[petsc-users] What does PCASMSetOverlap do?

Wed Apr 13 08:55:26 CDT 2022

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/>
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