Discussion Forum

Hi, I have a function f(p,T) defined on a 3D subdomain x=0..a, y=0..b and z=0..c. I want to calculate at each point (x,y,z) the Integral I1:
I1(x,y,z)=int_0^z f(p,T) dz'
where p is a x,y dependent function, and T is x,y,z dependent.

I tried the four methods:

(1).In a 1D model, this can be done using an Integration coupling variable and the dest operator :
for example I2(x) = int_0^x f(x') dx' is done by writing as integrand : f*(x<dest(x))
In 3D if I write f*dest(z) it performs int_0^a int_0^b int_0^z f(p,T) dz' dy dx and I don't want my expression to be integrated over x and y.

(2).I've tried a projection from my 3D domain on a 2Ddomain x=0..a and then extrude it again on a 3D domain x=0..a y=0..b and z=0..c but it calculates the integral from 0 to c : I3(x,y,z)=int_0^c f(p,T) dz

(3).I used the "quad" operator to try to solve, but it's value is wrong.

(4).In 3D I try to add a general form PDE to set as
F=uz-f(p,T), the lower boundary at z=0 is dirichlet boundary condition u=0
but because the p is a coupled from another geometry, so the solution of the varible u is vibrate and wrong.

Does anyone have an idea ?

I know that i could define subdomain but I want the value of the integral at every point of the 3D domain so it makes a lot of subdomain to create.

Thanks a lot!

Obidos Yu