Discussion Forum

Hi,
This is Sarita, a grad student at Hopkins. I have a license for comsol 4.3 through school . I attended the COMSOL workshop at Hopkins on 3/27/14 and was asked to submit a support case for my problem. I thought I might also get help putting it on the forums.

I am trying to solve a PDE in 2D using the coefficient form PDE unit.
The equation looks like-
dudt - d2u/dx2 - (1/epsilon)d2u/dy2 - d/dx(f(x,y)u) - d/dy(g(x,y)u)

where function f is linear in x and y and g is nonlinear in y
f=constant1*(x-y);
g=constant2*((y^2-1)*y-K(x-y));

where K is also a constant.

The constraints I have are that u is a probability and hence it should be conserved to the initial value (=1). That is the quantity should always sum upto 1 at every time step.
The boundary conditions are that the probability goes to zero at the boundaries.

I have a square shaped domain, with values of x and y both ranging from -2 to 2.

The initial condition is a delta function which looks like this
u(x,y,0) = delta(x+1)*delta(y+1)
which means that u =1 at (-1,-1) and is equal to zero at all other points on the domain at the initial time point.

I have attached my mph file with this email. The value u is not conserved using this method. It does not get normalized. The way I implemented the delta function is that I created an extremely small square domain at (-1,-1) and said that the value u is equal to 1 at t=0 in that domain. I also have zero flux conditions to make sure that u does not flow out of the boundaries.

It would be of great help if you could look into this. Please let me know if there is anything unclear or any other information that you need. Thanks a lot!!!