Waveguides: asymptotic methods and numerical analysis
During last decades, models of waveguides attracted much attention by physicists, mathematicians and engineers. This was motivated by many interesting mathematical questions and by the progress in different fields of physics (semiconductor physics, optics, acoustics, water waves, elasticity…).
The waveguides are usually modeled by infinite planar strips and multidimensional cylinders or layers. From the mathematical point of view, the study of waveguides is strongly connected with the asymptotic analysis of problems involving differential operators, with some large scale ratio.
From one hand, theoretical works on asymptotic analysis (singularities at corners, boundary layers at periodic walls…) often involve the treatment of waveguides problems and spectral theory related questions.
Conversely, asymptotic approaches are useful in the study of waveguides: in particular, existence of guided modes can be proved by perturbation techniques (for a small deformation of the boundary for instance). Also asymptotic models can lead to efficient numerical methods.
The main aim of the workshop is to present and discuss recent results on asymptotic methods and numerical analysis for the study of the waveguides. Moreover, it will help to reinforce the already existing cooperation between researchers of different countries and to contribute to the creation of new collaborations.