass flux through the segment (face) of the dual mesh, at the same time the value of the solution is searched as a linear combination of the values of the solution at all the vertices of the finite element. We prove that the difference between the classical quadrature approximation and our approximation has a disapearing w.r.t. h order of magnitude. We demonstrate that it is possible to find such a linear combination from a profile of the solution taking into account the flow direction, such as f.e. element-Peclet-number based profiles of the solution, that are exponential in the direction of the flow and linear in the normal direction. Such principle will be shown to include the selebrated skewed upwind differencing schemes, also known as mass-flow-weighted upwind schemes. The principle allows to construct the upwind schemes for all the known types of finite volume dual partitions and arbitrary polygonal meshes, f.e. with the element-Peclet-number based profiles constructed on the upstream edge and the downstream node. We consider the principle as to be of course of high practical importance.

November 2009

• 18 November 2009: Seminar of Olavi Nevanlinna on A roadmap for practical holomorphic functional calculus.
  • Speaker: Prof. Olavi Nevanlinna, Institute of Mathematics, Helsinki University of Technology
  • Date and time: Wednesday November 18, 2009, 14h00-15h00
  • Place: Department of Mathematics, Celestijnenlaan 200B.02.18
  • Abstract:
    We discuss a series of results which provide tools for practical holomorphic calculus in Banach algebras and in particular for bounded operators in Banach spaces. The results are nontrivial already for matrices with moderately large dimensional spaces. The key result is the existence of an algorithm which creates a sequence of compact sets in inclusion such that the intersection equals the polynomial convex hull of the spectrum. Outside each such compact set we can write the resolvent explicitly as a converging series.

October 2009

• 7-9 October 2009: The Thirty-fourth Woudschoten Conference:
  • On 7-9 October 2009 the thirty-fourth Woudschoten Conference will be held at the Woudschoten Conference Centre, Zeist, The Netherlands. Themes of the conference are Latest developments in iterative solution methods and Numerics and stochastics in applications.
  • More information on the conference website.
• 1 October 2009: Seminar of Marianna Khanamiryan on Numerical methods for systems of highly oscillatory ordinary differential equations.
  • Speaker: Marianna Khanamiryan, Trinity College, Cambridge
  • Date and time: Thursday, October 1, 16h30-17h30
  • Place: Room 200A.05.128, Dept of Computer Science, Celestijnenlaan 200A, B-3001
  • Abstract:
    Phenomena of high oscillation are considered a major computational problem occurring in Fourier analysis, computational harmonic analysis, quantum mechanics, electrodynamics and fluid dynamics. Classical methods based on Gaussian quadrature fail to approximate oscillatory integrals. In this work we introduce numerical methods which share the remarkable feature that the accuracy of approximation improves as the frequency of oscillation increases. Asymptotically, our methods depend on inverse powers of the frequency of oscillation, turning the major computational problem into an advantage.
    Evolving ideas from the stationary phase method, we first apply the asymptotic method to solve highly oscillatory linear systems of differential equations. The asymptotic method provides a background for our next, the Filon-type method, which is highly accurate and requires computation of moments. We also introduce two novel methods. The first method, we call it the FM method, is a combination of Magnus approach and the Filon-type method, to solve matrix exponential. The second method, we call it the WRF method, a combination of the Filon-type method and the waveform relaxation methods, for solving highly oscillatory nonlinear systems. Finally, completing the theory, we show that the Filon-type method can be replaced by a less accurate but moment free Levin-type method.

September 2009

• 14-18 September 2009: 14th Belgian-French-German Conference on Optimization Leuven:
  • The conference is the 14th of the series of French-German meetings which started in Oberwolfach in 1980. This time, it is organized jointly with Belgian optimizers, and takes place in Belgium's oldest university town, Leuven, in the heart of Europe, close to Brussels. The conference will consist of 12 invited plenary talks, parallel contributed sessions, mini-symposia, and a poster session. It will address all aspects of optimization and its applications.
  • More information on the '09 BFG website.

July 2009

• 7 July 2009: Seminar of Pieter Ghysels on Multiscale modeling of biological viscoelastic tissue.
  • Speaker: Pieter Ghysels
  • Date and time: Tuesday July 7th, 13h00-14h00
  • Place: Room 200A.05.001, Dept of Computer Science, Celestijnenlaan 200A, B-3001 Leuven
  • Abstract:
    We present a multiscale method for the simulation of large viscoelastic deformations and show its applicability to biological tissue. At the microscopic level we use a combination of Smoothed Particle Hydrodynamics (SPH) and discrete elements to model the geometrical structure and basic properties of individual cells. The macroscopic equation and stress tensor are derived from the SPH model by means of the Generalized Mathematical Homogenization (GMH) technique. The macroscopic domain is discretized using standard finite elements, where the stress tensor is computed from microscopic simulations in small subdomains, called Representative Volume Elements (RVEs). Our emphasis is on solving the microscopic problem inside the RVE for a given macroscopic deformation and velocity gradient. We propose a scheme to initialize the RVE consistently not only with the macroscopic variables, but also with the microscopic dynamics. At the finite element level, implicit time-stepping codes can be used. Therefore, the anisotropic Eulerian elasticity tensor is estimated using a forward finite difference approximation for the Truesdell rate of the Cauchy stress tensor. A similar approach is used for the computation of the fourth order viscosity tensor, from which a damping matrix can be constructed.

