We then define the matrices
[math]\displaystyle{
A_{\mu\nu} = \mathrm{Re} \left\{ -\frac{\mathrm{i}}{\omega}\rho\iint_{\partial\Omega_{B}}
\phi_{\nu}^{\mathrm{R}} \mathbf{n}_{\mu}\, dS \right\}
}[/math]
which is called the added mass matrix and
We then define the matrices
[math]\displaystyle{
B_{\mu\nu} = \mathrm{Im} \left\{ \rho\iint_{\partial\Omega_{B}}
\phi_{\nu}^{\mathrm{R}} \mathbf{n}_{\mu}\, dS \right\}
}[/math]
which is called the damping matrix and the forcing vector is
[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]
