Element- or vertex-wise boundary conditions

Hi,

in real world applications one often has measured process data that form the bounday conditions of the PDE, e.g. cooling or heating of a product. Therefore it is necessary for each time step of a time dependent PDE to apply new element- or vertex-wise boundary conditions from data.

Up to now I did’nt find any example in the web. Does anyone know how can this be done? I’m sure this is possible.

Hi,

do you already know about PointSource? Depending on your application this might be already good enough.

In my own work I created a CustomExpression that interpolates given point data, since I had to use a DirichletBC that receives an expression. For a CustomExpression you can define your own eval function. This allows you to put anything you like behind this function. For the interpolation we used RBF interpolation, since it does not require any connectivity information of the point data. You can also find a few more resources and a link to our paper in the repository, if you are interested.

I hope this helps.
Best regards,
Benjamin