Thank you for your reply. I think I gave an example of an unrealistic problem.
I just wanted to know how to compute the inverse matrix, so I was wondering if there is an example of computing the inverse matrix in PETSc. Alternatively, I want to know how to link the LAPACK library. best, Seung Lee Kwon 2023년 4월 25일 (화) 오후 6:44, Matthew Knepley <knep...@gmail.com>님이 작성: > On Mon, Apr 24, 2023 at 11:47 PM 권승리 / 학생 / 항공우주공학과 <ksl7...@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 <bsm...@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 <ksl7...@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 : ksl7...@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 : ksl7...@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/> > -- 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 : ksl7...@snu.ac.kr Office : +82-2-880-7389 C. P : +82-10-4695-1062