PETScWrappers::MatrixBase implement clear_rows_columns

[stefanozampini]

Add missing support for zeroing rows and columns of a PETSc matrix.

Note that it is still not possible with block operators. That will require PETSc support in MATNEST

[bangerth]

Very nice! I love that you bring all of that knowledge of what PETSc can do these days to these interfaces!

There is a comment in matrix_tools.h that relates to the function you change:

  /**
   * Apply Dirichlet boundary conditions to the system matrix and vectors as
   * described in the general documentation of this namespace. This function
   * works on the classes that are used to wrap PETSc objects.
   *
   * <b>Important:</b> This function is not very efficient: it needs to
   * alternatingly read and write into the matrix, a situation that PETSc does
   * not handle well. In addition, we only get rid of rows corresponding to
   * boundary nodes, but the corresponding case of deleting the respective
   * columns (i.e. if @p eliminate_columns is @p true) is not presently
   * implemented, and probably will never because it is too expensive without
   * direct access to the PETSc data structures. (This leads to the situation
   * where the action indicated by the default value of the last argument is
   * actually not implemented; that argument has <code>true</code> as its
   * default value to stay consistent with the other functions of same name in
   * this namespace.)
   *
   * This function is used in step-17 and step-18.
   *
   * @note If the matrix is stored in parallel across multiple processors
   * using MPI, this function only touches rows that are locally stored and
   * simply ignores all other rows. In other words, each processor is
   * responsible for its own rows, and the @p boundary_values argument needs
   * to contain all locally owned rows of the matrix that you want to have
   * treated. (But it can also contain entries for degrees of freedom not
   * owned locally; these will simply be ignored.) Further, in the context of
   * parallel computations, you will get into trouble if you treat a row while
   * other processors still have pending writes or additions into the same
   * row. In other words, if another processor still wants to add something to
   * an element of a row and you call this function to zero out the row, then
   * the next time you call compress() may add the remote value to the zero
   * you just created. Consequently, you will want to call compress() after
   * you made the last modifications to a matrix and before starting to clear
   * rows.
   */
  void
  apply_boundary_values(
    const std::map<types::global_dof_index, PetscScalar> &boundary_values,
    PETScWrappers::MatrixBase &                           matrix,
    PETScWrappers::VectorBase &                           solution,
    PETScWrappers::VectorBase &                           right_hand_side,
    const bool eliminate_columns = true);

Is this still current after your changes?

[stefanozampini]

@bangerth I have implemented your suggestions. This is ready to go

[bangerth]

/rebuild