[petsc-users] What does PCASMSetOverlap do?

Wed Apr 13 08:58:02 CDT 2022

Thank you, Matt! I will do that.

On Wed, Apr 13, 2022 at 9:55 PM Matthew Knepley <knepley at gmail.com> wrote:

> On Wed, Apr 13, 2022 at 9:53 AM Zhuo Chen <chenzhuotj at gmail.com> wrote:
>
>> Dear Pierre,
>>
>> Thank you! I looked into the webpage you sent me and I think it is not
>> the situation that I am talking about.
>>
>> I think I need to attach a figure for an illustrative purpose. This
>> figure is Figure 14.5 of "Iterative Method for Sparse Linear Systems" by
>> Saad.
>> [image: domaindecompostion.png]
>>
>> If I divide the domain into these three subdomains, as you can see, the
>> middle block has two interfaces. In the matrix form, its rows are not
>> contiguous, i.e., distributed in different processors. If ASM only expands
>> in the contiguous direction, the domain decomposition become ineffective, I
>> guess.
>>
>
> No, we get exactly this picture. Saad is talking about exactly the
> algorithm we use.
>
> Maybe you should just look at the subdomains being produced, -mat_view
> draw -draw_pause 3
>
>    Matt
>
>
>> On Wed, Apr 13, 2022 at 9:36 PM Pierre Jolivet <pierre at joliv.et> wrote:
>>
>>>
>>>
>>> On 13 Apr 2022, at 3:30 PM, Zhuo Chen <chenzhuotj at gmail.com> wrote:
>>>
>>> Dear Matthew and Mark,
>>>
>>> Thank you very much for the reply! Much appreciated!
>>>
>>> The question was about a 1D problem. I think I should say core 1 has row
>>> 1:32 instead of 1:32, 1:32 as it might be confusing.
>>>
>>> So the overlap is extended to both directions for the middle processor
>>> but only toward the increasing direction for the first processor and the
>>> decreasing direction for the last processor. In 1D, this makes sense as the
>>> domain is contiguous. However, in 2D with domain decomposition with spacial
>>> overlaps, this overlapping would not work as one subdomain can have several
>>> neighbor domains. Mark mentioned generalized ASM, is that the correct
>>> direction that I should look for?
>>>
>>>
>>> What is it that you want to do exactly?
>>> If you are using a standard discretisation kernel, e.g., piecewise
>>> linear finite elements, MatIncreaseOverlap() called by PCASM will generate
>>> an overlap algebraically which is equivalent to the overlap you would have
>>> gotten geometrically.
>>> If you know that “geometric” overlap (or want to use a custom definition
>>> of overlap), you could use
>>> https://petsc.org/release/docs/manualpages/PC/PCASMSetLocalSubdomains.html
>>>
>>> Thanks,
>>> Pierre
>>>
>>> Best regards.
>>>
>>>
>>> On Wed, Apr 13, 2022 at 9:14 PM Matthew Knepley <knepley at gmail.com>
>>> wrote:
>>>
>>>> On Wed, Apr 13, 2022 at 9:11 AM Mark Adams <mfadams at lbl.gov> wrote:
>>>>
>>>>>
>>>>>
>>>>> On Wed, Apr 13, 2022 at 8:56 AM Matthew Knepley <knepley at gmail.com>
>>>>> wrote:
>>>>>
>>>>>> On Wed, Apr 13, 2022 at 6:42 AM Mark Adams <mfadams at lbl.gov> wrote:
>>>>>>
>>>>>>> No, without overlap you have, let say:
>>>>>>> core 1:   1:32, 1:32
>>>>>>> core 2:   33:64,  33:64
>>>>>>>
>>>>>>> Overlap will increase the size of each domain so you get:
>>>>>>> core 1:   1:33, 1:33
>>>>>>> core 2:   32:65,  32:65
>>>>>>>
>>>>>>
>>>>>> I do not think this is correct. Here is the algorithm. Imagine the
>>>>>> matrix is a large graph. When you divide rows, you
>>>>>> can think of that as dividing the vertices into sets. If overlap = 1,
>>>>>> it means start with my vertex set, and add all vertices
>>>>>> that are just 1 edge away from my set.
>>>>>>
>>>>>
>>>>> I think that is what was said. You increase each subdomain by one row
>>>>> of vertices.
>>>>> So in 1D, vertex 32 and 33 are in both subdomains and you have an
>>>>> overlap region of size 2.
>>>>> They want an overlap region of size 1, vertex 33.
>>>>>
>>>>
>>>> This is true, but I did not think they specified a 1D mesh.
>>>>
>>>>   Matt
>>>>
>>>>
>>>>>
>>>>>>   Thanks,
>>>>>>
>>>>>>      Matt
>>>>>>
>>>>>>
>>>>>>> What you want is reasonable but requires PETSc to pick a separator
>>>>>>> set, which is not well defined.
>>>>>>> You need to build that yourself with gasm (I think) if you want this.
>>>>>>>
>>>>>>> Mark
>>>>>>>
>>>>>>> On Wed, Apr 13, 2022 at 3:17 AM Zhuo Chen <chenzhuotj at gmail.com>
>>>>>>> wrote:
>>>>>>>
>>>>>>>> Hi,
>>>>>>>>
>>>>>>>> I hope that everything is going well with everybody.
>>>>>>>>
>>>>>>>> I have a question about the PCASMSetOverlap. If I have a 128x128
>>>>>>>> matrix and I use 4 cores with overlap=1. Does it mean that from core 1 to
>>>>>>>> core 4, the block ranges are (starting from 1):
>>>>>>>>
>>>>>>>> core 1:   1:33, 1:33
>>>>>>>> core 2:   33:65,  33:65
>>>>>>>> core 3:   65:97,  65:97
>>>>>>>> core 4:   95:128, 95:128
>>>>>>>>
>>>>>>>> Or is it something else? I cannot tell from the manual.
>>>>>>>>
>>>>>>>> Many thanks in advance.
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> --
>>>>>>>> Zhuo Chen
>>>>>>>> Department of Astronomy
>>>>>>>> Tsinghua University
>>>>>>>> Beijing, China 100084
>>>>>>>> *https://czlovemath123.github.io/
>>>>>>>> <https://czlovemath123.github.io/>*
>>>>>>>>
>>>>>>>
>>>>>>
>>>>>> --
>>>>>> 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
>>>>>>
>>>>>> https://www.cse.buffalo.edu/~knepley/
>>>>>> <http://www.cse.buffalo.edu/~knepley/>
>>>>>>
>>>>>
>>>>
>>>> --
>>>> 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
>>>>
>>>> https://www.cse.buffalo.edu/~knepley/
>>>> <http://www.cse.buffalo.edu/~knepley/>
>>>>
>>>
>>>
>>> --
>>> Zhuo Chen
>>> Department of Astronomy
>>> Tsinghua University
>>> Beijing, China 100084
>>> *https://czlovemath123.github.io/ <https://czlovemath123.github.io/>*
>>>
>>>
>>>
>>
>> --
>> Zhuo Chen
>> Department of Astronomy
>> Tsinghua University
>> Beijing, China 100084
>> *https://czlovemath123.github.io/ <https://czlovemath123.github.io/>*
>>
>
>
> --
> 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
>
> https://www.cse.buffalo.edu/~knepley/
> <http://www.cse.buffalo.edu/~knepley/>
>

-- 
Zhuo Chen
Department of Astronomy
Tsinghua University
Beijing, China 100084
*https://czlovemath123.github.io/ <https://czlovemath123.github.io/>*
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