Hello all, This is a follow up discussion to the Jean-Paul answer to the question "Is the approach for the electrostatic Bi-linear form correct?". The question (and answer) can be found at the following link:
https://groups.google.com/forum/#!topic/dealii/i8P4JTwm7kQ In short, I am modeling the maxwell equations for the electric field and voltage scalar field. The equations that I am using are displayed below: div(*E*) = rho / epsilon where epsilon = epsilon_{0} * epsilon_{r} and rho is the charge density of the material. -grad(V) = *E* Using Dr. Bangerth's recommendation, I am solving for the scalar voltage field first then taking the gradient of my solution using the DataPostprocessorVector class. This has worked extremely well in my test program. For more information on that, see this post: https://groups.google.com/forum/#!topic/dealii/XIiPyMh0Jz4 However, now that I am actually coding the solver of the simulation, I will need to expand on my test simulation to include modeling anisotropic materials. When the material is anisotropic, the epsilon value (the permittivity) of the material is represented by a tensor. To make things slightly simplified, I am only running 2D simulations. I am attempting to determine the best method on modeling these types of materials. One approach that I have considered is to still solve for the voltage scalar field. If I go with this approach, then I will end up simulating a Possion equation where f = rho / epsilon and epsilon is a tensor. My concern for this direction would be that the Laplacian operator results in a scalar value. So I am not sure how I would handle the tensor on the RHS. Unless Deal.II has some sort of provision for this. I have also been kicking around the idea of solving for the displacement vector *D*(i)= epsilon(i)(j) * *E *by substituting this equation into one of the equations above. Or at the very least, to use this equation as a constitutive relation to the equations above. A third approach that I haven't quite explored very much is solving for the polarization of the material. But I am not sure if this is a practical approach since I could unnecessarily complicate the problem. I wanted to post a discussion on this form to discuss what the best direction I should take to model anisotropic materials in Deal.ii? I have been looking at 3 different approaches and I would like to discuss which one of these 3 directions is the better. Or if there might be others that I have not considered yet. -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to dealii+unsubscr...@googlegroups.com. For more options, visit https://groups.google.com/d/optout.
