Doctoral student in numerical analysis - Hiring in process/Finished, not possible to apply

The position will be placed at the Division of Mathematics LTH and Numerical Analysis at the Centre for Mathematical Sciences. Today the division has circa 60 employees working in a broad spectrum of applied and pure mathematics. The research in numerical analysis is foremost focused on the design and analysis of approximation methods for partial differential equations (PDEs).

Examples of ongoing research projects include splitting schemes for nonlinear parabolic equations, domain decomposition methods for fluid-structure interactions, PDE based schemes for machine learning and integral methods for elliptic equations. The research is connected to several international collaborations and the successful candidate will be part of a stimulating and rewarding work environment within a trending research area.

Project description
The overall purpose of the project is to design and analyze the next generation of partitioning methods for time dependent PDEs. These equations are frequently encountered in applications and are numerically challenging due to the lack of smooth solutions and the need for implicit time integration. The latter typically results in large-scale computations that require the usage of parallel and distributed hardware.

Partitioning strategies, such as splitting schemes and domain decomposition methods, are often proposed as an efficient way to make use of such hardware. However, the full potential of the partitioning approach is rarely utilized for time dependent PDEs. Thus, there is a large demand, from both industry and academia, to develop new partitioning strategies tailored for time dependent systems.

We are going to develop a genuinely new approach for partitioning schemes, by merging elements from numerical analysis of splitting schemes and domain decomposition with the framework of semigroup theory. The schemes developed in the project will be used in our interdisciplinary collaborations, e.g., in machine learning and stress corrosion simulations.

Work duties
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 can also include teaching and other departmental duties (no more than 20%).

Admission requirements
A person meets the general admission requirements for third-cycle courses and study programmes if he or she:

• has been awarded a second-cycle qualification, or
• has satisfied the requirements for courses comprising at least 240 credits of which at least 60 credits were awarded in the second cycle, or
• has acquired substantially equivalent knowledge in some other way in Sweden or abroad. 

A person meets the specific admission requirements for third cycle studies in numerical analysis if he or she has

• at least 90 credits of relevance to the subject area, of which at least 60 credits from the second cycle and a specialised project of at least 30
  second-cycle credits in the field, or
• a second second-cycle degree in a relevant field

In practice this means that the student should have achieved a level of knowledge in mathematics that corresponds to that of a Master of Science program in Engineering Mathematics or Engineering Physics or a Master’s degree in mathematics or applied mathematics.

Additional requirements:

• Very good oral and written proficiency in English.
• A project-relevant master's thesis.
• Good programming skills in Matlab or Python. 

Assessment criteria
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:

1. Knowledge and skills relevant to the thesis project and the subject of study.
2. An assessment of ability to work independently and to formulate and tackle research problems.
3. Written and oral communication skills
4. Other experience relevant to the third-cycle studies, e.g., professional experience.
    

Other assessment criteria:

• Experience of semigroup theory and numerical analysis of time dependent PDEs. 

Consideration will also be given to good collaborative skills, drive 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 programme.

Terms of employment
Only those admitted to third cycle studies may be appointed to a doctoral studentship. Third cycle studies at LTH 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 §§.

Instructions on how to apply
Applications should be written in 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, degree certificate or equivalent, and other documents you wish to be considered (grade transcripts, contact information for your references, letters of recommendation, etc.). You are also required to answer the job specific questions.