On 11/02/2016 05:54 PM, benhour.amiria...@gmail.com wrote:
I want to use half_hyper_ball for my domain. Unfortunately, I cannot refine
the mesh around the center. I attached my geometry below. The code that I am
using has been written as follows:
Point <2> center;
  const double radius = 30e-9;
  GridGenerator::half_hyper_ball(triangulation,
                                center,
                                radius);
  triangulation.set_all_manifold_ids(0);
  const SphericalManifold<2> manifold_description(center);
  triangulation.set_manifold (0, manifold_description);
  GridTools::copy_boundary_to_manifold_id(triangulation);
  triangulation.refine_global (4);
  triangulation.set_manifold (0);
  const double angle = numbers::PI / 2.0;
  GridTools::rotate (angle, triangulation);

I have doubt related to the fact that the SpericalManifold cannot be used for
the cell containing the center of the coordinate system and consider it as a
singular point. It would be very kind of you if you let me know what I should
use instead?

Benhour,
there is a lengthy discussion of how to deal with essentially your situation in the "Possibilities for extensions" section of step-6.

Best
 W.

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

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