In applications such as very large scale integration chip design models are typically huge. The same is true in mechanical engineering, especially when the models are complex finite element discretizations. To speed up ...

Sampling inequalities play an important role in deriving error estimates for various reconstruction processes. They provide quantitative estimates on a Sobolev norm of a function, defined on a bounded domain, in terms of ...

The numerical simulation of non-Newtonian fluids is of high practical relevance since most complex fluids developed in the chemical industry are not correctly modeled by classical fluid mechanics. In this thesis, we implement ...

In this thesis, we discuss numerical methods for the solution of the high-dimensional backward Kolmogorov equation, which arises in the pricing of options on multi-dimensional jump-diffusion processes.
First, we apply ...

Diese Arbeit befasst sich mit Dünngitterverfahren zur Lösung von höherdimensionalen Problemen. Sie zeigt drei neue Aspekte von Dünnen Gittern auf: Erweiterungen der elementaren Werkzeuge zur Arbeit mit Dünnen Gittern, eine ...

Peridynamics is an accepted method in engineering for modeling crack propagation on a macroscopic scale. However, the sensitivity of the method to two important model parameters – elasticity and the particle density – has ...

In this paper we deal with the construction of lower-dimensional manifolds from high-dimensional data which is an important task in data mining, machine learning and statistics. Here, we consider principal manifolds as the ...

In this paper, we will discuss the discretization error for the regression setting and derive error bounds relying on the approximation properties of the discretized space. Furthermore, we will point out how the sampling ...

We compare the cost complexities of two approximation schemes for functions f ∈ H^p(Ω₁ × Ω₂) which live on the product domain Ω₁ × Ω₂ of sufficiently smooth domains ......

We present a computationally efficient sparse grid approach to allow for multiscale simulations of non-Newtonian polymeric fluids. Multiscale approaches for polymeric fluids often involve model equations of high dimensionality. ...