Dear Wolfgang, What you said makes sense.
Now that my LinearOperator is defined as B_0 + W * M * W^T, I only need to find an appropriate iterative solver that can solve the inverse of this operator (the underlying matrix is fully dense) efficiently. Best, Tao On Friday, April 19, 2024 at 11:25:10 PM UTC-4 Wolfgang Bangerth wrote: > On 4/19/24 19:42, Tao Jin wrote: > > > > Thank you so much for your reply. I think my problem has two potential > issues: > > 1. W * M * W^T will be an n by n fully dense matrix with n > 100k. Even > if it > > is valid to use LinearOperator to perform W * M * W^T, will memory > required to > > store this operator be an issue? > > 2. I still have to solve B x= (B_0 + W * M * W^T) x = p. Whether linear > > solvers such as CG will be efficient enough is also an issue since W * M > * W^T > > is fully dense. > > Tao, > like I mentioned, a line like > S = linear_operator(W) * linear_operator(M) * transpose_operator(W) > does not actually compute the product of these matrices. The documentation > of > step-20 and step-22 goes to great length in explaining this issue. All the > object S provides is the ability to multiple S by a vector, for which you > only > need matrix-vector products because > S x > = (W M W^T) x > = W (M (W^T x)) > > The product of matrices is never computed because it is never needed. > > Best > W. > > -- > ------------------------------------------------------------------------ > Wolfgang Bangerth email: [email protected] > www: http://www.math.colostate.edu/~bangerth/ > > > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/c9d2909f-749f-422d-942b-4cb0ca78b6edn%40googlegroups.com.
