Doctoral students in Numerical Analysis

Job assignments
The main duties of doctoral students are to devote themselves to their research studies, which includes participating in research projects and third cycle courses. The work duties may also include teaching and other departmental duties (no more than 20%). A list of possible research areas is included below. The final choice of project and thesis advisor will be made jointly by the candidate and the department.

Possible research areas
In this call we have two projects within some of the department's areas of expertise, and we are planning to fill two positions. The areas are listed alphabetically with no particular priority. Please note in the application which area(s) you are interested in.

 Area 1: Design and analysis of parallel-adaptive high-order finite element solvers for multi-phase flow

The project is in the field of Numerical Analysis and Scientific Computing. A competitive fully implicit parallel and adaptive solver for multi-phase flow (e.g. binary droplet collision) based on contemporary structure preserving methods for the Navier-Stokes Cahn-Hilliard equations is to be designed, mathematically analyzed and implemented in the Distributed and Unified Numerics Environment (DUNE, https://dune-project.org). The implementation in DUNE will also include the consideration of modern hardware accelerators such as GPUs. Application to relevant test cases stemming from X-ray multi-projection imaging experiments at MAX IV and other facilities is planned. (Contact: Robert Klöfkorn)

Area 2: Gaussian process approximation for partial differential equations

This project is positioned at the interface of Numerical Analysis, Uncertainty Quantification, and Scientific Machine Learning. Manifold Gaussian processes will be used to approximate the solutions to parametric partial differential equations with data, and their approximation properties will be analyzed mathematically and tested with numerical experiments. Both error estimation and uncertainty quantification for this data-driven numerical method are to be investigated, and efforts will be made to discuss and develop strategies for overcoming the curse of dimensionality when the parametrization lies in a high-dimensional space. (Contact: Mengwu Guo)

Eligibility
A person meets the general entry requirements for third-cycle courses and study programmes if he or she: 1. has been awarded a second-cycle qualification, or 2. has satisfied the requirements for courses comprising at least 240 credits of which at least 60 credits were awarded in the second cycle, or 3. has acquired substantially equivalent knowledge in some other way in Sweden or abroad. The head of department may permit an exemption from the general entry requirements for an individual applicant, if there are special grounds.

To be admitted to the third-cycle programme in Numerical Analysis the student must have passed second-cycle courses in mathematics comprising at least 60 credits including at least 15 credits in Numerical Analysis. A degree project of at least 30 credits must be included. Equivalent knowledge acquired through corresponding programmes will be assessed individually. In order to enable interdisciplinary initiatives and important specialisations in certain areas, students with qualifications in subjects other than Numerical Analysis may be considered for admission.

Basis of Assessment

Selection for third-cycle studies is based on the student’s potential to profit from such studies. The assessment of potential is made primarily on the basis of academic results from the first and second cycle. Special attention is paid to the following

• Knowledge and skills in numerical analysis, specifically numerical methods for differential equations and numerical linear algebra are required.
• For Area 1: Programming skills, specifically Python and C++ are a strong merit. Experience with Linux based systems and knowledge of the software package DUNE is a merit (https://dune-project.org).
• For Area 2: Knowledge in uncertainty quantification, computational statistics, and/or machine learning is a strong merit.
• An assessment of ability to think independently and to formulate and tackle research problems.
• Very good oral and written proficiency in English.

Consideration will also be given to good collaborative skills, motivation and independence, and how the applicant, through his or her experience and skills, is deemed to have the abilities necessary for successfully completing the third cycle program.

The employment of doctoral students is regulated in the Swedish Code of Statues 1998: 80. Only those who are or have been admitted to PhD-studies may be appointed to doctoral studentships. When an appointment to a doctoral studentship is made, the ability of the student to benefit from PhD-studies shall primarily be taken into account. In addition to devoting themselves to their studies, those appointed to doctoral studentships may be required to work with educational tasks, research and administration, in accordance with specific regulations in the ordinance.

Type of employment

Only those admitted to third cycle studies may be appointed to a doctoral studentship. Third cycle studies at Lund University consist of full-time studies for 4 years. A doctoral studentship is a fixed-term employment of a maximum of 5 years (including 20% departmental duties). Doctoral studentships are regulated in the Higher Education Ordinance (1993:100), chapter 5, 1-7 §§.

Application procedure
Applications shall be written in Swedish or English and include a cover letter stating the reasons why you are interested in the position and in what way the research project corresponds to your interests and educational background. The application must also contain a CV, a copy of your Master’s thesis (or a summary text if the thesis is not yet completed), contact details of at least two references, copies of grade certificates, and any other documents that you wish to refer to.