Discussion Forum

I am trying to solve a set of three "Helmholtz-type" equations using the Equation-Based Modeling of Comsol. There are three independent variables, call them u1, u2, and u3. The equations are (with some constant coefficients in front of each term):

∇^2 u2 + u1 + u2 + u3 = 0
∇^2 (u1+u2+u3) + u1 +u2 + u3 = 0
u1 + u2 + u3 = 0

I know how to set up such a set of equations using either the Coefficient Form PDE Interface or the General Form PDE Interface. The problem is the boundary conditions, which apparently cannot be defined arbitrarily (?). I would like to use the following boundary conditions on all but one boundary:

n · ∇u1 = 0
n · ∇u2 = 0
n · ∇u3 = 0

and on the final boundary:

n · ∇u1 = 0
n · ∇u2 = const.
n · ∇u3 = 0

I don't know how to do this because if a set the zero-flux boundary condition, for example, it is of the form

n · (c∇u) = 0,

where c is the matrix used to mix the nabla-squares of the different independent variables and u is the transpose of [u1, u2, u3]. In my case

c = (1,0,0; 1,1,1; 0,0,0)

Thus the zero-flux boundary condition is not what I want. So is there a way to get the boundary conditions above?

I am also wondering, whether the boundary conditions I have actually make any sense. Perhaps what Comsol is suggesting is in fact right. Because zero-flux (independently for all three independent variables?) is what I am looking for. The equations at least are correct. Any thoughts on this? But since the last three elements of c are zeros, it would reduce the number of boundary conditions to 2. Is this OK?