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Wednesday, 01.03.2017, 15.15 Uhr (WIAS-406)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. P. Colli, University of Pavia, Italien:
About a non-smooth regularization of a forward-backward parabolic equation
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
A variation of the Cahn-Hilliard equation, describing diffusion of species by a suitable regularization of a "forward-backward" parabolic equation is discussed. In the concerned system, the general viscous regularization is expressed by a maximal monotone graph acting on the time derivative of the concentration and presenting a strong coerciveness property. The phase variable stands for the concentration of a chemical species and it evolves under the influence of a non-convex free energy density. For the chemical potential a non-homogeneous Dirichlet boundary condition is assumed. Existence and continuous dependence results are shown. The talk reports on a joint work with E. Bonetti and G. Tomassetti.

Further Informations
Berliner Oberseminar ``Nichtlineare Partielle Differentialgleichungen'' (Langenbach Seminar)

Host
WIAS Berlin
Humboldt-Universität zu Berlin
Thursday, 02.03.2017, 09.00 Uhr (WIAS-406)
Halbleiterseminar
Dr. D. H. Doan, WIAS:
A unified Scharfetter Gummel scheme
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Further Informations
Halbleiterseminar

Host
WIAS Berlin
Thursday, 02.03.2017, 14.00 Uhr (WIAS-ESH)
Seminar Numerische Mathematik
Dr. L. O. Müller, Norwegian University of Science and Technology:
A local time stepping solver for one-dimensional blood flow
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We present a finite volume solver for one-dimensional blood flow simulations in networks of elastic and viscoelastic vessels, featuring high-order space-time accuracy and local time stepping (LTS). The solver is built on:
(i) a high-order finite-volume type numerical scheme,
(ii) a high-order treatment of the numerical solution at internal vertexes of the network (junctions);
(iii) an accurate LTS strategy.
Several applications of the method will be presented. First, we apply the LTS scheme to the Anatomically Detailed Arterial Network model (ADAN), comprising 2142 arterial vessels. Second, we show results of a computational study where the ADAN model is coupled to automatically generated microvascular networks in order to elucidate aspects on the pathopysiology of small vessel disease for cerebral arteries.

Host
WIAS Berlin
Friday, 03.03.2017, 10.00 Uhr (WIAS-ESH)
Seminar Partielle Differentialgleichungen
S. Melchionna, University of Vienna, Österreich:
A variational approach to symmetry, monotonicity and comparison for doubly-nonlinear equations
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We advance a variational method to prove qualitative properties such as symmetries, monotonicity, upper and lower bounds, sign properties, and comparison principles for a large class of doubly-nonlinear evolutionary problems including gradient flows, some nonlocal problems, and systems of nonlinear parabolic equations. Our method is based on the so-called Weighted-Energy-Dissipation (WED) variational approach. This consists in defining a global parameter-dependent functional over entire trajectories and proving that its minimizers converge to solutions to the target problem as the parameter goes to zero. Qualitative properties and comparison principles can be easily proved for minimizers of the WED functional and, by passing to the limit, for the limiting problem. Several applications of the abstract results to systems of nonlinear PDEs and to fractional/nonlocal problems are presented.

