[seminar] Zajednicki seminar FO i MO, Engstrom

[hbuljan at phy.hr]

Predavanje je danas u 12.15 sati (tocno)!
Pozdrav
HB


--------------------------- Originalna poruka ----------------------------
Naslov: [fizika] Zajednicki seminar FO i MO, Engstrom
Šalje:  hbuljan at phy.hr
Datum:  Pet, svibanj 13, 2011 4:14 pm
Prima:  fizika at phy.hr
        seminar at phy.hr
--------------------------------------------------------------------------

Poštovani kolege,

iduću srijedu s početkom u 12.15 sati (točno), u predavaonici F201 na
Fizičkom odsjeku, predavanje naslovljeno
"Approximation of nonlinear eigenvalue problems with applications
to lossy photonic crystals and metamaterials"
održati će nam Christian Engstrom sa ETH iz Zuricha.

Predavanje je zajednicki Seminar FO i
Seminar za numericku matematiku i racunarstvo MO.

Sazetak predavanja nalazi se u nastavku poruke.

Srdačan pozdrav
Hrvoje Buljan

------------------------------------------------------
ZAJEDNIČKI SEMINAR FIZIČKOG I MATEMATIČKOG ODSJEKA
------------------------------------------------------

Vrijeme: srijeda, 18.05.2011.
Mjesto:  Fizički odsjek, soba F201, II kat

Approximation of nonlinear eigenvalue problems
with applications to lossy photonic crystals and metamaterials

         Christian Engstrom

Seminar for Applied Mathematics, ETH Zurich,
Ramistrasse 101, and
Electromagnetic Fields and Microwave Electronics Laboratory,
ETH Zurich, Gloriastrasse 35, Zurich 8092, Switzerland

A large number of processes are accurately described by operator functions
with a nonlinear dependence of a spectral parameter, but a linear
dependence on the field. Problems involving operator functions arise from
important applications in fluid dynamics, acoustics, quantum mechanics,
and electromagnetic field theory.

In this talk, I show examples for which the finite-element approximation
of the spectrum of a differential operator may fail. These examples
illustrate the importance of a mathematical analysis of the underlying
PDE. I focus on Galerkin spectral approximation theory for operator
functions with periodic coefficients and the computation of physically
meaningful solutions. The main applications are metallic photonic crystals
and metamaterials, which are promising materials for controlling and
manipulating electromagnetic waves. In these materials, the spectral
parameter is usually related to the time frequency and the Floquet-Bloch
wave vector is a parameter. This leads to a rational spectral problem when
the frequency dependence of a Lorentz material model is included. A
different approach is based on a quadratic spectral problem in the
amplitude of the Floquet-Bloch wave vector. The strengths and weaknesses
of both approaches are discussed in the talk.

We use high-order finite element methods with curvilinear elements to
discretize the quadratic and the rational eigenvalue problem. The
resulting matrix problems are transformed into linear eigenvalue problems
and approximate eigenpairs are computed with a Krylov space method. Two
different linearization techniques for rational eigenvalue problems and
the connection between the two spectral problems will be discussed. The
presentation illustrates the importance of the interplay between physical
modeling, spectral theory, finite element discretization, and linear
algebra.

		Hrvoje Buljan i Luka Grubišić
------------------------------------------------------





_______________________________________________
fizika mailing list
http://www.phy.hr/cgi-bin/mailman/listinfo/fizika