In order to make the discussion simple, we can just assume the sparse block is a diagonal matrix. How to take the advantage of the diagonal block matrix?
Fande, On Thu, Sep 20, 2018 at 12:28 PM Fande Kong <[email protected]> wrote: > > > On Thu, Sep 20, 2018 at 12:09 PM Matthew Knepley <[email protected]> > wrote: > >> On Thu, Sep 20, 2018 at 1:26 PM Fande Kong <[email protected]> wrote: >> >>> Hi Developers, >>> >>> MATBAIJ actually assumes that the point-block is dense. It is fine if >>> the block size is small for example less than 50, but we may suffer from a >>> memory issue if the block is large such as 1000. The block is not necessary >>> dense. In my application, neutron transport equations, the block is >>> actually sparse (coming from direction and energy grids). Now I am using >>> MATAIJ, but I want to take into consideration there are many variables on >>> each spatial grid when doing some ILU(0). ILU(0) is used as a subdomain >>> solver for ASM and BJACOBI. >>> >>> I would like to support point-block ILU(0) in MATAIJ (not MATBAIJ) >>> because the block is sparse. Any comments? It is worthwhile to do that? I >>> think we might reduce the symbolic factor time when considering the block. >>> >> >> What optimization do you hope to take advantage of? >> > > The inverse of sparse block can be approximated with the inverse of the > block diagonal. > > Does it help reduce the compute time in symbolic factorization? > > Fande, > > >> The main optimization in sparse LU is finding dense blocks, >> and it should do a good job of that. I do not see what defining huge, >> sparse blocks does for you. >> > >> Thanks, >> >> Matt >> >> >>> Thanks, >>> >>> Fande, >>> >> >> >> -- >> 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/> >> >
