Re: [Getfem-users] Neumann Boundary Condition Normal to Level-Set Boundary

[Yves Renard]

Dear Patrick,

The "Normal" vector is indeed only defined on element faces. In order to obtain the normal vector of a level-set, the standard way is to use "Normalized(Grad_lambda)" where "lambda" is the scalar field of the level-set function (that you have to add as a data to the model). Note also, that you have access to discontinuities across the level-set of Xfem fields (mesh_fem_level_set objects) thanks to the Xfem_plus and Xfem_minus command of the language (see http://getfem.org/userdoc/gasm_high.html#xfem-discontinuity-evaluation-with-mesh-fem-level-set)

Best regards,

Yves.


Le 28/08/2017 à 20:44, Patrick Schmidt a écrit :

Dear Getfem users,

I am new to getFem and made my way through the demo_crack.py file in order to use the implemented XFEM formulation.

Now I would like to set up a boundary value problem where a pressure acts orthogonal to the surface of the discontinuity. I tried to find some way in order to apply source terms orthogonal on the surface of the discontinuity. In terms of the boundary condition that's as far as I got:

applied_force = 1.e7
md.add_initialized_data('Fx', [applied_force, 0]);

mim_bound1 = gf.MeshIm('levelset', mls, 'boundary(a)',
                       gf.Integ('IM_STRUCTURED_COMPOSITE(IM_TRIANGLE(6),3)'))
md.add_source_term_generic_assembly_brick\
(mim_bound1, 'Fx.Test_u')

I tried to use the 'Normal' keyword within the string, but since the integration takes part within the element and the normal seems to be defined on surfaces only, my python script failed.

Is there a way to apply Neumann Boundary conditions orthogonal to the surface of the discontinuity?

Kind regards,

Patrick

-- 

  Yves Renard (address@hidden)       tel : (33) 04.72.43.87.08
  Pole de Mathematiques, INSA-Lyon             fax : (33) 04.72.43.85.29
  20, rue Albert Einstein
  69621 Villeurbanne Cedex, FRANCE
  http://math.univ-lyon1.fr/~renard

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