Applied Mathematics

The objective of this research group is to study the whole chain from the physical modeling, over mathematical analysis and approximation theory to software development. In particular, the research concerns the analysis and numerical solution of non- linear spectral problems and simulation of wave phenomena.

One research direction of the group is photonic crystals, which are periodic structures with promising optical properties. These structures have many applications in optical communication, spectroscopy and photonic crystal nanocavity lasers. This project aims for a greater understanding of how quantum mechanical effects and losses affect the performance of these structures.

Another research focus is the analysis and computation
of resonances in open structures. Possible applications include calculations of sound pressure levels in compressor blade rows, instabilities in aircraft engines, semiconductor lasers, single- atom detection using micro disk resonators, and plasmonic nano-antennas.

Several of the proposed projects require interplay between spectral theory, finite element discretization and linear algebra. Physical understanding and optimization are also highly important for the success of the projects. Therefore, members of the group collaborate closely with the physics department and other groups within UMIT Research Lab.


Page Editor: Martin Servin

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Keywords: spectral theory, qudratic eigenvalue problems, high order finite element methods, wave phenomena, nano-optics.

Projects: Spectral analysis and approximation theory for a class of operator functions

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People

Dr. Christian Engström

Juan Carlos Araujo-Cabarcas

Axel Torshage

Contact

Christian Engström

Christian Engström

christian.engstrom@math.umu.se