> In solving a Laplace-Beltrami problem on an advecting surface one should > identify the Gauss points on the manifold dim-1 cell and retrieve at > such locations relevant information from the solution of the advection > problem, using the dim dof_handler of the volume. I wonder how to > connect a manifold dim-1 cell to the volumetric cell it was extracted > from. The GridGenerator::extract_boundary_mesh method seem to provide > some information, since "it returns A map that for each cell of the > surface mesh (key) returns an iterator to the corresponding face of a > cell of the volume mesh (value). " . I am not sure how I can use this > map to link a manifold cell to the corresponding volume cell.
Alberto, the way this is supposed to be used is as follows: When you are assembling the linear system for the surface problem, you will have an FEValues<dim-1,dim> object for the surface shape functions. You initialize it with a Quadrature<dim-1>. But then you also need to evaluate the volume solution on the same quadrature points. You do this by creating an FEFaceValues<dim> object, which requires you to also provide a Quadrature<dim-1> object -- which you want to choose the same as above. Now, if you need the volume solution when assembling something for the surface problem, you are sitting on a cell of the surface mesh; use the map returned by the extract_boundary_mesh() function to obtain what the corresponding face of the volume mesh is and reinit() the FEFaceValues for that cell. You can then use the FEFaceValues object to evaluate the volume solution at the same quadrature points as you use for the FEValues object of the surface mesh. The only thing you may have to pay attention to is that the surface cell may be inverted compared to the volume cell's face -- in which case the quadrature points of the two objects match, but are in a different order. You'll have to translate between these permutations then. Best W. -- ------------------------------------------------------------------------ Wolfgang Bangerth email: [email protected] www: http://www.math.colostate.edu/~bangerth/ -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/a60b9b5e-fef3-fd88-5e54-65bed698a5bc%40colostate.edu.
