Spring Meeting WSC 2010
Spring Meeting WSC 2010
Participants of the WSC spring meeting 2010
Monday May 3-rd, 2010, the Werkgemeenschap Scientific Computing is organizing, together with the Scientific Computing Group of the University of Antwerp, a spring meeting in Antwerp. A mixture of eight young and senior researchers have been selected to give a presentation on their research.
Location
The Middelheimcampus of the University of Antwerp will warmly welcome us for this spring meeting.
Dept Wis-Inf
Gebouw G, lokaal G0.10
Middelheimlaan 1
B-2020 Antwerpen-Wilrijk
Vervoer
Did you know that the Thalys will bring you in 1 hour and 12 minutes from Amsterdam CS to Antwerp CS? Then take a taxi from Antwerp CS and you will be in less than one and a half hour from Amsterdam at your destination.
Travelling by car or by train via Brussel, Gent, Luik, Hasselt, Breda or Eindhoven then the next URL will help you with a good trip description.
Program
| 10.00-10.30 uur | Registration, coffee/tea, reception | |
| 10.30-11.20 uur | Prof.dr. Karl Meerbergen (Katholieke Universiteit Leuven) | |
| On parametrized linear systems, moments, eigenvalues, gradients, and Krylov methods [abstract] | ||
| 11.20-11.45 uur | Anna Mozartova (Centrum Wiskunde & Informatica, Amsterdam) | |
| Monotonicity and boundedness properties of general linear methods[abstract] | ||
| Break | ||
| 12.05-12.30 uur | Andrey Chesnokov (Katholieke Universiteit Leuven) | |
| Recurrence relations for multivariable orthogonal polynomials and discrete least-squares approximations [abstract] | ||
| 12.30-12.55 uur | Patricio Rosen Esquival (Technische Universiteit Eindhoven) | |
| Flow in Corrugated Pipes [abstract] | ||
| Lunch | ||
| 14.00-14.25 uur | Paulien van Slingerland (Technische Universiteit Delft) | |
| Extracting the Hidden Accuracy of DG Solutions -- Improving an Existing Post-Processing Technique near Boundaries and Shocks [abstract] |
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| 14.25-14.50 uur | Nico Schlömer (Universiteit Antwerpen) | |
| Symmetry breaking bifurcations in the Ginzburg--Landau equations on the square [abstract] | ||
| Break | ||
| 15.15-15.40 uur | Tim Op 't Root (Universiteit Twente) | |
| One-Way Wave Propagation with Symmetric Square Root [abstract] | ||
| 15.40-16.30 uur | Prof.dr. Jan Verwer (Centrum Wiskunde & Informatica, Amsterdam) | |
| Numerical integration of Maxwell's equations [abstract] | ||
Organisation and participation
Organiserend comité:
Prof.dr. Annie Cuyt(UA-CMI), Prof.dr. Karel in 't Hout (UA), Prof.dr. Wim Vanroose (UA), Prof.dr. Jan Verwer (CWI,UvA-KdvI), Drs. Margreet Nool (CWI, secretaris).
Participation (including lunch) is free of charge but registration is obligatory. Please registrate before April 26-th 2010.
Questions? Please ask: Margreet Nool
Abstracts
Prof. dr. Karl Meerbergen (Katholieke Universiteit Leuven)
On parametrized linear systems, moments, eigenvalues, gradients, and Krylov methods
The solution of large scale linear systems with parameters is an important problem in many applications. It is tightly connected to the wide field of model order reduction and therefore with rational approximation. In this talk, we review Krylov methods for parametrized linear systems and their connection with moment matching. A characterization using eigenvalues is often more practical to understand the convergence of such methods.
We also discuss more recent work on the use of parametrized linear system solvers for quasi-Newton numerical optimization methods and the solution of parametrized linear systems with multiple right-hand sides.
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Anna Mozartova (Centrum Wiskunde & Informatica, Amsterdam)
Monotonicity and boundedness properties of general linear methods
For Runge-Kutta methods, linear multistep methods and other classes of general linear methods much attention has been paid in the literature to important nonlinear stability properties such as total-variation-diminishing (TVD), strong stability preserving (SSP) and monotonicity. Unfortunately, for many useful methods it has turned out that these properties cannot be proved. For this reason attention has been paid in the recent literature to related and more general properties referred to by the terms total-variation-bounded (TVB) and boundedness.
In this work an analysis of monotonicity and boundedness properties is provided for the class of general linear methods. We present a framework for deriving optimal step-size conditions which guarantee boundedness. General results are presented for linear multistep methods. Several numerical illustrations will be given to verify the theory.
