On 06/19/2013 11:21 AM, Alexander Mihailov wrote:
Thank you, Robert.
Adding a new variable is a great way! Very likely I can just add another equation to bind u=grad(G) and G fields instead of post_process, I think that's a little bit more explicit and evident than hook magic.
But it is not the same thing:
- the problem is more difficult to solve (1 more equation)
- the resulting G = grad(u) only in the weak sense, which is probably not what you want.
field_1 = { 'name' : 'gravity', 'dtype' : nm.float64, 'shape' : (3,), 'region' : 'Omega', 'approx_order' : 1, } field_2 = { 'name' : 'gravity_potential', 'dtype' : nm.float64, 'shape' : (1,), 'region' : 'Omega', 'approx_order' : 1, } variables = { 'G' : ('unknown field', 'gravity', 1), 'g' : ('test field', 'gravity', 'G'), 'u' : ('unknown field', 'gravity_potential', 0), 'v' : ('test field', 'gravity_potential', 'u'), } equations = { 'Gravity_potential' : """dw_laplace.1.Omega( v, u ) = dw_volume_lvf.1.Omega( m.rho, v )""", 'Gravity' : """ dw_volume_dot.2.Omega( g, G ) = dw_v_dot_grad_s.2.Omega( g, u ) """, }
But here is another issue... When I run an updated task, the answer is u(x) = 0, G(x) = [0,0,0] for all x.
I think it's the wrong specifying or material, or the boundary conditions issue.
First, check your region definitions by using:
./simple.py my.py --save-regions-as-groups --solve-not
and inspect the resulting my_regions.vtk - it seems that the regions used in the material 'm' definition are empty. Maybe you want to use 'elements of group i' selector, where i = 1, 2, 3?
r.
<http://ft.trillian.im/b820c2e0aaf525034498f9740f19cbbd7b172056/6hunxpA0mh8e7...>
среда, 19 июня 2013 г., 14:11:37 UTC+7 пользователь Robert Cimrman написал:
Hi Alexander
On 06/19/2013 04:42 AM, Alexander Mihailov wrote:
Hi all.
I have already asked my question at
http://math.stackexchange.com/questions/422928/modeling-gravity-field-with-f...
and
http://stackoverflow.com/questions/17160835/modeling-gravity-field-with-fini...
seems there are no people there, who knows sfepy and finite elements, in particular.
I want to model the gravity field on 3D rectangular area. It can be described by the equation: div(G) = rho. Here G is vector unknown function, rho is scalar parameter, which is constant at the selected point and fully determined by material.
The weak form is: int( div(G) * g ) = int( rho * g ). Here g is vector test function. Using sfepy syntax: {'Gravity' : """dw_div_grad.1.Omega( g, G ) = dw_volume_lvf.1.Omega( m.rho, g )"""}
The terms you use do not correspond to the equation. As div(G) is a scalar, it cannot be used with a vector test function, but a scalar test function - the term that does that is dw_stokes, but then the matrix would not be square.
Try using a different approach - use the scalar gravity potential u as your function, such that G = grad(u). As div(grad(u)) = rho is the Poisson equation, use dw_laplace and dw_volume_lvf terms with scalar unknown and test fields. Check the equation in [1]. Then G could be computed in a postprocess hook function by evaluating ev_grad term - see [2] for an example of a similar hook function (post_process()).
r.
[1] http://sfepy.org/doc-devel/examples/diffusion/poisson_parametric_study.html [2] http://sfepy.org/doc-devel/examples/biot/biot_npbc.html
I used gmsh to build .mesh file. My .geo, .mesh and .py files attached to this message.
When I try to run sfepy, it says that matrix is singular, so the solving process does not converge.
What I have to do to correct the model?
Thanks in advance.