Re: elliptic solver, fourier

On Mar 29, 2:50 pm, Nico <nicolas.au...@xxxxxxx> wrote:
Hello,

I'm looking for your help to solve a little elliptic system in 2D.
I will tell you about what I think I could do and what are my problems.
Please tell me if I say something wrong and/or if you have a method for
my problems.

I would like to solve a bilinear (electromagnetic) system : S =
(1-d^2*Laplacian)B

I know S, d is a constant, and I want B.

I can have two kind of BC : Neumann (homogeneous for a start) or periodic.

My vectors S and B have 3 components but are only functions of x and y,
so this is a 2D problem.

* For x and y periodic boundary conditions, I can solve my system with a
simple 2D fourier transform, which is the correct basis to find a
periodic B from S.

*For a fully non periodic box, I want the normal derivative of both
normal and tangential component to be zero.

Example at x=L border :

dBx/dx = 0
dBy/dx = 0
dBz/dx = 0

This is done by using a cosine transform, which is the appropriate basis
for neumann conditions.

But I would also like to have the tangential derivative of the
tangential component do be zero, example at the x=L border :

dBy/dy = 0
(dBz/dz always 0 because d/dz = 0 (2D))

I want this because I have to impose Div(B)=0 everywhere (so at the
border too), so if dBx/dx =0, I must be sure that dBy/dy is 0 too.

Would someone know how to do that ?

* For mixed BC, x-periodic and y-neumann, I don't know I to do.
How could I do a fourier transform in one dimension and a cosine
transform in the other one ?

Thanks a lot,

Nico

hello Nico.This is amit from India.R u in college.wd U plz join me on
orkut.I need Ur help in solving these
problems.waiting................amit Bhopal,India
.

Relevant Pages

  • Re: elliptic solver, fourier
    ... I'm sure solving this bilinear system for these BCs and for a divergence free vector is something very classic, but I really don't know how to do that, would somebody know? ... *For a fully non periodic box, I want the normal derivative of both normal and tangential component to be zero. ... But I would also like to have the tangential derivative of the tangential component do be zero, example at the x=L border: ... How could I do a fourier transform in one dimension and a cosine transform in the other one? ...
    (sci.math.num-analysis)
  • elliptic solver, fourier
    ... I'm looking for your help to solve a little elliptic system in 2D. ... *For a fully non periodic box, I want the normal derivative of both normal and tangential component to be zero. ... But I would also like to have the tangential derivative of the tangential component do be zero, example at the x=L border: ... How could I do a fourier transform in one dimension and a cosine transform in the other one? ...
    (sci.math.num-analysis)