Skip to content
GitLab
  • Menu
Projects Groups Snippets
  • /
  • Help
    • Help
    • Support
    • Community forum
    • Submit feedback
    • Contribute to GitLab
  • Sign in / Register
  • getdp getdp
  • Project information
    • Project information
    • Activity
    • Labels
    • Members
  • Repository
    • Repository
    • Files
    • Commits
    • Branches
    • Tags
    • Contributors
    • Graph
    • Compare
  • Issues 56
    • Issues 56
    • List
    • Boards
    • Service Desk
    • Milestones
  • Merge requests 0
    • Merge requests 0
  • CI/CD
    • CI/CD
    • Pipelines
    • Jobs
    • Schedules
  • Deployments
    • Deployments
    • Releases
  • Wiki
    • Wiki
  • Activity
  • Graph
  • Create a new issue
  • Jobs
  • Commits
  • Issue Boards
Collapse sidebar
  • getdp
  • getdpgetdp
  • Issues
  • #90
Closed
Open
Created Jun 15, 2021 by Jules Koenig@JulesKoenig

Time dependent permittivity/permeability

Hello,

I am following up on the questions I have already asked you here : How to create time varying material property ?

I need more clarification if possible.

I am working on a project where we study the propagation of an electromagnetic wave in a medium where the dielectric permittivity and the magnetic permeability vary according to time and space.

The problem consists of a rectangle where there is a sinusoidal electric field excitation on the left edge, PMC conditions on the top and bottom edges and an absorbing condition on the right edge (cf. image). The wave crosses 3 media with the following properties :

  1. ε0, μ0
  2. ε = ε(x,t) = ε0*(εr0+δεcos(ωt-kx)), μ = μ(x,t) = μ0(μr0+δμ*cos(ωt-kx))
  3. ε0, μ0

Capture1

I wish to adapt the variational formulation for this problem but I have some difficulties. Here is my weak formulation :

Capture2

My questions are therefore:

  1. Is it enough to take into account the electric excitation on the left edge as a constraint? Or should we add a term in the variational formulation?
  2. I don't see the possibility of writing the Laplacian operator, is there one? If not, do I have to go through a Green formula?
  3. How to write the temporal derivatives? I understand that "DtDof" only applies to the unknown in "Dof" and we cannot use "Dt".
  4. I have defined permittivity and permeability in "Function" as follows: epsilon [Domain 1] = eps0; epsilon [Domain 2] = eps0 * (epsr0 + d_eps*Cos[w*$Time-k*X[]]; epsilon [Domain 3] = eps0; Is this the right way to go? I used X[] instead of $X because $X didn't seem to work.
  5. Should we work in BF_Node or in BF_PerpendicularEdge?

Best regards,

KOENIG Jules

Edited Jun 15, 2021 by Jules Koenig
Assignee
Assign to
Time tracking