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Voorjaarsbijeenkomst WSC 2012

Deelnemers WSC voorjaarsbijeenkomst 2011 in Delft

Op vrijdag 11 mei 2012 organiseert de Werkgemeenschap Scientific Computing i.s.m. de Scientific Computing Group van de Universiteit Antwerpen (departement Wiskunde-Informatica) een voorjaarsbijeenkomst aan de Campus Middelheim in Antwerpen. Op deze bijeenkomst zullen AIOs/OIOs en senior onderzoekers op het gebied van Scientific Computing een voordracht geven.

Wij zijn blij dat het dit jaar gelukt is de voorjaarsbijeenkomst te combineren met de PhDays. Sinds 1998 is de PhDays een jaarlijks terugkerend evenement voor AIO's en OIO's in Scientific Computing uit België en Nederland. De PhDays 2012 worden gehouden van 11 t/m 13 mei 2012 in Vielsalm, België.

Locatie

Als locatie is Middelheimcampus van de Universiteit Antwerpen gekozen.

Departement Wiskunde-Informatica
Gebouw G, lokaal G0.10
Middelheimlaan 1
B-2020 Antwerpen-Wilrijk

Vervoer

Wist u dat u met de Thalys in 1 uur en 12 minuten vanaf Amsterdam CS naar Antwerpen CS reist? Neemt u vervolgens de taxi dan bent u vanaf Amsterdam in anderhalf uur op de plek van bestemming.

Komt u met de auto of met de trein via Brussel, Gent, Luik, Hasselt, Breda of Eindhoven dan geeft de volgende URL een goede routebeschrijving.

Programma

Organisatie, deelname en registratie

Abstracts

Prof.dr. Kees Vuik (TUDelft)
A decade of fast and robust Helmholtz solvers

Many wave phenomena are well described by the wave equation. When the considered wave has a fixed frequency the wave equation is mostly re-written in the frequency domain which results in the Helmholtz equation. It also possible to approximate the time domain solution with a summation of solutions for several frequencies. Applications are the propagation of sound, sonar, seismics, and many more. We take as an example the search for oil and gas using seismics. It is well known that an increase of the frequency leads to a higher resolution, so more details of the underground become visible.

The Helmholtz equation in its most simple form is a combination of the symmetric positive Poisson operator and a negative constant, the so-called wave number, multiplied with the identity operator. In order to find the solution in a complicated domain a discretization has to be done. There are two characteristic properties of the discretized system:

If damping is involved the operator also has a part with an imaginary value. The resulting matrix is however not Hermitian.

In the years around 2000 no good iterative solvers are known. The standard approaches: Krylov and multi-grid break down if the wavenumber increases. Around 2005 a new preconditioner based on the shifted Laplace preconditioner was proposed, which leads to a class of fast and robust Helmholtz solvers. It appears that the amount of work increases linearly with the wavenumber. At this moment, this is the method of choice to solve the Helmholtz equation. Various papers have appeared to analyze the good convergence behavior. Recently a multi level Krylov solver has been proposed that seems to be scalable, which means that the number of iterations is also independent of the wavenumber. An analysis of this method is given and recent results for industrial problems are given.
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Sam Corveleyn (KULeuven)
The numerical solution of fuzzy elliptic PDEs

Fuzzy sets were introduced as a generalization of classical sets to express subjective or vague linguistic concepts. With classical sets there is a hard distinction between elements which belong or don't belong to a set. A fuzzy set however can contain elements up to any degree between 0 (not an element of) and 1 (element of). Soon after, it was recognized that fuzzy sets could serve as a basis for possibility theory and thus fit in the larger framework of imprecise probabilities. The need for alternatives like imprecise probabilities to probability theory can simply be motivated by the fact that in mathematical modeling of real-world problems the information about parameters is not always given in the form of a probability distribution. Forcing the quantification of uncertainties into the framework of probability can lead to very unrealistic and hard to interpret results, and may not be very efficient from a computational point of view.

We describe and analyze a numerical method for solving elliptic partial differential equations (PDE) with a fuzzy diffusion coefficient. This problem can be recast as a parameterized PDE followed by global optimization over nested boxes in the parameter domain. To guarantee accuracy of the numerical solution in the fuzzy sense, we show that it is sufficient for the solution to the parameterized PDE to be accurate in the supremum norm over the parameter domain. This motivates us to choose a Galerkin discretization with Chebyshev polynomials in the parameter domain. We derive an a-priori error bound for this approximation and prove (sub-)exponential convergence.
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Marjon Ruijter (CWI, Centraal Planbureau)
Two-dimensional Fourier cosine series expansion method for pricing financial options

The COS method for pricing European and Bermudan options with one underlying asset was developed in Fang and Oosterlee (2008, 2009). We extend the method to higher dimensions, with a multi-dimensional asset price process. The algorithm can be applied to, for example, pricing multi-color rainbow options, but also to pricing under the popular Heston stochastic volatility model. For smooth density functions, the resulting method converges exponentially in the number of terms in the Fourier cosine series summations.
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Annie Cuyt, Wen-shin Lee and Sem Peelman (UAntwerpen)
Interpolation in Sparse Signal Reconstruction

Sparse signals admit a representation by a linear combination of only a few elementary waveforms or atoms. Currently the acquisition and reconstruction of such signals receives a great deal of attention in signal processing. The ultimate goal is to determine the underlying sparse representation directly from as few data samples as possible, rather than first acquire a massive amount of data which are then compressed. In this talk, we discuss the use of interpolation methods in this setting.

