The Standard Linear Wave Scattering Problem
in Finite Depth for a fixed body is
[math]\displaystyle{
\nabla^{2}\phi=0, \, -h\lt z\lt 0,\,\,\,\mathbf{x}\notin \Omega
}[/math]
[math]\displaystyle{
\frac{\partial\phi}{\partial z}=0, \, z=-h,
}[/math]
[math]\displaystyle{
\frac{\partial\phi}{\partial z} = \alpha \phi,\,z=0,\,\,\mathbf{x}\notin\Omega,
}[/math]
[math]\displaystyle{
\frac{\partial\phi}{\partial n} = 0, \, \mathbf{x}\in\partial\Omega.
}[/math]
where [math]\displaystyle{ n }[/math] is the outward from the fluid) normal.