June 2009

• 15 June 2009: Seminar of Yves Frederix on Multiscale computation of the solution of coarse Fokker-Planck equations.
  • Speaker: Yves Frederix
  • Date and time: Monday June 15th, 10h30-11h30
  • Place: Room 200A.05.001, Dept of Computer Science, Celestijnenlaan 200A, B-3001 Leuven
  • Abstract:
    In this talk, we consider a class of multiscale stochastic systems for which the evolution of the probability density for the coarse variable can be described by a convection-diffusion equation, the so-called Fokker-Planck equation. We present a multiscale procedure that builds on the equation-free and heterogeneous multiscale framework to numerically integrate this equation. To this end, we estimate the unknown parameters (drift and diffusion) in the macroscopic description using only appropriately chosen realizations of the full multiscale system. The solution of the Fokker-Planck equation is then computed via standard numerical methods. We also present stability and error bounds on the result as a function of the quality of the estimation.
• 8 June 2009: Seminar of Eveline Rosseel on Nonlinear stochastic Galerkin and collocation simulations: application to a ferromagnetic cyclinder rotating at high speed.
  • Speaker: Eveline Rosseel
  • Date and time: Monday June 8th, 16h30-17h30
  • Place: Room 200A.00.144, Dept of Computer Science, Celestijnenlaan 200A, B-3001 Leuven
  • Abstract:
    The stochastic collocation and Galerkin method are two state-of-the-art tools for solving stochastic partial differential equations (PDE). The former method is based on sampling the random variables present in a stochastic PDE into a set of multidimensional collocation points. The latter converts a stochastic PDE into a coupled set of deterministic PDEs after applying a spectral discretization in the stochastic dimension. While the stochastic collocation method can straightforwardly be extended to nonlinear stochastic PDEs, it is not trivial to apply the stochastic Galerkin procedure to a nonlinear PDE and approximations are required. In this talk, we shall apply both stochastic solvers to a particular nonlinear stochastic PDE and compare their accuracy and computational cost. We shall consider the stochastic simulation of a ferromagnetic cylinder rotating at high speed. This type of model can be found as part of solid-rotor induction machines in various machining tools. A precise design requires to take ferromagnetic saturation effects into account and needs to deal with uncertainty on the nonlinear magnetic material properties. We shall determine to what extent uncertainty on the material properties influences the machine properties. Both the stochastic collocation as well as the stochastic Galerkin method yield high-order accurate stochastic solutions. The stochastic collocation procedure applies either a tensor product grid or a sparse grid of collocation points. The stochastic Galerkin method requires in general more computational time than the stochastic collocation method to reach the same level of accuracy.

May 2009

• 5 May 2009: Master theses info market for the students of the master Wiskundige Ingenieurstechnieken.

April 2009

• 27 April 2009: Seminar of Tony Roberts on Choose interelement coupling to preserve consistent and self-adjoint dynamics in multiscale modelling.
  • Speaker: Tony Roberts, University of Adelaide
  • Date and time: Monday, April 27, 2009, 11h-12h
  • Place: Room 00.144, Celestijnenlaan 200A, B-3001 Leuven
  • Abstract:
    Developments in dynamical systems theory provides new support for discrete models of PDEs and other microscale systems. By systematically resolving subgrid microscale dynamics the new approach constructs asymptotically accurate, macroscale closures of discrete models of the PDE. Reaction-diffusion in two spatial dimensions illustrates the approach. Special coupling of finite elements ensures that the discrete models are consistent with the PDE to as high an order as desired. Such coupling generalises to support the patch dynamics of equation-free simulation. New developments ensure coarse scale discrete models preserve important self-adjoint properties of the microscale dynamics. Dynamics on a fine lattice are mapped to lattice a factor of two coarser (as in multigrids). Such mapping of discrete lattice dynamics may be iterated to empower us in future research to explore scale dependent emergent phenomena. As given examples demonstrate, the approach developed here ensures the preservation of important properties of the fine scale dynamics.
• 24 april 2009: Spring Meeting WSC 2009
  • Friday April 24, 2009, the Werkgemeenschap Scientific Computing is organizing a spring meeting at the Technical University Eindhoven. A mixture of eight young and senior researchers have been selected to give a presentation on their research.
  • More information can be found on the webpage.
• 24-26 april 2009: PhDays 2009, an annual event that joins PhD students from Numerical Mathematics from the Netherlands and Flanders (Belgium).
  • More information can be found on the PhDays 2009 website.
• Francqui chair 2008-2009: Prof. Philippe Toint (FUNDP Namur) will teach a course on: Advanced Algorithms in Nonlinear Optimization. More information can be found on this page.

March 2009

• 27 march 2009: Inauguration lesson of Wim Michiels. This lesson will take place on March 27 in Auditorium 00.225, Celestijnenlaan 200A, 3001 Heverlee.
• 23 march 2009: Launch event Flemish Supercomputer Center
  • The Flemish Supercomputer Center (abbreviated VSC, which stands for Vlaams Supercomputer Centrum) is a virtual supercomputer center. The VSC is a partnership of the five Flemish university associations: The K.U.Leuven association, awlp Ghent University Association, the Universitaire Associatie Brussel, the Antwerp University Association and the Associatie Universiteit-Hogescholen Limburg. The VSC is funded by the Flemish Government - Department of Economy, Science and Innovation.
  • More information can be found on the website.

January 2009

• 19 January 2009: Seminar of Jerzy Gawad on Cellular Automata - Finite Element (CAFE) approach applied in multiscale modelling of polycrystalline material.
  • Speaker: Jerzy Gawad, Scientific Computing Group (TWR), Department of Computer Science
  • Date and Time: Monday, January 19, 2009, 13h-14h
  • Place: Celestijnenlaan 200A, Auditorium 00.225, 3001 Leuven
• 5 January 2009: Kris Demarsin defends her thesis on Extraction of Closed Feature Lines from Point Clouds based on Graph Theory.

To submit an item to the events, contact the editor.