Conventional interpolation algorithms don’t take sparsity into consideration and depend on the total degree or the maximum possible size of the target signal. Whereas so-called sparse interpolation algorithms are sensitive to the number of nonzero terms in the underlying representation and thus account for the sparsity of a function. In terms of the number of samples required for reconstruction, sparse interpolation algorithms achieve the theoretical minimum, in some cases surpassing traditional sampling theorems.

A case-study in synthetic audio analysis is used to walk through the different stages that compose a sparse interpolation algorithm and the numerical issues en- countered therein. The keynote will be a strong relation with numerical linear algebra.
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Shavarsh Nurijanyan (UTwente)
Compatible Numerical Simulation of Linear Inertial Waves

A compatible numerical discretisation of Hamiltonian structure for the linearized (in)compressible fluid flow in a three-dimensional rotating domain is presented. The presence of vorticity and Coriolis terms in the equa- tions allows the modeling of currents and waves in the interior of the domain. The waves involved are so-called inertial 'gyroscopic' waves, relevant to lake hydrodynamics and also for (filled) rotating fuel tanks. These inertial waves display multi-scale features with chaotic attractors in the zones of intense wave activity, which are narrow in relation to the domain size but, at the same time, span the domain's interior. Numerical algorithms and simulations of inertial waves are thus nontrivial.

The numerical model is based on a discontinuous Galerkin finite element dis- cretization that preserves the Hamiltonian structure of the linear rotating Eu- ler equations. This ensures conservation of important mathematical properties of the partial differential equations (e.g., mass, energy, phase space volume). Dirac theory is applied to derive the incompressible limit of the compressible Euler or acoustic equations which are used as a starting point in the numer- ical discretization. Several test cases, including a comparison with a recently derived semi-analytical solution in a cuboid, will be presented to assess the quality of the numerical model. [full abstract]
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Francesco Ferranti(Universiteit Gent)
Multivariate Macromodels for Efficient Computer Aided Design

Surface approximation techniques are often used to approximate the variation of the complex electromagnetic behavior of microwave systems in terms of design variables that describe physical properties of the structure. Such analytical models are frequently used for efficient design space exploration, design optimization, and sensitivity analysis.

Several numerical modeling techniques have been applied to tackle this problem, such as artificial neural networks (ANNs), the multivariate Cauchy method, the use of orthogonal Chebyshev polynomials and a multivariate extension of Thiele-type continued fractions. The use of radial basis functions and Kriging has also been considered, but it was found that these methods provide less favorable results since they lack a theoretical connection with the physical problem at hand. This talk gives an overview of some recent developments in this area. Although the algorithms are applied to EM modeling problems, the basic concepts can be generalized to several other modeling problems in the field of computer-aided design.
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Nico Banagaaya (TUEindhoven)
Model Order Reduction for index-2 DAEs

There exist many model order reduction (MOR) methods for differential systems (ODE), but for differential algebraic systems (DAEs), the reductions become cumbersome for higher index systems.

In this talk, we will present a new strategy of reducing DAEs by first decoupling it into differential and algebraic parts. We will do this using the projector and matrix chain introduced by März in 1996 with some modification. We will then apply the existing MOR methods on the differential part and develop new reductions methods for algebraic parts. At the end, we will test these techniques on simple and industrial problems of index 1 and index 2 systems.
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Laurent Sorber (KULeuven)
Efficient algorithms for tensor decompositions

The canonical polyadic and rank-(L_r,L_r,1) block term decomposition (CPD and BTD, respectively) are two closely related tensor decompositions. The CPD is an important tool in psychometrics, chemometrics, neuroscience and data mining, while the rank-(L_r,L_r,1) BTD is an emerging decomposition in signal processing and, recently, blind source separation. We present a decomposition that generalizes these two and develop algorithms for its computation. Among these algorithms are alternating least squares schemes, several general unconstrained optimization techniques, as well as matrix-free nonlinear least squares methods. In the latter we exploit the structure of the Jacobian's Gramian by means of efficient expressions for its matrix-vector product. Combined with an effective preconditioner, numerical experiments confirm that these methods are among the most efficient and robust currently available for computing the CPD, rank-(L_r,L_r,1) BTD and their generalized decomposition.
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