Veranstaltungen

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Dienstag, 28.03.2017, 13.30 Uhr (WIAS-ESH)
Seminar Numerische Mathematik
G. Pitton, SISSA, Italien:
Accelerating augmented and deflated Krylov space methods for convection-diffusion problems
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
In this talk I will recall some basic notions of augmented and deflated Krylov space methods for the iterative solution of linear systems. Then I will discuss a few strategies to apply these techniques to the solution of linear systems coming from nonlinear convection-diffusion equations . In particular, I will argue that in some cases it may be convenient to exploit some alternative recycling strategies based on the SVD selection of previous solutions. Some numerical tests in scalar nonlinear convection-diffusion problems discretized with Finite Elements and Spectral Elements will be discussed.

Veranstalter
WIAS Berlin
Dienstag, 28.03.2017, 14.30 Uhr (WIAS-ESH)
Seminar Numerische Mathematik
Prof. L. Heltai, SISSA, Italien:
Immersed Finite Element Methods for interface and fluid structure interaction problems: An overview and some recent results
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
Immersed Finite Element Methods (IFEM) are an evolution of the original Immersed Boundary Element Method (IBM) developed by Peskin in the early seventies for the simulation of complex Fluid Structure Interaction (FSI) problems. In the IBM, the coupled FSI problem is discretised using a single (uniformly discretised) background fluid solver, where the presence of the solid is taken into account by adding appropriate forcing terms in the fluid equation. Approximated Dirac delta distributions are used to interpolate between the Lagrangian and the Eulerian framework in the original formulation by Peskin, while a variational formulation was introduced by Boffi and Gastaldi (2003), and later generalised by Heltai and Costanzo (2012). By carefully exploiting the variational definition of the Dirac distribution, it is possible to reformulate the discrete Finite Element problem using non-matching discretisations without recurring to Dirac delta approximation.
One of the key issues that kept people from adopting IBM or IFEM techniques is related to the loss in accuracy attributed to the non-matching nature of the discretisation between the fluid and the solid domains, leading to solvers that converge only sub-optimally.
In this talk I will present a brief overview of Immersed Finite Element Methods, and will present some recent results that exploit techniques introduced by D?Angelo and Quarteroni (2012), to show that, for the variational finite element formulation, the loss in accuracy is only restricted to a thin layer of elements around the solid-fluid interface, and that optimal error estimates in all norms are recovered if one uses appropriate weighted norms when measuring the error.

Veranstalter
WIAS Berlin
Dienstag, 28.03.2017, 15.00 Uhr (WIAS-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. E. Burnaev, Skolkovo Institute of Science and Technology , Russische Föderation:
Minimax approach to variable fidelity data interpolation
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstrakt
In this work we obtain minimax interpolation errors for single and variable fidelity scenarios for a multivariate Gaussian process regression. Evaluation of the minimax errors allows us to identify cases when the variable fidelity data provides better interpolation accuracy than the exclusively high fidelity data for the same computational budget. These results allow us to calculate the optimal shares of variable fidelity data samples under the given computational budget constraint. Real and synthetic data experiments suggest that using the obtained optimal shares often outperforms natural heuristics in terms of the regression accuracy.
References:

Gaussian Models for Data Fusion - Minimax Error of Interpolation and Optimal Design of Experiments for Variable Fidelity Data (https://goo.gl/CjgLBE) - Surrogate modeling of multifidelity data for large samples (https://goo.gl/QFkrxf)

Gaussian Process Regression and its Properties - Regression on the Basis of Nonstationary Gaussian Processes with Bayesian Regularization (https://goo.gl/haZsfM) - The Bernstein-von Mises theorem for regression based on Gaussian Processes (https://goo.gl/9whF3z) - Properties of the bayesian parameter estimation of a regression based on gaussian processes (https://goo.gl/dMd4mD)

Efficient Learning of Gaussian Process regression - Computationally Efficient Algorithm for Gaussian Process Regression in Case of Structured Samples (https://goo.gl/uXzDfW) - Adaptive Design of Experiments Based on Gaussian Processes (https://goo.gl/EjE9kt)

Surrogate Modeling for Industrial Design - GTApprox: Surrogate modeling for industrial design (https://goo.gl/mz7QtV)
Weitere Informationen
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics

Veranstalter
WIAS Berlin

Mittwoch, 29.03.2017, 13.15 Uhr (WIAS-ESH)
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Prof. Ch. Clason, Universität Duisburg-Essen:
Convex relaxation of hybrid discrete-continuous control problems
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Veranstalter
WIAS Berlin
Mittwoch, 29.03.2017, 15.15 Uhr (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. M. Demuth, Technische Universität Clausthal:
On eigenvalues of non-selfadjoint operators: A comparison of two approaches
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Weitere Informationen
Berliner Oberseminar ``Nichtlineare Partielle Differentialgleichungen'' (Langenbach Seminar)

Veranstalter
WIAS Berlin
Humboldt-Universität zu Berlin
Donnerstag, 30.03.2017, 14.00 Uhr (WIAS-ESH)
Seminar Numerische Mathematik
Prof. J.H.M. ten Thije Boonkkamp, Eindhoven University of Technology, Netherlands:
Complete flux schemes fOR conservation laws of advection-diffusion-reaction typ
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
Complete flux schemes are recently developed numerical flux approximation schemes for conservation laws of advection-diffusion-reaction type; see e.g. [1, 2]. The basic complete flux scheme is derived from a local one-dimensional boundary value problem for the entire equation, including the source term. Consequently, the integral representation of the flux contains a homogeneous and an inhomogeneous part, corresponding to the advection-diffusion operator and the source term, respectively. Suitable quadrature rules give the numerical flux. For time-dependent problems, the time derivative is considered a source term and is included in the inhomogeneous flux, resulting in an implicit semi-discretisation. The implicit system proves to have much smaller dissipation and dispersion errors than the standard semidiscrete system, especially for dominant advection. Just as for scalar equations, for coupled systems of conservation laws, the complete flux approximation is derived from a local system boundary value problem, this way incorporating the coupling between the constituent equations in the discretization. Also in the system case, the numerical flux (vector) is the superpostion of a homogeneous and an inhomogeneous component, corresponding to the advection-diffusion operator and the source term vector, respectively. The scheme is applied to multispecies diffusion and satisfies the mass constraint exactly.
References:
[1] J.H.M. ten Thije Boonkkamp and M.J.H. Anthonissen, ``The finite volume-complete flux scheme for advection-diffusion-reaction equations'', J. Sci. Comput., 46, 47--70, (2011).
[2] J.H.M. ten Thije Boonkkamp, J. van Dijk, L. Liu and K.S.C. Peerenboom, ``Extension of the complete flux scheme to systems of comservation laws'', J. Sci. Comput., 53, 552?568, (2012).

Veranstalter
WIAS Berlin