### DISSERTATION JKU LINZ

For details, please refer to the curriculum of the given doctoral program as the online course cataloge KUSSS. For its solution we use the subspace version of the locally optimal preconditioned gradient method. A main advantage is that we can choose an arbitrary polynomial order on each edge, face, and cell without destroying the global exact sequence. In particular, the condition number of the corresponding preconditioned system is bounded in terms of a logarithmic expression in the local problem size. This requires the solution of a potential problem, which can be done approximately by a couple of PCG-iterations. Finally, we consider nonlinear stationary magnetic field problems in two dimensions, as an important application of our preceding analysis.

Further practical advantages will be discussed by means of the following two issues. The dissertation itself is usually written cumulatively, i. A short outline of the construction is as follows. The main contribution of this work is a general, unified construction principle for H curl – and H div -conforming finite elements of variable and arbitrary order for various element topologies suitable for unstructured hybrid meshes. Our results are again confirmed in numerical experiments.

## Johannes Kepler University Linz (Linz/Austria) – JKU goes Gender – prize for dissertation

A short outline of the construction is as follows. Our results are confirmed in numerical experiments. Since the desired eigenfunctions belong to the orthogonal complement of the gradient functions, we have to perform an orthogonal projection in each iteration step. To be more precise, if the coefficient varies only moderately in a layer near the boundary of each subdomain, the method is proved to be robust with respect to arbitrary variation in the interior of each subdomain and with respect to coefficient jumps across subdomain interfaces.

Toward an assessment of generalized opinion leadership: Prospective doctoral students should send their applications to Univ.

Generally, the dissertations written in our department are based on quantitative-empirical research studies. The hp -version of FEM combines local mesh refinement h and local increase of the polynomial order of the approximation space p.

PhD thesis as PDF file 2. A challenging topic in computational electromagnetics is the Maxwell eigenvalue problem. The fact that this exterior domain can touch arbitrarily many interior subdomains and that the diameter of its boundary is larger than those of the interior subdomains leads to special difficulties in the analysis.

Finally, we consider nonlinear stationary magnetic field problems in two dimensions, as an important application of our preceding analysis. Ulrich Langer External Referee: Finite and boundary element discretizations of elliptic partial differential equations result in large linear systems of algebraic equations.

For a listing of open PhD positions, see the latest news. This requires the solution of a potential problem, which can be done approximately by a couple of PCG-iterations.

The gradient fields of higher-order H 1 -conforming shape functions are H curl -conforming and can be chosen explicitly as shape functions for H curl. Behaviour, Risk Taking and Personality Asc.

Timo Gnambs Toward an assessment of generalized opinion leadership: Considering benchmark problems involving highly singular eigensolutions, we demonstrate the performance of the constructed preconditioners and the eigenvalue solver in combination with hp -discretization on geometrically refined, anisotropic meshes. We provide explicit condition number bounds that depend on a few geometric dissertaation, and which are quasi-optimal in special cases.

# NUMA: Finished PhD Theses – Dipl.-Ing. Clemens Pechstein

Robust Schwarz-type methods for Maxwell’s equations rely on a FE-space splitting, which also has to provide a correct splitting of the kernel of the curl-operator. For details, please refer to the curriculum of the given doctoral program as the online course cataloge KUSSS. Further practical advantages will be discussed by means of the following two issues. In particular, the condition number of the corresponding preconditioned system is bounded in terms of a logarithmic expression in the local disseetation size.

An analogous principle is used for the construction of H div -conforming basis functions.

Kurt Hoffmann Using e-learning in college Mag. The key point is dkssertation respect the de Rham Complex already in the construction of the finite element basis functions and not, as usual, only for the definition of the local FE-space.

PhD thesis as PDF file 1. Tanja Jardin Computer-aided cooperative learning Furthermore, the bound is independent of jumps in the diffusion coefficient across subdomain interfaces. Current dissertations Author Working title Mag.

The main difficulty in the construction of efficient and parameter-robust preconditioners for electromagnetic problems is indicated by the different scaling of solenoidal and irrotational fields in the curl-curl problem.

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