PhD Position in Mathematics (University of Basel)

Space-time adaptive methods are essential for the efficient simulation of wave phenomena in the presence of complex geometry or material interfaces. Locally refined finite element meshes, however, hamper any explicit time-marching scheme as the global time-step will be dictated by a few tiny elements. By taking smaller steps in smaller and larger steps in larger elements, local time-stepping (LTS) methods overcome that severe bottleneck without sacrificing the inherent explicitness or parallelism. Research project 1) Derive rigorous a posteriori error bounds for leapfrog (LF) based LTS methods applied to wave equations. 2) Devise a space-time adaptive algorithm which locally adapts "on the fly" the finite element mesh and the time-step to control the numerical error. Your position You will be integrated into the Numerical Analysis research group of Prof. Marcus Grote. Your main task will be to conduct research on the SNSF project "Space-time Adaptive Explicit Time- Stepping for Wave Propagation”, funded by the Swiss National Science Foundation. The position also includes a small teaching load (one homework session per week) as a teaching assistant. Your profile M.Sc. in Mathematics or Applied/Computational Mathematics strong background in standard numerical methods for ODE's, PDE's strong background in finite element methods (theory and Matlab programming) good English communication skills Application / Contact Please send (.PDF only) your cv, transcript and, if available, certificate of Master's degree together with the names and addresses of two references to marcus.grote@unibas.ch. Applications will be accepted until the position is filled. For further inquiries please contact: Prof. Marcus Grote Dept. of Mathematics and Computer Science University of Basel Spiegelgasse 1 4051 Basel Switzerland www.unibas.ch If you apply for this position please say you saw it on Academicoxy

Space-time adaptive methods are essential for the efficient simulation of wave phenomena in the presence of complex geometry or material interfaces. Locally refined finite element meshes, however, hamper any explicit time-marching scheme as the global time-step will be dictated by a few tiny elements. By taking smaller steps in smaller and larger steps in larger elements, local time-stepping (LTS) methods overcome that severe bottleneck without sacrificing the inherent explicitness or parallelism.

Research project
1) Derive rigorous a posteriori error bounds for leapfrog (LF) based LTS methods applied to wave equations.
2) Devise a space-time adaptive algorithm which locally adapts "on the fly" the finite element mesh and the time-step to control the numerical error.

Your position

You will be integrated into the Numerical Analysis research group of Prof. Marcus Grote.
Your main task will be to conduct research on the SNSF project "Space-time Adaptive Explicit Time- Stepping for Wave Propagation”, funded by the Swiss National Science Foundation.
The position also includes a small teaching load (one homework session per week) as a teaching assistant.

Your profile

M.Sc. in Mathematics or Applied/Computational Mathematics
strong background in standard numerical methods for ODE's, PDE's
strong background in finite element methods (theory and Matlab programming)
good English communication skills

Application / Contact

Please send (.PDF only) your cv, transcript and, if available, certificate of Master's degree together with the names and addresses of two references to marcus.grote@unibas.ch.
Applications will be accepted until the position is filled. For further inquiries please contact:

Prof. Marcus Grote
Dept. of Mathematics and Computer Science University of Basel
Spiegelgasse 1
4051 Basel Switzerland

www.unibas.ch

If you apply for this position please say you saw it on Academicoxy

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