Thomas,
My initial mesh is not great - here's where I begin:
|
|GridGenerator::hyper_sphere(triangulation,Point<spacedim>(0,0,0),1.0);
triangulation.set_all_manifold_ids(0);
triangulation.refine_global(initial_global_refinement);
|
|/* interpolate the map from triangulation to desired geometry for the first
time
a,b,c are the axes of an ellipsoid */|
|VectorTools::interpolate(bending_dof_handler,
Initial_map_sphere_to_ellipsoid<spacedim>(a,b,c),
global_euler_vector);
|
const MappingQEulerian<dim,Vector<double>,spacedim> mapping (2, dof_handler,
euler_vector);
doubleInitial_map_sphere_to_ellipsoid<spacedim>::value(constPoint<spacedim>&p,constunsignedintcomponent)
const
{
doublenorm_p =p.distance(Point<spacedim>(0,0,0));
// return the difference between the point on the ellipse and the point on
the original geometry
returnabc_coeffs[component]*p(component)/norm_p -p(component);
}
|
This gets me an ellipsoid, but the corners of the original hyper_sphere are
just translated onto the ellipsoid by euler_vector. (The color map shows the
mean curvature of the surface.)
<https://lh3.googleusercontent.com/-tO37r5w5pMg/WCvK3kE48oI/AAAAAAAAFq4/kMmbQ6kBMq0GBVGAk4w6g29HP9TOK-q_gCLcB/s1600/Screen%2BShot%2B2016-11-15%2Bat%2B9.55.44%2BPM.png>
I want to deform this shape in response to a scalar function (illustrated by
the new colormap) on the surface, so I adaptively refine and then let the
evolution go forward (the deformation will reduce a global free energy on the
surface) - here's how that looks:
<https://lh3.googleusercontent.com/-kJCXHwbjHUA/WCvMEWPD7gI/AAAAAAAAFrA/mdvLijljl7cITiw7lGTR6lOcnqbN-CBIACLcB/s1600/Screen%2BShot%2B2016-11-15%2Bat%2B9.59.21%2BPM.png>
A few timesteps later the surface (and mesh) evolve to look like this: (the
color map shows the mean curvature again)
<https://lh3.googleusercontent.com/-dunjJsO_ka8/WCvMd_nofbI/AAAAAAAAFrE/9SQV3Kpp0FcFBgGA6Tu-wA-zjVRNdWodACLcB/s1600/Screen%2BShot%2B2016-11-15%2Bat%2B10.02.30%2BPM.png>
This eventually crashes as the quadrilaterals become distorted.
It's not my research field, but there should be literature on these sorts of
phenomena. I think that ultimately, you need to find a way to relax mesh nodes
in tangential directions.
Best
W.
--
------------------------------------------------------------------------
Wolfgang Bangerth email: [email protected]
www: http://www.math.colostate.edu/~bangerth/
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