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... but 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.

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:

1. the problem is more difficult to solve (1 more equation)
2. 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.

On 06/19/2013 12:56 PM, Alexander Mihailov wrote:

Yes, Robert, you are right, regions were empty.

After correcting regions and setting post_process_hook, I have got some solution, slowly but surely it becomes believable, but the matrix is still singular and residual is high...

sfepy: nls: iter: 0, residual: 1.528953e-02 (rel: 1.000000e+00) warning: (almost) singular matrix! (estimated cond. number: 6.06e+15) sfepy: rezidual: 0.01 [s] sfepy: solve: 0.01 [s] sfepy: matrix: 0.00 [s] sfepy: linear system not solved! (err = 1.782581e-02 < 1.000000e-10) sfepy: linesearch: iter 1, (3.34778e-02 < 1.52894e-02) (new ls: 1.000000e-01) sfepy: nls: iter: 1, residual: 1.435926e-02 (rel: 9.391562e-01) sfepy: equation "tmp": sfepy: ev_grad.1.Omega( u ) sfepy: updating materials... sfepy: ...done in 0.00 s

There are still some subtleties that need to be considered?

The scalar field needs to be fixed somewhere, at least in a single vertex, as:

regions = { 'Node' : ('node 0', {}), }

ebcs = { 'fix' : ('Node', {'u.0' : 0.0}), }

Does it help?

r.

<http://ft.trillian.im/b820c2e0aaf525034498f9740f19cbbd7b172056/6husEB3Ixmr7K...>

среда, 19 июня 2013 г., 16:58:44 UTC+7 пользователь Robert Cimrman написал:

...

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:

1. the problem is more difficult to solve (1 more equation)
2. 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

...

...

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

написал: -

...

...

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.

Robert,

I have set boundary conditions, but the matrix is still singular.

regions = {
    'Top'         : ('nodes in (z >  0.9999)', {}),
    'Bottom'      : ('nodes in (z < -0.9999)', {}),
    'Right'       : ('nodes in (y >  0.9999)', {}),
    'Left'        : ('nodes in (y < -0.9999)', {}),
    'Far'         : ('nodes in (x >  0.9999)', {}),
    'Near'        : ('nodes in (x < -0.9999)', {}),
}

ebcs = {
    'fix0' : ('Top',    {'u.0' : 0.0},),
    'fix1' : ('Bottom', {'u.0' : 0.0},),
    'fix2' : ('Left',   {'u.0' : 0.0},),
    'fix3' : ('Right',  {'u.0' : 0.0},),
    'fix4' : ('Far',    {'u.0' : 0.0},),
    'fix5' : ('Near',   {'u.0' : 0.0},),
}

sfepy: nls: iter: 0, residual: 1.528953e-01 (rel: 1.000000e+00) warning: (almost) singular matrix! (estimated cond. number: 3.76e+15) sfepy: rezidual: 0.00 [s] sfepy: solve: 0.00 [s] sfepy: matrix: 0.00 [s] sfepy: nls: iter: 1, residual: 4.692475e-17 (rel: 3.069077e-16) sfepy: equation "tmp": sfepy: ev_grad.1.Omega( u ) sfepy: updating materials... sfepy: ...done in 0.00 s

среда, 19 июня 2013 г., 19:04:08 UTC+7 пользователь Robert Cimrman написал:

On 06/19/2013 12:56 PM, Alexander Mihailov wrote:

...

Yes, Robert, you are right, regions were empty.

After correcting regions and setting post_process_hook, I have got some solution, slowly but surely it becomes believable, but the matrix is still singular and residual is high...

sfepy: nls: iter: 0, residual: 1.528953e-02 (rel: 1.000000e+00) warning: (almost) singular matrix! (estimated cond. number: 6.06e+15) sfepy: rezidual: 0.01 [s] sfepy: solve: 0.01 [s] sfepy: matrix: 0.00 [s] sfepy: linear system not solved! (err = 1.782581e-02 < 1.000000e-10) sfepy: linesearch: iter 1, (3.34778e-02 < 1.52894e-02) (new ls: 1.000000e-01) sfepy: nls: iter: 1, residual: 1.435926e-02 (rel: 9.391562e-01) sfepy: equation "tmp": sfepy: ev_grad.1.Omega( u ) sfepy: updating materials... sfepy: ...done in 0.00 s

There are still some subtleties that need to be considered?

