I am working on the schur complement for eigenvalue problems, following
step - 55. My stiffness block matrix is like this:
*| AB.T |
*
*| BC |*
*
*
and my mass block matrix is structured:
*| M 0 |
*
*| 00 |*
*
*
To obtain A_condensed, inversion of C is required. I have constructed
the linear operators for C_inv and A_condensed using the
inverse_operator and schur_complement functions based on the
documentation here (https://dealii.org/developer/doxygen/deal.II/
group__LAOperators.html#ga76acca911f21089cd3bb385d20ccc995). However,
SLEPcWrappers eigensolvers, such as SLEPcWrappers::SolverKrylovSchur and
SLEPcWrappers::::SolverGeneralizedDavidson, only accept
PETScWrappers::MatrixBase rather than linear operators as said in their
documentations. Is there an easy way to form a
PETScWrappers::MPI::SparseMatrix from the linear operator? I am trying
not to calculate the schur_complement explicitly, however, it seems i
may have to. I would really appreciate it for any suggestions.
Yuchen:
you want to look at PETScWrappers::MatrixFree, which is a class that
from the perspective of PETSc looks like a matrix, but implements its
own matrix-vector product. You'll have to derive your own class from
PETScWrappers::MatrixFree where you implement the vmult() function by
calling the vmult() function of the LinearOperator object you have.
Best
W.
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