Dear Sebastian, have you tried using a simple SphericalManifold for your problem?
The way spherical manifold works is by interpolating *both* the radius and the angles, so that points intermediate between two points with different radii get an average radius between the two. This may not be the exact solution you were looking for, but if you have a sphere which is uniformly deformed along one axis, then SphericalManifold should do the correct job for you. L. > On 13 Jun 2019, at 12:31, SebG <[email protected]> wrote: > > Hi Wolfgang, > > that is exactly the way how I tried to implement this. For a section of a > sphere the approach of step-53 works perfectly well for my case too. But I > need a full sphere. For the full sphere the problem is that SphericalManifold > (like Manifold) does not have the a function called push_forward anymore. So > I tried to overload the functions get_intermediate_point, get_new_point and > get_new_points. I am not sure which member functions I need to overload if I > derive my from class SphericalManifold. I am also not sure if I should derive > my class from SphericalManifold or Manifold. It would be great if you could > give some advice. > > Best wishes, > Sebastian > > > Am Dienstag, 11. Juni 2019 17:39:44 UTC+2 schrieb Wolfgang Bangerth: > On 6/11/19 1:06 AM, SebG wrote: > > > > actually I was not aware of this class. But this class is unfortunately > > only > > implemented in 2D. I am not exactly looking for an ellipsoid but for a > > sphere > > with a peturbed radius, where r = R * (1 + e * Y^m_n(\theta, \phi) ). Here > > R > > is the reference radius, e > 0 is a scalar and Y^m_n is a real-valued > > spherical harmonic. > > > > To implement this, I thought that I could map a point from the perturbed > > sphere to the reference sphere. Then the updated point is computed on the > > reference sphere and mapped back to the perturbed one. > > > > As a first step, I tried this approach based on the step-53 tutorial. But I > > realized that closing the sphere at the poles and in azimuthal direction > > does > > not work. Then I thought that it might easier to program the example of an > > ellipsoid from this discussion. > > > > It would interessting to know why my approach of mapping back to a > > reference > > sphere is not working with the updated version of SphericalManifold. But > > maybe > > this is worth a new discussion. > > I don't know what the issue is, but the way I would write this is a > concatenation of two operations. The first would be the transformation from > reference coordinates to the sphere (done by the push_forward() function of > the SphericalManifold) and the second the scaling in radial direction (done > by > your own code). step-53 does this same kind of 2-step procedure, but instead > of using the WGS84 transformation used there, you'd just defer to > SphericalManifold::push_forward. > > 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/5d4bb9c2-d11c-4c4f-aaf9-035352f1c839%40googlegroups.com. > For more options, visit https://groups.google.com/d/optout. -- 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/29BDB2F9-96BD-4578-B622-471F640398CC%40gmail.com. For more options, visit https://groups.google.com/d/optout.