The scalar field needs to be fixed somewhere, at least in a single vertex, as:

regions = { 'Node' : ('node 0', {}), }

ebcs = { 'fix' : ('Node', {'u.0' : 0.0}), }

Does it help?

r.

...

< http://ft.trillian.im/b820c2e0aaf525034498f9740f19cbbd7b172056/6husEB3Ixmr7K...>

...

среда, 19 июня 2013 г., 16:58:44 UTC+7 пользователь Robert Cimrman

написал:

...

...

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:

1. the problem is more difficult to solve (1 more equation)
2. 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...

...

...

...

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]

...

...

...

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

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.

Hmm, it might be caused by the second equation. I would really just solve the Poisson equation and used the post-processing. But the solver converged even if it complained - did you look at the solution?

r.

On 06/19/2013 05:40 PM, Alexander Mihailov wrote:

Robert,

I have set boundary conditions, but the matrix is still singular.

 regions = {
     'Top'         : ('nodes in (z >  0.9999)', {}),
     'Bottom'      : ('nodes in (z < -0.9999)', {}),
     'Right'       : ('nodes in (y >  0.9999)', {}),
     'Left'        : ('nodes in (y < -0.9999)', {}),
     'Far'         : ('nodes in (x >  0.9999)', {}),
     'Near'        : ('nodes in (x < -0.9999)', {}),
 }

 ebcs = {
     'fix0' : ('Top',    {'u.0' : 0.0},),
     'fix1' : ('Bottom', {'u.0' : 0.0},),
     'fix2' : ('Left',   {'u.0' : 0.0},),
     'fix3' : ('Right',  {'u.0' : 0.0},),
     'fix4' : ('Far',    {'u.0' : 0.0},),
     'fix5' : ('Near',   {'u.0' : 0.0},),
 }

sfepy: nls: iter: 0, residual: 1.528953e-01 (rel: 1.000000e+00) warning: (almost) singular matrix! (estimated cond. number: 3.76e+15) sfepy: rezidual: 0.00 [s] sfepy: solve: 0.00 [s] sfepy: matrix: 0.00 [s] sfepy: nls: iter: 1, residual: 4.692475e-17 (rel: 3.069077e-16) sfepy: equation "tmp": sfepy: ev_grad.1.Omega( u ) sfepy: updating materials... sfepy: ...done in 0.00 s

среда, 19 июня 2013 г., 19:04:08 UTC+7 пользователь Robert Cimrman написал:

...

On 06/19/2013 12:56 PM, Alexander Mihailov wrote:

...

Yes, Robert, you are right, regions were empty.

After correcting regions and setting post_process_hook, I have got some solution, slowly but surely it becomes believable, but the matrix is still singular and residual is high...

sfepy: nls: iter: 0, residual: 1.528953e-02 (rel: 1.000000e+00) warning: (almost) singular matrix! (estimated cond. number: 6.06e+15) sfepy: rezidual: 0.01 [s] sfepy: solve: 0.01 [s] sfepy: matrix: 0.00 [s] sfepy: linear system not solved! (err = 1.782581e-02 < 1.000000e-10) sfepy: linesearch: iter 1, (3.34778e-02 < 1.52894e-02) (new ls: 1.000000e-01) sfepy: nls: iter: 1, residual: 1.435926e-02 (rel: 9.391562e-01) sfepy: equation "tmp": sfepy: ev_grad.1.Omega( u ) sfepy: updating materials... sfepy: ...done in 0.00 s

There are still some subtleties that need to be considered?

The scalar field needs to be fixed somewhere, at least in a single vertex, as:

regions = { 'Node' : ('node 0', {}), }

ebcs = { 'fix' : ('Node', {'u.0' : 0.0}), }

Does it help?

r.

...

< http://ft.trillian.im/b820c2e0aaf525034498f9740f19cbbd7b172056/6husEB3Ixmr7K...>

...

среда, 19 июня 2013 г., 16:58:44 UTC+7 пользователь Robert Cimrman

написал:

...

...

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:

1. the problem is more difficult to solve (1 more equation)
2. 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...

...

...

...

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]

...

...

> 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

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. >

I got it!

<http://ft.trillian.im/b820c2e0aaf525034498f9740f19cbbd7b172056/6hvU8yZbxn7ko...>

That really was a bad mesh file: elements of brick and the remaining ones were inconsistent.

Thanks all! :)