Thu, 21 May 2015

16:00 - 17:00
L5

Anabelian Geometry with étale homotopy types

Jakob Stix
(University of Heidelberg)
Abstract

Classical anabelian geometry shows that for hyperbolic curves the etale fundamental group encodes the curve provided the base field is sufficiently arithmetic. In higher dimensions it is natural to replace the etale fundamental group by the etale homotopy type. We will report on progress obtained in this direction in a recent joint work with Alexander Schmidt.

 

**Joint seminar with Logic. 

Thu, 21 May 2015

16:00 - 17:00
L5

Anabelian Geometry with étale homotopy types

Jakob Stix
(University of Heidelberg)
Abstract

Classical anabelian geometry shows that for hyperbolic curves the etale fundamental group encodes the curve provided the base field is sufficiently arithmetic. In higher dimensions it is natural to replace the etale fundamental group by the etale homotopy type. We will report on progress obtained in this direction in a recent joint work with Alexander Schmidt.

 

**Joint seminar with Number Theory. Note unusual time and place**

Thu, 14 Feb 2002

14:00 - 15:00
Comlab

Adaptive finite elements for optimal control

Dr Roland Becker
(University of Heidelberg)
Abstract

A systematic approach to error control and mesh adaptation for

optimal control of systems governed by PDEs is presented.

Starting from a coarse mesh, the finite element spaces are successively

enriched in order to construct suitable discrete models.

This process is guided by an a posteriori error estimator which employs

sensitivity factors from the adjoint equation.

We consider different examples with the stationary Navier-Stokes

equations as state equation.

Fri, 20 Feb 2004

14:00 - 15:00
Comlab

A discontinuous Galerkin method for flow and transport in porous media

Dr Peter Bastian
(University of Heidelberg)
Abstract

Discontinuous Galerkin methods (DG) use trial and test functions that are continuous within

elements and discontinuous at element boundaries. Although DG methods have been invented

in the early 1970s they have become very popular only recently.

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DG methods are very attractive for flow and transport problems in porous media since they

can be used to solve hyperbolic as well as elliptic/parabolic problems, (potentially) offer

high-order convergence combined with local mass balance and can be applied to unstructured,

non-matching grids.

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In this talk we present a discontinuous Galerkin method based on the non-symmetric interior

penalty formulation introduced by Wheeler and Rivi\`{e}re for an elliptic equation coupled to

a nonlinear parabolic/hyperbolic equation. The equations cover models for groundwater flow and

solute transport as well as two-phase flow in porous media.

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We show that the method is comparable in efficiency with the mixed finite element method for

elliptic problems with discontinuous coefficients. In the case of two-phase flow the method

can outperform standard finite volume schemes by a factor of ten for a five-spot problem and

also for problems with dominating capillary pressure.

Thu, 31 May 2007

14:00 - 15:00
Rutherford Appleton Laboratory, nr Didcot

Model based design of optimal experiments for dynamic processes

Dr Ekaterina Kostina
(University of Heidelberg)
Abstract

The development and quantitative validation of complex nonlinear differential equation models is a difficult task that requires the support by numerical methods for sensitivity analysis, parameter estimation, and the optimal design of experiments. The talk first presents particularly efficient "simultaneous" boundary value problems methods for parameter estimation in nonlinear differential algebraic equations, which are based on constrained Gauss-Newton-type methods and a time domain decomposition by multiple shooting. They include a numerical analysis of the well-posedness of the problem and an assessment of the error of the resulting parameter estimates. Based on these approaches, efficient optimal control methods for the determination of one, or several complementary, optimal experiments are developed, which maximize the information gain subject to constraints such as experimental costs and feasibility, the range of model validity, or further technical constraints.

Special emphasis is placed on issues of robustness, i.e. how to reduce the sensitivity of the problem solutions with respect to uncertainties - such as outliers in the measurements for parameter estimation, and in particular the dependence of optimum experimental designs on the largely unknown values of the model parameters. New numerical methods will be presented, and applications will be discussed that arise in satellite orbit determination, chemical reaction kinetics, enzyme kinetics and robotics. They indicate a wide scope of applicability of the methods, and an enormous potential for reducing the experimental effort and improving the statistical quality of the models.

(Based on joint work with H. G. Bock, S. Koerkel, and J. P. Schloeder.)

Thu, 18 Nov 2010

14:00 - 15:00
Gibson Grd floor SR

Optimization with time-periodic PDE constraints: Numerical methods and applications

Mr. Andreas Potschka
(University of Heidelberg)
Abstract

Optimization problems with time-periodic parabolic PDE constraints can arise in important chemical engineering applications, e.g., in periodic adsorption processes. I will present a novel direct numerical method for this problem class. The main numerical challenges are the high nonlinearity and high dimensionality of the discretized problem. The method is based on Direct Multiple Shooting and inexact Sequential Quadratic Programming with globalization of convergence based on natural level functions. I will highlight the use of a generalized Richardson iteration with a novel two-grid Newton-Picard preconditioner for the solution of the quadratic subproblems. At the end of the talk I will explain the principle of Simulated Moving Bed processes and conclude with numerical results for optimization of such a process.

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