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Andrey Chesnokov (Katholieke Universiteit Leuven)
Recurrence relations for multivariable orthogonal polynomials and discrete least-squares approximations
We present an algorithm computing recurrence relation coefficients for bivariate polynomials, orthonormal with respect to a discrete inner product. To compute these coefficients, we pose two coupled inverse eigenvalue problems and solve them efficiently and in a stable way, using a sequence of Givens rotations. We also show how to generalize the algorithm for the case of polynomials in more variables.
As one of many applications, these polynomials make it possible to give the solution of a discrete least squares approximation problem. The polynomial p from some polynomial space P that minimizes || f - p||, where f is some multivariate function, can be found as follows. Find a basis {φ1,...,φn} for P which is orthonormal with respect to a given inner product. The solution p, is the generalized Fourier expansion of f with respect to this basis, truncated after some term. These Fourier coefficients can be computed parallel to the recurrence relation coefficients.
Several numerical experiments show the validity of the approach.
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Patricio Rosen Esquival (Technische Universiteit Eindhoven)
Flow in Corrugated Pipes
The effect of wall shape in the friction factor of a forced flow through pipes or hoses is of interest in many applications. Several numerical and experimental studies have shown that the contribution of wall shape on the flow is not trivial even in the laminar case. The friction factor in corrugated pipes has been found to differ from the classical Moody diagram which presents the laminar friction factor as independent of wall roughness.
Available CFD computation techniques allow to predict flows in arbitrary geometry, based on these computations, the friction factor can be calculated, but this kind of procedures can become prohibitively expensive in terms of calculation time. In this talk we discuss a method for estimating the pressure losses for laminar forced flow in axially symmetric pipes with varying radius. The approach is based on an analytic expression for the friction factor, obtained after integrating the Navier-Stokes equations and an asymptotic expansion for the flow field. Examples for the validation of the method are presented.
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Paulien van Slingerland (Technische Universiteit Delft)
Extracting the Hidden Accuracy of DG Solutions
The Discontinuous Galerkin (DG) method approximates the solution of PDEs in the form of discontinuous piecewise polynomials of degree k. For a certain class of problems, application of an existing post-processor enhances the accuracy from order k+1 to 2k+1. Furthermore, the solution becomes k-1 times differentiable. What is counterintuitive, is that this post-processor needs to be applied only once, at the final time, and that it does not contain any information of the underlying physics or numerics. During the presentation, we demonstrate the mechanism of the post-processor and our solution to problems near boundaries and shocks.
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Nico Schlömer (Universiteit Antwerpen)
Symmetry breaking bifurcations in the Ginzburg--Landau equations on the square
Since Abriskov's discovery in 1957, vortex pattern formation in superconductors has attracted great attention in various fields of physics and mathematics. This talk will focus on vortex configurations arising in extreme type-II superconductors on a 2D square-shaped domain for which the magnetic flux and the superconducting current can be considered decoupled; this leads to the simplified Ginzburg--Landau equations. Upon altering system parameters, such as the strength of the magnetic field applied to the sample, a complex solution landscape unfolds. This talk will highlight some of the intricacies of the numerical solution process, and in parameter continuation show how the appearing bifurcations will influence the symmetry of the solution branches.
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Tim Op 't Root (Universiteit Twente)
One-Way Wave Propagation with Symmetric Square Root
We derive the one-way wave equation with geometrical amplitude by using a symmetric square root operator and applying a normalization on the wave field. A symmetric quantization maps the square root symbol into a symmetric square root operator, which provides geometrical amplitude without calculating lower order terms. The advantage of the symmetry argument is its applicability to numerical methods. We applied it to a new spectral method and to the 60 degree finite-difference one-way method. The simulations show in both cases a significant correction to the amplitude. With symmetric square root operator the amplitudes are correct.
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Prof. dr. Jan Verwer (Centrum Wiskunde & Informatica, Amsterdam)
Numerical integration of Maxwell's equations
Maxwell's equations are a set of partial differential equations describing the fundamentals of electromagnetic wave phenomena in space and time. Modern scientific computing with these equations demands sophisticated numerical algorithms, in particular 3D finite-element methods to discretize space and integration methods to advance the computed waves in time. In this talk I will focus on time integration which is my main field of research. The talk is prepared for non-experts in numerical PDEs and sketches recent research motivated by applications (from the INRIA team NACHOS) for which existing classical methods have become inefficient.
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