Thank you, Praveen and Peter. Seems like what you've suggested meets my
needs.
Have a great weekend!
Best,
--Xuefeng Li, (504)865-3340(phone)
Chair, Department of Mathematics and Computer Science
Like floating clouds, the heart rests easy
Like flowing water, the spirit stays free
Loyola University New Orleans
New Orleans, Louisiana (504)865-2051(fax)
On Wed, Oct 2, 2024 at 8:36 AM Peter Munch <[email protected]> wrote:
> I guess what you need is something like VectorTools::point_values() (
> https://www.dealii.org/developer/doxygen/deal.II/namespaceVectorTools.html#a4638b2ccdbf190a9b1f6bbbee98a2978)
> and VectorTools::point_gradients(
> https://www.dealii.org/developer/doxygen/deal.II/namespaceVectorTools.html#aa96d29e9f7275de7556d6222d8023849).
> If you need more control, you can take a look at the underlying classes:
> RemotePointEvaluation (
> https://www.dealii.org/developer/doxygen/deal.II/classUtilities_1_1MPI_1_1RemotePointEvaluation.html)
> and FEPointEvaluation (
> https://www.dealii.org/developer/doxygen/deal.II/classFEPointEvaluation.html).
> A good starting point might be step-87 and step-89:
> https://www.dealii.org/developer/doxygen/deal.II/step_87.html and
> https://www.dealii.org/developer/doxygen/deal.II/step_89.html.
>
> Best,
> Peter
>
> On Wednesday 2 October 2024 at 15:00:00 UTC+2 [email protected] wrote:
>
>> I apologize for hitting the Send button before completing my questions.
>>
>> I realize that the evaluation of a FEM function is an expensive process
>> due to the fact that we'll need to determine the cell in the mesh where a
>> point belongs before interpolation takes place. That's why I'm just asking
>> for the possibility of existence of such a capability in dealii.
>>
>> Your suggestions are greatly appreciated!
>>
>> Best,
>>
>> --Xuefeng Li, (504)865-3340(phone)
>> Department of Mathematics and Computer Science
>> Like floating clouds, the heart rests easy
>> Like flowing water, the spirit stays free
>> Loyola University New Orleans
>> New Orleans, Louisiana (504)865-2051(fax)
>>
>>
>> On Tue, Oct 1, 2024 at 3:13 PM 'Xuefeng Li' via deal.II User Group <
>> [email protected]> wrote:
>>
>>> Hi, everyone!
>>>
>>> This is a problem related to post-processing. But I can't find a
>>> solution from the DataPostprocessor class. Here is the description of my
>>> problem.
>>>
>>>
>>> 1. Solve a PDE on a 2D domain [0, 1]X[0, 1] in the x-y plane by FEM
>>> with a fixed mesh, say, a 16X16 mesh. The FEM solution is a Vector u=u(x,
>>> y). Information of u(x, y) is known if (x, y) is a grid point of the
>>> mesh.
>>> 2. I need to solve for a curve x=f(y) defined by u(f(y), y)=f(y),
>>> for 0<y<1, where f(0) is known.
>>> 3. On paper, we can solve for curve x=f(y) using Newton's method so
>>> long as u(x, y) and derivatives of u(x,y) are known for all (x, y) in [0,
>>> 1]X[0, 1].
>>> 4. Is it possible to evaluate solution u and its derivatives at (x,
>>> y) which is not a grid point of the mesh?
>>> 5. Ultimately, curve x=f(y) will be approximated by f(0), f(y_1),
>>> f(y_2), ..., f(y_{15}), f(1). Here is a related problem. Is there a way
>>> to
>>> get a 1D projection of a 2D mesh in dealii? In this case, I need the
>>> projection of the 16X16 mesh onto the y-axis.
>>>
>>>
>>> --
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>>> .
>>>
>> --
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