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Automated goal-oriented adaptivity at just one point in the computational domain

+2 votes

Hello,

I would like to implement goal-oriented mesh adaptivity at just one point in the computational domain $\Omega$.

The code below is taken from lecture 11 of the Fenics course, the goal function $M$ is the integral of the solution over the whole computational domain, i.e.

$$
M = \int_{\Omega} u dx.
$$

I would just like to refine the mesh at a region of interest (ROI), i.e.

$$
M = u(x_{ROI})
$$

How would I have to modify the code below?

Many thanks!


u = Function ( V )

M = u * dx

solver_parameters = { "error_control " :
  { " dual_variational_solver " :
  { " linear_solver " : "cg " } } }

solve ( a = = L , u , bc , tol = tol , M =M , solver_parameters = solver_parameters )
asked Feb 19, 2015 by wilhelmbraun FEniCS User (2,070 points)

Hi, I think this will be difficult to achieve without you subclassing the AdaptiveLinearVariationalSolver (see here) on the cpp side of DOLFIN. Anyways, it's a great question so I suggest bringing it up on the mailing list to get the attention of experts.

Hi, thank you very much. I will do this.

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