Pierre Jolivet Pierre.Jolivet at lip6.fr
Tue Apr 25 04:52:20 CDT 2023

```> On 25 Apr 2023, at 11:43 AM, Matthew Knepley <knepley at gmail.com> wrote:
>
> On Mon, Apr 24, 2023 at 11:47 PM ­권승리 / 학생 / 항공우주공학과 <ksl7912 at snu.ac.kr <mailto:ksl7912 at snu.ac.kr>> wrote:
>> Dear all
>>
>> It depends on the problem. It can have hundreds of thousands of degrees of freedom.
>
> Suppose your matrix was dense and had 1e6 dofs. The work to invert a matrix is O(N^3) with a small
> constant, so it would take 1e18 = 1 exaflop to invert this matrix and about 10 Terabytes of RAM to store
> it. Is this available to you? PETSc's supports Elemental and SCALAPACK for this kind of calculation.
>
> If the system is sparse, you could invert it using MUMPS, SuperLU_dist, or Pardiso. Then the work and
> storage depend on the density. There are good estimates for connectivity based on regular grids of given
> dimension. The limiting resource here is usually memory, which motivates people to try iterative methods.
> The convergence of iterative methods depend on detailed properties of your system, like the operator spectrum.

And to wrap this up, if your operator is truly dense, e.g., BEM or non-local discretizations, their are available hierarchical formats such as MatH2Opus and MatHtool.
They have efficient matrix-vector product implementations such that you can solve linear systems without having to invert (or even store) the coefficient matrix explicitly.

Thanks,
Pierre

>   Thanks,
>
>      Matt
>
>> best,
>>
>> Seung Lee Kwon
>>
>> 2023년 4월 25일 (화) 오후 12:32, Barry Smith <bsmith at petsc.dev <mailto:bsmith at petsc.dev>>님이 작성:
>>>
>>>   How large are the dense matrices you would like to invert?
>>>
>>>> On Apr 24, 2023, at 11:27 PM, ­권승리 / 학생 / 항공우주공학과 <ksl7912 at snu.ac.kr <mailto:ksl7912 at snu.ac.kr>> wrote:
>>>>
>>>> Dear all
>>>>
>>>> Hello.
>>>> I want to make an inverse matrix like inv(A) in MATLAB.
>>>>
>>>> Are there some methods to inverse matrix in petsc?
>>>>
>>>> If not, I want to use the inverse function in the LAPACK library.
>>>>
>>>> Then, how to use the LAPACK library in petsc? I use the C language.
>>>>
>>>> Best,
>>>>
>>>> Seung Lee Kwon
>>>>
>>>> --
>>>> Seung Lee Kwon, Ph.D.Candidate
>>>> Aerospace Structures and Materials Laboratory
>>>> Department of Mechanical and Aerospace Engineering
>>>> Seoul National University
>>>> Building 300 Rm 503, Gwanak-ro 1, Gwanak-gu, Seoul, South Korea, 08826
>>>> E-mail : ksl7912 at snu.ac.kr <mailto:ksl7912 at snu.ac.kr>
>>>> Office : +82-2-880-7389
>>>> C. P : +82-10-4695-1062
>>>
>>
>>
>> --
>> Seung Lee Kwon, Ph.D.Candidate
>> Aerospace Structures and Materials Laboratory
>> Department of Mechanical and Aerospace Engineering
>> Seoul National University
>> Building 300 Rm 503, Gwanak-ro 1, Gwanak-gu, Seoul, South Korea, 08826
>> E-mail : ksl7912 at snu.ac.kr <mailto:ksl7912 at snu.ac.kr>
>> Office : +82-2-880-7389
>> C. P : +82-10-4695-1062
>
>
> --
> 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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