Further Informations
Seminar Partielle Differentialgleichungen

Host
WIAS Berlin
Tuesday, 14.03.2017, 10.15 Uhr (WIAS-406)
Seminar Nichtlineare Optimierung und Inverse Probleme
Dr. J. Linn, Fraunhofer-Institut für Techno- und Wirtschaftsmathematik, Kaiserslautern:
Simulation of flexible cables in car assembly
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Host
WIAS Berlin
Thursday, 16.03.2017, 14.00 Uhr (WIAS-ESH)
Seminar Numerische Mathematik
M. Cicuttin, CERMICS - ENPS, Frankreich:
Implementation of Discontinuous Skeletal methods on arbitrary-dimensional, polytopal meshes using generic programming
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Discontinuous Skeletal methods are devised at the mathematical level in a dimension-independent and cell-shape-independent fashion. Their implementation, at least in principle, should conserve this feature: a single piece of code should be able to work in any space dimension and to deal with any cell shape. It is not common, however, to see software packages taking this approach. In the vast majority of the cases, the codes are capable to run only on few very specific kinds of mesh, or only in 1D or 2D or 3D. On the one hand, this can happen simply because a fully general tool is not always needed. On the other hand, the programming languages commonly used by the scientific computing community (in particular Fortran and Matlab) are not easily amenable to an implementation which is generic and efficient at the same time. The usual (and natural) approach, in conventional languages, is to have different versions of the code, for example one specialized for 1D, one for 2D and one for 3D applications, making the overall maintenance of the codes rather cumbersome. The same considerations generally apply to the handling of mesh cells with various shapes, i.e., codes written in conventional languages generally support only a limited (and set in advance) number of cell shapes.
Generic programming offers a valuable tool to address the above issues: by writing the code generically, it is possible to avoid making any assumption neither on the dimension (1D, 2D, 3D) of the problem, nor on the kind of mesh. In some sense, writing generic code resembles writing pseudocode: the compiler will take care of giving the correct meaning to each basic operation. As a result, with generic programming there will be still differents versions of the code, but they will be generated by the compiler, and not by the programmer. As these considerations suggest, generic programming is a static technique: if correctly realized, the abstractions do not penalize the performance at runtime, because they will leave no trace in the generated code.
In this talk we will discuss how the Hybrid High Order method is implemented atop of DiSk++, a newly developed library for the generic implementation of Discontinuous Skeletal methods.

Host
WIAS Berlin
Monday, 20.03.2017, 14.00 Uhr (WIAS-ESH)
Seminar Quantitative Biomedizin
Th. Niendorf, Charité Max Delbrück Center for Molecular Medicine:
Explorations into ultrahigh field magnetic resonance
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
The development of ultrahigh field magnetic resonance (UHF-MR) is moving forward at an amazing speed that is breaking through technical barriers almost as fast as they appear. UHF-MR has a staggering number of potential uses in neuroscience, neurology, radiology, cardiology, internal medicine, physiology, oncology, nephrology, ophthalmology and other related clinical fields. With almost 40,000 MR examinations already performed at 7.0 Tesla, the reasons for moving UHF-MR into clinical applications are more compelling than ever.

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

Host
WIAS Berlin
Wednesday, 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
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Berliner Oberseminar ``Nichtlineare Partielle Differentialgleichungen'' (Langenbach Seminar)

Host
WIAS Berlin
Humboldt-Universität zu Berlin
Thursday, 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
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
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).

Host
WIAS Berlin
Thursday, 06.04.2017, 14.00 Uhr (WIAS-ESH)
Seminar Numerische Mathematik
Prof. D. Silvester, University of Manchester, GB:
Accurate time-integration strategies for modelling incompressible flow bifurcations
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Eigenvalue analysis is a well-established tool for stability analysis of dynamical systems. However, there are situations where eigenvalues miss some important features of physical models. For example, in models of incompressible fluid dynamics, there are examples where linear stability analysis predicts stability but transient simulations exhibit significant growth of infinitesimal perturbations. In this study, we show that an approach similar to pseudo-spectral analysis can be performed inexpensively using stochastic collocation methods and the results can be used to provide quantitive information about the nature and probability of instability.

Host
WIAS Berlin
Wednesday, 26.04.2017, 10.00 Uhr (WIAS-ESH)
Forschungsseminar Mathematische Statistik
J. Weed, Massachusetts Institute of Technology, USA:
Optimal rates of estimation for the multi-reference alignment problem
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
How should one estimate a signal, given only access to noisy versions of the signal corrupted by unknown circular shifts? This simple problem has surprisingly broad applications, in fields from structural biology to aircraft radar imaging. We describe how this model can be viewed as a multivariate Gaussian mixture model whose centers belong to an orbit of a group of orthogonal transformations. This enables us to derive matching lower and upper bounds for the optimal rate of statistical estimation for the underlying signal.. These bounds show a striking dependence on the signal-to-noise ratio of the problem. Joint work with Afonso Bandeira and Philippe Rigollet.

Further Informations
Forschungsseminar ``Mathematische Statistik''

Host
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
International Research Training Group 1792