The Department of Mathematics and Mathematical Statistics is opening a PhD position in the project computational methods for wave propagation. The position involves four years of doctoral studies, including participation in research and postgraduate courses. Last day to apply is May 31, 2022.
Project description and tasks
There are many challenges to simulate wave propagation in realistic 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 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, analyze, and implement fast and reliable numerical methods for solving wave propagation problems. Much attention will be placed on the numerical analysis perspective, such as stability analysis, error estimates, conditioning, and time-step restriction. The project will be carried out in collaboration with the computational mathematics group at Umeå University and our external collaborators.
The doctoral student will be admitted for studies at third-cycle level in subject 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 ECTS credits, of which at least 60 ECTS 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 ECTS credits in computational science and engineering courses, of which at least 30 ECTS 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 computing science, mathematics and mathematical statistics. Applicants who in some other system either within Sweden or abroad have acquired largely equivalent skills are also eligible.
Good knowledge of English language are key requirements. Documented knowledge and experience in numerical methods for partial differential equations are required. Programming skills, for example Matlab, Python, or Julia, are required. Experience in C/C++/Fortran and parallel computing is a merit. Documented knowledge in geophysics and astrophysics is also a merit.
You are expected to play an active role in the development of this doctoral project and also within 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 can work in a structured, flexible, and solution-oriented manner.
Assessments of the applicants are based on their qualifications and ability to benefit from the doctoral study they will receive.
About the employment
The position is intended to result in a doctoral degree. The main task of the doctoral student is to pursue their doctoral studies, including active participation in research and doctoral courses. The duties may include teaching or 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 part-time. Salary is set in accordance with the established salary ladder for PhD positions at Umeå University. The employment starts on September 1, 2022, or according to agreement.
Application is made through our recruitment system by May 31, 2022. Log in and apply via the button at the bottom of the page. The application must consist of the following documents written in English:
- Personal letter with a brief description of your qualifications and research interests. Justify why you are applying for the position and describe how your qualifications and merits are relevant to the employment. Maximum 2 pages.
- Curriculum vitae.
- Authenticated copies of bachelor and master’s degree certificates, diplomas or equivalent, including documentation of completed academic courses, received grades, and possibly other certificates.
- Copies of relevant work such as master’s thesis or articles that you have authored or co-authored. If the master’s thesis has not been completed before the application deadline, a summary of the master’s thesis project and current progress shall be included. The summary can at most be 5 pages, including figures and references.
- GMAT (or GRE) and TOEFL/IELTS test scores, if available.
- Contact information for two references.
The Department of Mathematics and Mathematical Statistics values the qualities that a gender balance brings to the department and therefore we particularly encourage female applicants.
More information about the position is provided by Assistant Professor Siyang Wang ([email protected])
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