Wave 2D Case 2#
Solves the two-dimensional wave equation using the position Verlet algorithm. This example uses the fourth order mimetic Laplacian, and extends the domain
\[
\frac{\partial^2 U}{\partial t^2} - c^2\frac{\partial^2 U}{\partial x^2} = 0
\]
where \(U=u(x,y,t)\) defined on the domains \(x\in[-5,10], y\in[-5,10]\) and \(t\in[0,0.3]\), and wave speed \(c=100\). The boundaries are Dirichlet. Initial position and velocity are given as
\[\begin{split}
u(x,y,0) = \begin{cases}
\sin(\pi x)\sin(\pi y) & 2 < x < 3,\,\,2 < y < 3 \\
0 & \text{ otherwise }
\end{cases}
\end{split}\]
\[
u'(x,y,0) = 0
\]