Parametric domains

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Variable node density and dirchlet boundary conditions in 2D

With medusa, we can also solve partial differential equations on parametric domains. Consider the solution of a simple 2D Poisson equation with Dirichlet boundary conditions: <math> \begin{align*}

   	\Delta u &= 0.5      &&\text{in } \Omega, \\
   	  u &= 0           &&\text{on } \partial \Omega,

\end{align*} </math> where $u(x,y)$ is the solution to the problem. Let's define $\Omega$ to be the interior of the parametrically given curve $f(t)$:

<math> \begin{align*}

   	r(t) &=& |\cos(1.5 t)| ^ {\sin(3t)}
       f(t) &=& (r \cos(t), r \sin(t))

\end{align*} </math>

See Positioning of computational nodes TODO.