PhD in Pure and Applied Mathematics

Asymptotic and Computational Analysis of Waveguides

Asymptotic and Computational Analysis of Waveguides

Academic year 2018/2019

Sommario del corso

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Program

This course will introduce the basic principles of spectral theory for elliptic partial differential operators in open and closed wave-guides. In the preliminary part we recall the basic concepts of functional analysis and spectral theory of self-adjoint operators in Hilbert spaces. The students will learn, how the periodic modulation of the cylindrical waveguide creates band gaps to the spectrum.

As an model problem, we always consider the Dirichlet-Laplacian or Neumann-Laplacian. After that we return to the problem of the existence of bound states, i.e., eigenvalues below the continuous spectrum. Here, as the model problem, we consider simple
quantum wave-guides. After introducing the concept artificial or fictitious scattering operators, we study the conditions for existence of trapped modes. In the latter part of the course we concentrate on the computational issues. As the computational tool we use in the course the open source software FreeFem++.

The course will be oriented mainly to PhD students, but interested master level students will be also accepted.

Note

TIMETABLE

AULA BUZANO (DISMA)
   Tu 6.11
   Th 8.11
   Tu 13.11
   Th 15.11
   Tu 20.11
   Th 22.11
   Tu 27.11 (aula da definire)
   Th 29.11 (aula da definire)
   Tu 4.12
   Th 6.12
   Tu 18.12
   Th. 20.12

Per informazioni contattare: keijo.ruotsalainen@oulu.fi, valeria.chiadopiat@polito.it

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