Talks

Deformable image registration is a key technology in medical imaging; there the goal is to compute a meaningful spatial correspondence between two or more images of the same scene. One approach is to use an optimal control formulation to compute a stationary velocity field that parameterize the deformation map. The same methods can be used to estimate the motion of contrast agents from 3d ultrasound images.

This is work-in-progress; in the talk I’ll introduce the application problem and discuss computational techniques for its solution, with a focus on using parallelization in time to reduce the time-to-solution. It should be accessible for a broad audience.

An overview talk about interesting topics in mathematical physics I used over the last years. It should be accessible for a broader audience.

This will be an overview talk on Evolution Equations (and a bit on Evolutionary Equations).

We consider the Caffarelli-Silvestre problem in a Banach space $X$ which is finding a solution $u$ to the problem
\[
u''(t) + \frac{1-2\alpha}{t} u'(t) = Au(t), \quad u(0)=x
\]
where $\alpha \in (0,1)$ is a given parameter and $A \in \mathcal{S}_{\omega}$ is a sectorial operator. Goal of the presentation will be to sketch of a proof that a solution got to be unique (we will not deal with existence but this is a much easier anyway).
The proof is simpler and independent of what can be found in

J. Meichsner and C. Seifert. On the Harmonic Extension Aproach to Fractional Powers in Banach Spaces. arxiv preprint https://arxiv.org/abs/1905.06779

All existing QR decompositions for hierarchical matrices suffer from numerical drawbacks that limit their use in many applications. In this talk, I will present a new method based on the recursive WY-based QR decomposition by Elmroth and Gustavson. It is an extension of an already existing method for a subclass of hierarchical methods developed by Kressner and Susnjara.

I will try to keep things as simple as possible and give a short introduction to hierarchical matrices as well. Previous knowledge of hierarchical matrices is not necessary to understand the basic ideas and main obstacles of the new algorithm. Although this talk is similar to my last one in November I will try to focus on some aspects we have only touched upon and present some new results as well.

Partial differential equations can be solved numerically by the radial basis function-generated finite difference (RBF-FD) method, which can be viewed as a generalization of the finite difference method to unstructured point sets.
A so-called stencil is computed for each interior node and radial basis functions are used for the computation of the stencil weights. The discretization error depends on the type of the point set (i.e. on the number of interior and boundary nodes and their distribution), the stencil size, the RBF type and the shape parameter of the RBF.
In this talk, I present an introduction of the RBF-FD method and a numerical analysis of the influence of the various parameters on the discretization error. I focus on Poisson's equation and on the convection-diffusion equation in three-dimensions.

I will introduce myself and talk about my master thesis.

The topic of my thesis was "On periodic finite sections", which are an approximation method based on the regular finite section method. The methods are used to approximate (the inverses of) infite matrices by finite matrices.