[petsc-users] DMDAGetElements and global/local element number

Thu Sep 12 23:53:02 CDT 2019

El jue., 12 de sep. de 2019 a la(s) 17:01, Dave May (dave.mayhem23 at gmail.com)
escribió:

>
> Please always use "reply-all" so that your messages go to the list.
> This is standard mailing list etiquette.  It is important to preserve
> threading for people who find this discussion later and so that we do
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> answer faster that way too.
>

> On Thu, 12 Sep 2019 at 22:26, Emmanuel Ayala <juaneah at gmail.com> wrote:
>
>> Thank you for the answer.
>>
>> El jue., 12 de sep. de 2019 a la(s) 15:21, Dave May (
>> dave.mayhem23 at gmail.com) escribió:
>>
>>>
>>>
>>> On Thu, 12 Sep 2019 at 20:21, Emmanuel Ayala via petsc-users <
>>> petsc-users at mcs.anl.gov> wrote:
>>>
>>>> Hi everyone, it would be great if someone can give me a hint for this
>>>> issue, i have been trying to figure out how to solve it, but i did not
>>>> succeed
>>>>
>>>> I'm using DMDA to generate a 3D mesh (DMDA_ELEMENT_Q1). I'm trying to
>>>> fill a MPI matrix with some values wich are related to the dofs of each
>>>> element node, moreover i need to set this values based on the element
>>>> number. Something like:
>>>>
>>>> mpi_A(total_elements X total_dofs)
>>>>
>>>>                                                  total_dofs
>>>> row_0 (element_0)                      a_0 a_1 a_2 ... a_23
>>>> row_1 (element_1)                                     a_0 a_1 a_2 ...
>>>> a_23
>>>> row_2 (element_2)
>>>>     a_0 a_1 a_2 ... a_23
>>>> .
>>>> .
>>>> .
>>>> row_n (element_n)                            a_0 a_1 a_2 ... a_23
>>>>
>>>> The element number is related to the row index. And the matrix values
>>>> are set depending of the DOFs related to the element.
>>>>
>>>> With DMDAGetElements i can read the LOCAL nodes connected to the
>>>> element and then the DOFs associated to the element. I can handle the local
>>>> and global relations with DMGetLocalToGlobalMapping,
>>>> MatSetLocalToGlobalMapping and MatSetValuesLocal. BUT i CAN NOT understand
>>>> how to know the element number in LOCAL or GLOBAL contex. DMDAGetElements
>>>> gives the NUMBER OF ELEMENTS owned in the local process, but there is not
>>>> any information about the local or global ELEMENT NUMBER.
>>>>
>>>> How to know the local or global element number related to the data
>>>> provided by DMDAGetElements?
>>>>
>>>
>>> The DMDA defines cells of the same type (quads (2D) or hex (3D), hence
>>> every cell defines the same number of vertices.
>>>
>>
>>> DMDAGetElements(DM dm,PetscInt *nel,PetscInt *nen,const PetscInt *e[])
>>> nel - number of local elements
>>> nen - number of element nodes
>>> e - the local indices of the elements' vertices
>>>
>>> e[] defines the ordering of the elements. e[] is an array containing all
>>> of the element-vertex maps. Since each element in the DMDA has the same
>>> number of vertices, the first nen values in e[] correspond to the vertices
>>> (local index) associated with the first element. The next nen values in e[]
>>> correspond to the vertices of the second element.  The vertices for any
>>> (local) element with the index "cid" can be sought via e[nen*cid + i] where
>>> i would range from 0 to nen-1.
>>>
>>>
>> You are right. I can handle the local information, i think the idea is:
>>
>>     for ( PetscInt i = 0; i < nel; i++ )
>>             for (PetscInt j = 0; j < nen; j++)
>>                 PetscSynchronizedPrintf(PETSC_COMM_WORLD,"local element
>> %d : e[%d] = %d\n", i, j, e[i*nen+j]);
>>
>> BUT, it does not give information regarding to the ELEMENT identifier
>> (number). I need the element number to ordering the elements inside of a
>> MPI matrix. I want to access to each element data by means of the matrix
>> row . I mean, in the row_0 there is the information (spreading through the
>> columns) of the element_0.
>>
>
> I think this is a mis-understanding. The element number is not related to
> a row in the matrix.
>

Sorry, I did not express myself very well: I WANT TO CREATE a matrix which
let me "access to each element data by means of the matrix row".

> The element is associated with vertices (basis functions), and each vertex
> (basis) in the DMDA is given a unique index. The index of that basis
> corresponds to a row (column) if it's a test (trial) function. So if you
> have any element defined by the array e[], you know how to insert values
> into a matrix by using the vertex indices.
>
>
OK, i got it.

>
>>
>> The element vertices are numbered starting from 0, for each process. It
>> does not give information about the element number.
>>
>> Why would you ever want, or need, the global element number? What is the
>>> use case?
>>>
>>
>> I'm performing topology optimization, and it is part of gradient
>> computation. I'm already have the analytic gradient.
>> I need the global element number to link nodal displacements with the
>> element.
>>
>
> Any nodal displacement, except those at the corners of your physical
> domain are associated with multiple elements. There isn't a one-to-one map
> between nodes and elements.
>
>
>
>> I can use a local element number just if I have a equivalence between
>> this local number and the global element number.
>>
>
> I obviously don't understand what you want to do.
>
>
Actually this is (below) the information that i need, thanks! Let me try
it! :)

> However, here is one way to achieve what you are asking for: specifically
> relating local element indices to global indices.
> Assuming by "global element number" you are referring to what PETSc calls
> the "natural" ordering, then the dumbest way to convert from the local
> element index to the natural element index is the following:
> (i) upon creation, use DMSetUniformCoordinates to define a unit 1 box;
> (ii) compute the cell dimensions dx, dy associated with your uniform grid
> layout;
> (iii) traverse through the e[] array return by DMDAGetElements. For each
> element, get the vertices and compute the centroid cx, cy and then compute
>   PetscInt J = (PetscInt)(cy/dy);
>   PetscInt I = (PetscInt)(cx/dx);
>   PetscInt natural_id = I + J * mx;
> where mx is the number of elements in the i direction in your domain (not
> the sub-domain).
> You can determine mx by calling
>
> DMDAGetInfo(dm,NULL,&mx,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);
> (iv) after you have computed natural_id for every element, layout the
> global coordinates of the DMDA however you want. Following that, you must
> call the following
>
>   DM dm, cdm;
>   Vec coor,lcoor;
>
>   DMGetCoordinateDM(dm,&cdm);
>   DMGetCoordinates(dm,&coor);
>   DMGetCoordinatesLocal(dm,&lcoor);
>   DMGlobalToLocal(cmd,coor,INSERT_VALUES,lcoor);
>
> The above must be executed to ensure the new coordinates values are
> propagated to coords associated with your local sub-domain.
>
> I doubt this will solve your _actual_ problem.
>

Thanks for your time!
Best regards.

> Thanks,
> Dave
>
>
>>
>>> Thanks,
>>> Dave
>>>
>>>
>>>
>>>
>>>>
>>>> Thank you.
>>>>
>>>
>> Thanks!
>>
>
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