Thank you a lot! I`ve tried to play around and my conclusion is trivial and
exactly what you have said - we do really need to solve a full 3d equation
for 2D geometry too, it comes from physics, not from coding or math. Just
imagine a typical 1D (or 2D) problem - an infinite subwavelength plate made
from uniaxial crystal, with a wave passing it at normal incidence. Such a
1D setup (geometrically) we need all field components to describe a
phenomenon, an extraordinary ray for sure will move away form initial 1D
line and in general will move out of 2D plane of consideration.
I am still a bit confused. E.g. to simulate Fresnel equation in 1D should
I need to consider a 1D stack of hexahedral? I do actually need only 2
components for field out of six (one normal for electric field, and one
normal for magnetic for 1D case). However, to keep compatibility with 3D
case I need to evaluate all six components, so it will be easy to move to a
2D as a plane of hexahedra or to a 3d case with a volume. Probably I
should simply put a constraint for components that I am sure are not needed
to be equal zero. This way the number of DoF per element should be
reduced...
понедельник, 26 декабря 2016 г., 23:44:49 UTC+3 пользователь Timo Heister
написал:
>
> The problem is that .curl returns a scalar in 2d and a tensor in 3d. A
> typical definition of maxwell curl notation is to treat the 2d case as
> a 3d solution that is constant in the (implicit) 3rd dimension, right?
> Maybe you can do something like
>
> Tensor<1,3> make_3d_curl(double curl_2d)
> {
> Tensor<1,3> r; r[2] = curl_2d; return r;
> }
>
> Tensor<1,3> make_3d_curl(Tensor<1,3> curl_3d)
> {
> return curl_3d;
> }
>
> and then do all the math in 3d:
>
> Tensor<1,dim> curl_W_j = make_3d_curl(fe_values[E_field].curl (j, q));
>
> local_rhs_KT (i, j) += curl_W_j * ...
>
> etc.
>
>
>
>
>
> On Mon, Dec 26, 2016 at 1:00 PM, Konstantin Ladutenko
> <kosty...@gmail.com <javascript:>> wrote:
> > Dear all,
> >
> > Any ideas, what is the best way to go when implementing Maxwell
> equations to
> > make them dimension independent? Or at least to have the same code for
> 2d
> > and 3d cases?
> >
> > Simply using dim template parameter doesn`t work by definition - when
> > switching from 3D to 2D you need to specify, should it be TE or TM mode
> > (which field, electric of magnetic, should be normal to the 2D plane).
> > Introducing some boolean variable `isTEmode` to be True or False can
> help,
> > but this will lead to many if\then codes... As soon as it is still the
> same
> > Maxwell equation I hope there is a better way to do this. Any ideas?
> >
> > From the code point of view it does not work either at the moment. Using
> >
> > fe (FE_RaviartThomas<dim> (degree), 1, FE_Nedelec<dim> (degree),
> 1),
> >
> > where Raviart-Thomas face element is needed for magnetic field, Nedelec
> edge
> > element is needed for electric field and
> >
> > const FEValuesExtractors::Vector B_field (0);
> > const FEValuesExtractors::Vector E_field (dim);
> > const auto &curl_W_j = fe_values[E_field].curl (j, q);
> > const auto &F_i = fe_values[B_field].value (i, q);
> >
> > works fine for 3D (some wave is traveling in free space) and breaks down
> in
> > 2D during compilation of a weak-form integral local component.
> >
> >
> /home/tig/symlink/dealii/examples/step-maxwell-nonliner/step-maxwell-linear.cc:
>
>
> > In instantiation of ‘void Maxwell::MaxwellTD<dim>::assemble_system()
> [with
> > int dim = 2]’:
> >
> /home/tig/symlink/dealii/examples/step-maxwell-nonliner/step-maxwell-linear.cc:549:20:
>
>
> > required from ‘void Maxwell::MaxwellTD<dim>::run() [with int dim = 2]’
> >
> /home/tig/symlink/dealii/examples/step-maxwell-nonliner/step-maxwell-linear.cc:648:32:
>
>
> > required from here
> >
> /home/tig/symlink/dealii/examples/step-maxwell-nonliner/step-maxwell-linear.cc:394:51:
>
>
> > error: no match for ‘operator*’ (operand types are ‘const
> dealii::Tensor<1,
> > 1, double>’ and ‘const dealii::Tensor<1, 2, double>’)
> > local_rhs_KT (i, j) += curl_W_j * F_i * fe_values.JxW
> (q)
> >
> > Full example is available online at GitHub
> >
> >
> >
> https://urldefense.proofpoint.com/v2/url?u=https-3A__github.com_kostyfisik_dealii_blob_0188064ee4dd0cdd53d515f33932732b0a2d5d66_examples_step-2Dmaxwell-2Dnonliner_step-2Dmaxwell-2Dlinear.cc&d=CwIFaQ&c=Ngd-ta5yRYsqeUsEDgxhcqsYYY1Xs5ogLxWPA_2Wlc4&r=4k7iKXbjGC8LfYxVJJXiaYVu6FRWmEjX38S7JmlS9Vw&m=DjvKZYOEy46NTfpFc92OVXJsfNl6mHgZuzQYoA80LvQ&s=3pcGss3gRopgWpsIOGUaJCr3t5KJooO1atsssf2KC4w&e=
>
> >
> > Best regards,
> > Konstantin Ladutenko
> >
> >
> >
> > --
> > The deal.II project is located at
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>
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>
>
>
> --
> Timo Heister
> http://www.math.clemson.edu/~heister/
>
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