[petsc-users] better way of setting dirichlet boundary conditions

[Matthew Knepley]

On Wed, Aug 21, 2013 at 7:12 AM, Bishesh Khanal <bisheshkh at gmail.com> wrote:

>
>
>
> On Wed, Aug 21, 2013 at 1:57 PM, Matthew Knepley <knepley at gmail.com>wrote:
>
>> On Wed, Aug 21, 2013 at 4:59 AM, Bishesh Khanal <bisheshkh at gmail.com>wrote:
>>
>>>
>>>
>>>
>>> On Tue, Aug 20, 2013 at 3:06 PM, Matthew Knepley <knepley at gmail.com>wrote:
>>>
>>>> On Tue, Aug 20, 2013 at 7:19 AM, Bishesh Khanal <bisheshkh at gmail.com>wrote:
>>>>
>>>>> Hi all,
>>>>> In solving problems such as laplacian/poisson equations with dirichlet
>>>>> boundary conditions with finite difference methods, I set explicity the
>>>>> required values to the diagonal of the boundary rows of the system matrix,
>>>>> and the corresponding rhs vector.
>>>>> i.e.  typically my matrix building loop would be like:
>>>>>
>>>>> e.g. in 2d problems, using DMDA:
>>>>>
>>>>> FOR (i=0 to xn-1, j = 0 to yn-1)
>>>>>      set row.i = i, row. j = j
>>>>>      IF (i = 0 or xn-1) or (j = 0 or yn-1)
>>>>>             set diagonal value of matrix A to 1 in current row.
>>>>>      ELSE
>>>>>             normal interior points: set the values accordingly
>>>>>      ENDIF
>>>>> ENDFOR
>>>>>
>>>>> Is there another preferred method instead of doing this ? I saw
>>>>> functions such as MatZeroRows()
>>>>> when following the answer in the FAQ regarding this at:
>>>>> http://www.mcs.anl.gov/petsc/documentation/faq.html#redistribute
>>>>>
>>>>> but I did not understand what it is trying to say in the last sentence
>>>>> of the answer "An alternative approach is ... into the load"
>>>>>
>>>>
>>>> Since those values are fixed, you do not really have to solve for them.
>>>> You can eliminate them from your
>>>> system entirely. Imagine you take the matrix you produce, plug in the
>>>> values to X, act with the part of the
>>>> matrix  that hits them A_ID X, and move that to the RHS, then eliminate
>>>> the row for Dirichlet values.
>>>>
>>>
>>> Now I understand the concept, thanks! So how do I efficiently do this
>>> with petsc functions when I am using DMDA which contains the boundary
>>> points too? Conceptually the steps would be the following, I think, but
>>> which petsc functions would enable me to do this efficiently, for example,
>>> without explicitly creating the new matrix A1 in the following and instead
>>> informing KSP about it ?
>>> 1) First create the big system matrix (from DM da) including the
>>> identity rows for Dirichlet points and corresponding rhs, Lets say Ax = b.
>>> 2) Initialize x with zero, then set the desired Dirichlet values on
>>> corresponding boundary points of x.
>>> 3) Create a new matrix, A1 with zeros everywhere except the row,col
>>> positions corresponding to Dirchlet points where put -1.
>>> 4) Get b1 by multiplying A1 with x.
>>> 5) Update rhs with b = b + b1.
>>> 6) Now update A by removing its rows and columns that correspond to the
>>> Dirichlet points, and remove corresponding rows of b and x.
>>> 7) Solve Ax=b
>>>
>>
>> This is generally not a good thing to do with FD.
>>
>
> Do you mean that with FD, it is better to solve the bigger matrix with the
> identity row for Dirichlet points instead of excluding them (That is the
> way I illustrated in the pseudocode in the very first email above)?
> And why is it not a good thing ? (I thought by excluding the rows-cols of
> Dirichlet points would enable us to preserve the symmetry for symmetrical
> problems ?
>

If you want symmetry, you can do MatZeroRowColumns(). I said is generally
not a good idea because it is more complicated to eliminate
them in the FD case.

You can definitely do what you propose. With FEM, it makes more sense. You
eliminate constrained variables from the system, but
keep the values in the local vector. Then when you do an element integral,
you get the correct answer including the boundary
conditions, and everything is natural.

    Matt


>
>>    Matt
>>
>>
>>>>    Matt
>>>>
>>>> Thanks,
>>>>> Bishesh
>>>>>
>>>>
>>>>
>>>>
>>>> --
>>>> What most experimenters take for granted before they begin their
>>>> experiments is infinitely more interesting than any results to which their
>>>> experiments lead.
>>>> -- Norbert Wiener
>>>>
>>>
>>>
>>
>>
>> --
>> What most experimenters take for granted before they begin their
>> experiments is infinitely more interesting than any results to which their
>> experiments lead.
>> -- Norbert Wiener
>>
>
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20130821/d30afca9/attachment.html>