> On 25 Apr 2023, at 11:43 AM, Matthew Knepley <[email protected]> wrote: > > On Mon, Apr 24, 2023 at 11:47 PM 권승리 / 학생 / 항공우주공학과 <[email protected] > <mailto:[email protected]>> 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 <[email protected] >> <mailto:[email protected]>>님이 작성: >>> >>> How large are the dense matrices you would like to invert? >>> >>>> On Apr 24, 2023, at 11:27 PM, 권승리 / 학생 / 항공우주공학과 <[email protected] >>>> <mailto:[email protected]>> 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 : [email protected] <mailto:[email protected]> >>>> 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 : [email protected] <mailto:[email protected]> >> 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/>
