# Laplace equation with boundary condition

1. Jul 31, 2012

### ACG_PhD

Good afternoon,

I am a PhD student in motions of damaged ships. I am trying to find a solution of Laplace equation inside a box with a set of boundary conditions such that:

2$\phi$=0
$\phi$x=1 when x=-A and x=A
$\phi$y=0 when y=-B and y=B
$\phi$z=0 when z=Ztop and z=Zbot

I have tried different solutions that look like
$\phi$=x+Ʃ(cos(α(x+A))cos(β(y+B))cosh(γ(z-Ztop))

α=n*PI/A n=1...∞
β=m*PI/B m=1...∞
and α222

I can't find a solution that satisfy everything.
I either satisfy the boundary conditions or Laplace equation but not both.
The problem comes from the need to have a sinh(z)=0 for 2 values...
I can't figure out how to go around the problem.

Any advice would be really nice.

Thanks
Anne

PS: I have the three permutation to find $\phi$x=1 then $\phi$y=1 and $\phi$z=1
I have the same problem in the three cases.

2. Aug 11, 2012

### Staff: Mentor

Try x+c as the solution

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