Postdoctoral Position (2 years) in Cut Finite Element Methods

Updated: 6 months ago
Deadline: 03 Dec 2021

The Department of Mathematics and Mathematical Statistics at Umeå University is opening a postdoctoral position in computational mathematics focusing on development, analysis, and implementation of cut finite element methods on time dependent domains. The project is funded by the Swedish Research Council and the research program Essence. Last day to apply: December 3, 2021.

The appointment is for two years at the Department of Mathematics and Mathematical Statistics. The successful candidate is expected to take on the research question with enthusiasm and high ambitions, actively engage with collaborators, and to participate in the daily activities of the research environment. Starting date is in the beginning of 2022.

Project description and working tasks
The cut finite element method (CutFEM) is a new type of embedded method for solving partial differential equations that does not require the construction of a standard mesh that conforms to the domain boundary. Instead, the boundary is allowed to cut through the elements in an arbitrary fashion, facilitating very flexible geometry descriptions that are independent of the computational mesh. This feature makes cut finite element methods particularly suitable for problems where the domain is changing throughout the course of the simulation, for instance in problems with moving interfaces. Properly designed cut finite element methods have similar approximation and stability properties as standard finite element methods.

In this project we will focus on development, analysis, and implementation of cut finite element methods for parabolic problems on time dependent domains. In particular, we will develop:

  • Space time formulations and error estimates in space time norms
  • Techniques for stabilization of the cut finite element method
  • Error estimates for nonlinear problems where the evolution of the domain is coupled to the physics
  • Optimal order end time error estimates
  • A concept of discrete stability and discrete parabolic smoothing

Qualifications
The applicant must have earned a PhD or a foreign degree that is deemed equivalent to a PhD in computational mathematics, applied mathematics or equivalent academic competence. Applicants must have completed their PhD within three years of the application deadline but exceptions will be considered in case of illness, parental leave, clinical practice, positions of trust within labour unions, or other similar circumstances.

Documented knowledge and proven experience of development and analysis of cut finite element methods on time dependent domains is required. Excellent programming skills in MATLAB and excellent communication skills in written and spoken English are required.

The research tasks require great independence, accuracy and dedication. Documented scientific momentum and the ability to work independently as well as part of a research group are merits.

A track record of publication and experience in cut finite element methods is a strong merit. Experience of interdisciplinary research projects and cross-disciplinary collaboration, in particular within the specific application area, is qualifying.

Application
The complete application should contain the following documents:

  • A cover letter (one page) describing yourself, your previous research achievements, your preferred area of scientific application, and your motivation for your interest in this position.
  • A Curriculum Vitae with a list of publications.
  • Certified copies of doctoral degree certificate and other relevant degree certificates as well as relevant grades.
  • Copies of (maximum of five) relevant publications plus your PhD thesis.
  • A research plan, 3-4 pages in length, which describes your research interests and ideas on how you can contribute to the research project.
  • Contact details to two reference persons who are familiar with your qualifications.
  • Other possible documents you wish to claim.

The Department of Mathematics and Mathematical Statistics values the qualities that an even gender distribution brings to the department, and therefore we particularly encourage women to apply for the position.

The application, including attachments, should be written in Swedish or English. You apply via our e- recruitment system Varbi. Log in and apply via the button at the bottom of the page.

The deadline for applications is December 3, 2021.

Further information
Further information is provided by Professor Mats G. Larson, mats.larson@umu.se. You can also contact the Head of department Åke Brännström for additional questions at ake.brannstrom@umu.se

More information about the department: https://www.umu.se/en/department-of-mathematics-and-mathematical-statistics/


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