Template:Added mass damping and force matrices definition

We define the added mass matrix by

[math]\displaystyle{ A_{\mu\nu} = \mathrm{Re} \left\{\rho\iint_{\partial\Omega_{B}} \phi_{\nu}^{\mathrm{R}} \mathbf{n}_{\mu}\, dS \right\} }[/math]

and the damping matrix by

[math]\displaystyle{ B_{\mu\nu} = \mathrm{Im} \left\{ \omega \rho\iint_{\partial\Omega_{B}} \phi_{\nu}^{\mathrm{R}} \mathbf{n}_{\mu}\, dS \right\} }[/math]

and the forcing vector by

[math]\displaystyle{ f_{\mu} = \mathrm{i}\omega\rho\iint_{\partial\Omega_{B}} \left(\phi^{\mathrm{I}} + \phi^{\mathrm{D}} \right) \mathbf{n}_{\mu}\, dS }[/math]