Open PhD Positions in the Doctoral Program
Basic Information on the Open PhD Positions
We offer employment contracts for PhD students for the maximum duration of three years. The first year of employment will be a probationary year. A DK contract guarantees a yearly gross salary of EUR 28,350.00 (net salary: approx. 20,000.00) for full employment including a social and health insurance at the Austrian insurance agency for public employees.
Depending on the project, your place of work will either be at the JKU campus in Linz, or the RISC Institute at Hagenberg. There are students' accommodations near both places. An hourly shuttle bus is commuting between JKU and Hagenberg.
Projects with Open Positions
- DK4: Nonstandard Finite Element Solvers for Second-Order Elliptic Boundary Value Problems
We propose to investigate non-standard finite element schemes for solving second-order elliptic boundary value problems and time-dependent problems. In the first and second funding period (2008-2011-2014), we have successfully studied interface-concentrated finite element techniques, finite element methods which are based on boundary element technologies called now BEM-based FEM, and Multiharmonic Finite Element Methods for time-periodic parabolic boundary value problems. Other non-standard methods for the numerical solution of time-dependent Partial Differential Equations (PDEs) are the so-called space-time methods which permits not only a perfect parallelization in space and time, but also a big flexibility in space-time adaptivity. Moreover, moving spatial domains or interfaces are fixed in the space-time cylinder. In the proposed PhD project, we want to connect space-time methods
with the Isogeometric Analysis (IgA) Discretization technique, that was introduced by T.J.R. Hughes and co-authors in 2005 and uses the same basis functions (e.g. NURBS) for the representation of the geometry of the computational domain and for the approximation of the solution of the PDEs. The construction and analysis of stable space-time IgA schemes and fast parallel solvers for the resulting large-scale space-time systems of linear algebraic equations as well as their implementation on parallel computers are the ultimate goal of the PhD project.
The DK provides a very good infrastructure for supercomputing at the Johannes Kepler University Linz and at RICAM. The cooperation with other DK projects, in particular, the cooperation with DK3 (geometrical aspects of IgA) and with our international research partners will foster the research work of the PhD student. The specific choice of the PhD topic depends on the preparatory training, qualifications and knowledge of the PhD candidate.
- DK6: Computer Algebra Tools for Special Functions
Supervisor: Prof. Peter Paule
This project deals with the development of computer algebra tools for special function manipulation, including aspects of computer-assisted proving. For many years the proposer's group has been working in this area; see the web page of the RISC Algorithmic Combinatorics group. Despite these efforts this research area is still in its early stage and much remains to be done. Recent achievements in this subproject of the DK concerned the algorithmic treatment of elliptic functions, theta series, and modular forms. There are various options of continuing this kind of research; nevertheless, depending on the scientific expertise of the applicant, the project's scope is sufficiently wide to consider also other classes or aspects of special functions.
- DK13: Multivariate Symbolic Asymptotics
The goal of this project is the development of computer algebra algorithms for obtaining asymptotic information of functions and sequences in several variables. In view of recent developments in the interesting open questions ranging from rather theoretical considerations to very concrete applications connecting to other parts of mathematics and engineering.
- DK15: Extension of Algorithms for D-finite functions
Supervisor: Dr. Veronika Pillwein
The goal in this project part is to extend existing algorithms for the symbolic treatment of functions defined by linear ordinary differential equations with polynomial coefficients (D-finite functions) to more general classes of functions and to implement those algorithms. In particular we consider (a) closure properties for D-finite functions and algorithms introduced in the holonomic systems approach by Zeilberger (and subsequent work), and (b) certified arbitrary precision evaluation (and related topics such as uniform approximation or factorization) as recently investigated by Mezzarobba et al. (based on work of Chudnovsky & Chudnovsky, van der Hoeven,etc.). As the first more general class we consider DD-finite functions, that is, functions defined by linear ODEs with D-finite coefficients. This project combines both symbolic and numeric aspects.
Applications are welcome until June 30th, 2015. Start of the PhD project: October 1, 2015.
About Linz and Hagenberg
Linz is the capital of Upper Austria and the third-largest city of Austria. It is located in the north centre of Austria on both sides of the river Danube. Linz offers a perfect blend of cultural pursuits and fine sightseeing options, e.g. the Landstraße, the pilgrimage church on the Pöstlingberg hill, the Brucknerhaus (concert hall), and the Lentos Art Museum.
About 20 km north of Linz, surrounded by the beautiful countryside of the Mühlviertel, you can find the village Hagenberg, where the Research Institute for Symbolic Computation (RISC) is located. There is a direct bus connection between the RISC institute and the Johannes Kepler University (JKU) Linz.
Application Requirements and Procedure
In order to apply for a position in the Doctoral Program a candidate has to provide the following information/documents:
A letter of application stating clearly his/her background and why he/she is applying,
A curriculum vitae including a photo of the applicant,
The project(s) of the Doctoral Program that is/are of interest to the applicant,
A list of all courses that the applicant has taken during his/her university studies, including the number of hours credited and the grades,
Two recommendation letters (to be sent to email@example.com),
The diploma or master thesis.
In case of technical problems when submitting, please turn to firstname.lastname@example.org.