[Getdp] Vectorial Helmholtz equation

[Lars Rindorf]

Dear all 

I'm having some problems with vectorial functionspaces.

I'm building a model for an optical fiber waveguide. I have built a scalar Helmholtz on a circular domain in 2D. Now I'm trying to do a two component vectorial model using edge elements (E = (Ex,Ey,0)), but I'm unable to construct the right functionspace.  The governing equation is curl(curl(E)) = lambda^2 E => curl(E).curl(E) = lambda^2E.E, where lambda is the eigenvalue not the wavelength. By constructing a functionspace where (Ex,Ey) is in R^2 I can make problem work, but I have to add a penalty term div(E)*div(E) to avoid spurious eigensolutions. What is the functionspace for this problem? And how should I know how to construct it? The section on functionspaces in the getdp is rather rudimentary. E.g. the function "BF_Node_2E" is never explained. "_2E" is used in several examples. What does it mean? Can you help me with this problem.

I have attached my model.

Kind regards

Lars Rindorf

_________________________________________________
Lars Rindorf, M. Sc., PhD student
Fibers and Nonlinear Optics Group
COM*DTU Department of Communication, Optics and Materials
Technical University of Denmark
Building 345v/267
DK-2800 Lyngby
Denmark
Phone: +45 45256365
Fax: +45 45936581
Email: LHR at com.dtu.dk
 

 

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