Hello!
How can I write the weak form of the two following coupled-equations in FEniCS?
\partial u / \partial t = b \nabla \cdot \vec{v}
\partial \vec{v} / \partial t = a \nabla u
They represent the scalar wave equation \nabla \cdot (a \nabla u ) = \Large{\frac{1}{b}} \Large{\frac{\partial ^2 u}{\partial t ^2}}, but I need to use the coupled-equations formulation in order to implement a PML boundary condition.
Many thanks!
Hi,
if only the coupling is a problem, then have a look at the mixed poisson demo: https://fenicsproject.org/docs/dolfin/latest/python/demos/mixed-poisson/demo_mixed-poisson.py.html
There, the Laplacian is split exactly how you need it. I guess you already know this, but I’ll add it anyway: The time derivatives have to be discretized first, e.g., using finite differencing
@plugged, I have found a meaningful reference towards what I want to do, but now I’m stuck in a further step. I’ve created another question with more details, maybe you can help me with this. Thanks!