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PhD position in computational methods for wave phenomena

Department of Mathematics and Mathematical Statistics




  • Type of employment Temporary position longer than 6 months
  • Extent 100%
  • Place Umeå

The Department of Mathematics and Mathematical Statistics at Umeå University is opening a PhD position in computational science and engineering with specialization in mathematics. Apply latest November 28, 2021.

Project description and tasks
There are many challenges to simulate wave propagation in realistic geological models. For example, waves propagate for many periods in a domain much larger than the wavelength, thus requiring scalable high-order methods that are suitable for implementation on modern parallel computers; complex geometry at cracks, material interfaces and boundaries imposes difficulties for generating high-quality meshes; heterogeneous material properties with discontinuities and multiscale features require special techniques to achieve high-order accuracy.  As an example, the elastic wave equation models seismic waves generated by earthquakes that propagate through the Earth layers and on the Earth surface. The surface waves give rise to ground shaking, and can cause enormous damages to the surrounding communities. To mitigate such seismic hazards, reliable simulation of wave propagation is a vital tool. The governing equation in this example is expressed as a system of hyperbolic partial differential equations.

In this project, we will develop numerical methods that address the above challenges by combining the efficiency of finite difference methods and the flexibility of discontinuous Galerkin methods. Much attention will be placed on the numerical analysis perspective, such as stability analysis, error estimates, conditioning and time-step restriction. We will implement and verify the developed methods for large-scale benchmark problems in geophysics.

The PhD student will be admitted to third-cycle studies in computational science and engineering with specialization in mathematics.

To be admitted for studies at third-cycle level the applicant is required to have completed a second cycle level degree, or completed course requirements of at least 240 credits, of which at least 60 credits are at second-cycle level, or have an equivalent education from overseas, or equivalent qualifications.

To fulfil the specific entry requirements to be admitted for studies at third-cycle level in computational science and engineering, the applicant is required to have completed at least 90 credits in computational science and engineering courses, of which at least 30 credits shall have been acquired at second-cycle level. Computational science and engineering courses refers to courses with major quantitative, statistical or computing science elements, such as courses in mathematics, numerical analysis, computer science and relevant courses in physics and geology. Applicants who in some other system either within Sweden or abroad have acquired largely equivalent skills are also eligible.

Good knowledge of English language, both written and spoken, are key requirements. Documented knowledge in numerical methods for partial differential equations are required. Programming skills, preferrably Matlab or Python, are required. Experience in C/C++/Fortran and parallel computing is a merit. Documented knowledge in geophysics is also a merit.

You are expected to play an active role in the development of this doctoral project and also in the department. You are expected to have a scientific and result-oriented approach for your work. You should therefore have a very good communication and collaboration ability. You are able to work in a structured, flexible and solution-oriented manner.

The assessments of the applicants are based on their qualifications and their ability to benefit from the doctoral-level education they will receive.

About the employment
The position is intended to result in a doctoral degree and the main task of the PhD student is to pursue their doctoral studies which include participation in research and doctoral courses. The duties can include teaching and other departmental work (up to a maximum of 20%). The employment is limited to the equivalent of four years of full-time (48 months) or up to five years if teaching is included. The salary is fixed according to the established salary level for doctoral employment. The employment starts in the spring of 2022 or according to agreement.

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 2021-11-28. A complete application should contain the following documents:

  • A cover letter with a brief description of your academic background. Motivate why you are applying for the position and describe how your qualifications and merits are relevant to the project and requirements. (maximum 1 page)
  • A curriculum vitae.
  • Authenticated copies of degree certificates diplomas or equivalent, including documentation of completed academic courses, grades obtained, and possibly other relevant certificates.
  • Copies of relevant work such as Master’s thesis or articles that you have authored or co-authored. If the master thesis has not been completed before the application deadline, a summary of the master thesis project and current progress shall be included. The summary can be at most 5 pages including figures and references (fontsize 11).
  • Contact information for two reference persons.

Applicants with a degree not from a Swedish university are encouraged to provide results obtained from GMAT (and/or GRE) and TOEFL/IELTS tests if available.

The Department of Mathematics and Mathematical Statistics values ​​the qualities that an even gender distribution brings to the department, and therefore we particularly encourage female applicants. The procedure for recruitment for the position is in accordance with the Higher Education Ordinance (chapter 12, 2§) and the decision regarding the position cannot be appealed.

Further information
Further information is provided by Assistant Professor Siyang Wang, You can also contact the head of department Åke Brännström for additional questions at

More information about the department:

We look forward to receiving your application!


Spring 2022 according to agreement


Siyang Wang, assistant professor

+46 90 7867032,

Registration number

AN 2.2.1-1340-21


Monthly salary

Union representative


+46 90 7865365


+46 90 7865296


+46 90 7865431




Umeå University wants to offer an equal environment where open dialogue between people with different backgrounds and perspectives lay the foundation for learning, creativity and development. We welcome people with different backgrounds and experiences to apply for the current employment. We kindly decline offers of recruitment and advertising help.