Dear Jean-Paul, Thank you very much for your help. According to your prompt, after many reflections in the past two days, I have come up with a solution, but it has not been verified yet. With new progress, I will communicate with you again. Thanks again for your help.
Best， FU 在 2018年11月16日星期五 UTC+8下午2:59:45，Jean-Paul Pelteret写道： > > Dear FU, > > Yes, I think that the LinearOperator > <https://dealii.org/9.0.0/doxygen/deal.II/classLinearOperator.html> class > and family of helper functions > <https://dealii.org/9.0.0/doxygen/deal.II/group__LAOperators.html> can > help you here. This is because you never use the matrix “A” in isolation, > but rather have it operating on the vector “T” (or some increment of “T” in > your nonlinear solution algorithm). So you can use the LinearOperator class > to create the composite operator “A”, which does not ever compute or hold > the individual entries of “A” itself, but rather performs the action on a > vector that is equivalent to what “A” would. You should have a look at the > class documentation that I linked to earlier. The step-44 tutorial > <https://dealii.org/9.0.0/doxygen/deal.II/step_44.html#Solidsolve_linear_system> > also > provides an example of its use. > > I hope that this helps you move forward with your problem. > Best, > Jean-Paul > > On 16 Nov 2018, at 01:01, FU <fudany...@gmail.com <javascript:>> wrote: > > Hi， > I want to solve AT+BFT^4=C (1), > A, B, F are sparse matrix, T, T^4 are the solution vector. > By Newton method, we need to (1) derivation. > So I want to know how to get A. > Or what do you think of solving this equation? > > best， > FU > > > 在 2018年11月15日星期四 UTC+8下午10:45:24，Jean-Paul Pelteret写道： >> >> Hi, >> >> In general there is, to the best of my knowledge, no easy answer to your >> question. Can you explain what you intend to do with the matrix “A"? That >> would help a great deal, as there may still be some functionality in the >> library to help you. If you intend to perform some operations with “A” then >> we have some wrapper classes called LinearOperators that can produce an >> effective “A” (without computing it directly). But whether or not this >> makes sense depends on the context in which you want to use “A”. >> >> Best, >> Jean-Paul >> >> On 15 Nov 2018, at 15:28, FU <fudany...@gmail.com> wrote: >> >> Thank you very much for your reply. >> >> I probably understand the methods you mentioned, but there is no >> multiplication vector behind the sparse matrix of the solution I asked for. >> >> A=M- (N^T) (M^-1) N, >> >> This is the construction equation of the original sparse matrix. >> >> A is the sparse matrix that I want to get in the end, where N and M are >> sparse matrices. >> >> What else can you do to solve this problem? >> >> Thank you >> >> FU在 2018年11月14日星期三 UTC+8下午2:32:03，Jean-Paul Pelteret写道： >>> >>> Hi, >>> >>> To compute the sparse matrix inverse M^{-1} you would have to use a >>> direct solver such as SparseDirectUMFPACK >>> <https://dealii.org/9.0.0/doxygen/deal.II/classSparseDirectUMFPACK.html>. >>> If this operation (M^{-1})N appears in the context of matrix-vector >>> products, i.e. you’re actually computing something like y = (M^{-1})Nx then >>> you could use an iterative solver >>> <https://dealii.org/9.0.0/doxygen/deal.II/classSolverSelector.html> to >>> invert the system My = (Nx) = b. Here you could be computing the solution y >>> = M^{-1}b using an iterative method. >>> >>> I hope that this helps. >>> Best, >>> Jean-Paul >>> >>> On 14 Nov 2018, at 03:01, FU <fudany...@gmail.com> wrote: >>> >>> (M^-1)N, >>> M and N are sparse matrix, >>> so how to get the inverse of a sparse matrix? >>> >>> -- >>> 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 dealii+un...@googlegroups.com. >>> For more options, visit https://groups.google.com/d/optout. >>> >>> >>> >> -- >> 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 dealii+un...@googlegroups.com. >> For more options, visit https://groups.google.com/d/optout. >> >> >> > -- > 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 dealii+un...@googlegroups.com <javascript:>. > For more options, visit https://groups.google.com/d/optout. > > > -- 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. 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