Evaluating a field at a point

[andre...@gmail.com]

I currently have the solution to a PDE stored in a Vector<double> solution. I need to compute the solution at some Point<2> loc. I accomplish this using the function 

VectorTools::point_value(dof_handler, solution, loc, val);

which fills val with the value I care about. Similarly, I get the gradient with point_gradient. 

This accomplishes what I need but if I have a lot of points like loc and have to do this every timestep then it quickly becomes a computational bottleneck. 

If I am not refining the mesh, is there a more efficient why of accomplishing this? I assume by storing the specific cell that loc is in? 

[Wolfgang Bangerth]

If you have multiple points, and if the points are always the same, you are in
luck that someone has already implemented what you are looking for in this
program:

https://dealii.org/developer/doxygen/deal.II/code_gallery_MCMC_Laplace.html

:-)

Best
W.


--
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Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/

[Peter Munch]

I guess for your purpose, `VectorTools::point_values()` and `VectorTools::point_gradients()` are more useful and it works in parallel. If the location of the points do not change, they are cached in RemotePointEvaluation.

> If I am not refining the mesh, is there a more efficient why of accomplishing this? I assume by storing the specific cell that loc is in? 

Indeed, this is happening internally in RemotePointEvaluation. It stores the cell and the reference positions. In a second step the actual evaluation is done efficiently by FEPointEvaluation. If the interface is too high level for your purposes, you can take a look at the implementations of the setup routines, which uses GridTools::internal::distributed_compute_point_locations.

Hope this helps,

Peter