Parametric domains
From Medusa: Coordinate Free Mehless Method implementation
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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\[ \begin{align*} \Delta u &= 0.5 &&\text{in } \Omega, \\ u &= 0 &&\text{on } \partial \Omega, \end{align*} \] where $u(x,y)$ is the solution to the problem. Let's define $\Omega$ to be the interior of the parametrically given curve $f(t)$\[ \begin{align*} r(t) &=& |\cos(1.5 t)| ^ {\sin(3t)} f(t) &=& (r \cos(t), r \sin(t)) \end{align*} \]
See Positioning of computational nodes TODO.
