# Diffusion coefficient between two PDEs

Hi everyone!
I am sequentially solving two PDEs, correlated by the diffusion term:

After solving the first PDE (thus getting u) with

solve firstpde (u, v) = int3d (Th) ( A * grad(u)’ * grad(v) ) + BCs ) ;

where Th is the triangulation of the mesh Vh, I tried to define the diffusion coefficient B as

macro grad(f) [dx(f), dy(f), dz(f) ]
func B = int3d (Th) ( A * grad( u ) ) )

but it gives me error on the definition of B.

Does anyone can help me?
Thank you!

Where is the depend in x in definition of B, it is in function u ?

oh I’m sorry, I wrote it wrong.
B is constant through the domain.

so no problem just do:
real By = int2d(Th)(A
dy(u));

B is a vector because A is a scalar ,
so the third equation have no meaning

Ok, so B = [Bx, By], is that correct?
How can I then solve the third equation? I would be a simple laplace problem with constant coefficient B.
I tried to put Bx, By into a diagonal matrix

matrix B = [ [Bx, 0], [0, By] ];

and then solve the problem

macro grad(func) [dx(func), dy(func), dz(func) ] \
func rhs = 1;
solve secondPDE (w, v) = int2d(Th) ( B * grad(w)’ * grad(v) ) - int2d(Th) ( rhs * v ) + BCs

but it gives me error on the last line.
Is it related to the definition of the diffusion coefficient B as matrix? Should it be a constant?

Thank you very much for your help!

you have to write
with in 2d the grad definition is

``````    macro grad(u) [dx(u),dy(u)]//

Sorry, I have mixed 3D and 2D.
However, it still doesn’t work.

matrix B = [ [Bx, 0], [0, By] ];
func rhs = 1;
solve secondPDE (w, v) = int2d(Th) ( grad(w)’ * B * grad(v) ) …

It says

Error in (last) line, before token *
Compile error :
line number :176, *

the correct writing is in

monica.edp (310 Bytes)

Thank you very very much for your help!