[petsc-users] Question about linking LAPACK library

[Matthew Knepley]

On Mon, Apr 24, 2023 at 11:47 PM ­권승리 / 학생 / 항공우주공학과 <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.

  Thanks,

     Matt


> best,
>
> Seung Lee Kwon
>
> 2023년 4월 25일 (화) 오후 12:32, Barry Smith <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>
>> 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
>> 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
> 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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