<commit_before>//                       MFEM Example normal-bc - Parallel Version
//
// Compile with: make ex-normal
//
// Sample runs:  ex-normal
//               ex-normal --diffusion --boundary-attribute 1
//               ex-normal --mesh ../miniapps/meshing/icf.mesh
//               ex-normal --mesh sphere_hex27.mesh
//               ex-normal --elimination
//               ex-normal --penalty 1e+4
//
// Description:  Demonstrates solving a linear system subject to a linear
//               constraint, using the ConstrainedSolver object.
//
//               This particular example finds the global L2 projection of the
//               vector field (1, 0, 0) or (1, 0) onto the given mesh subject
//               to the constraint that the normal component of the vector
//               field vanishes on a particular (curved) boundary.
//
//               We recommend viewing example 2 before viewing this example.

/*
  Solve a problem with the constraint that the normal component
  of the (vector) solution on the boundary is zero.

  The way MFEM dofs work, this is not quite trivial for non-grid-aligned
  boundaries.

  TODO before making a PR:

  - clean up build #ifdefs, for hypre etc. (did a little...)
  - clean up example, for actual demo with sphere
  - write up some very basic results (ie, a pretty picture, very basic refinement results)
  - a few example command lines and figure out what actually works, eg partial assembly? (see run-normal.sh, see also normalcheck.py)

  TODO eventually:

  - timing / scaling of different solvers
  - parallel BuildNormalConstraints in this example
  - make elimination solver parallel
  - improve Schur complement block in Schur solver (user-defined preconditioner)
  - think about preconditioning interface; user may have good preconditioner for primal system that we could use in all three existing solvers?
  - make sure curved mesh works (is this a real problem or just VisIt visualization?)
  - hook up to Smith or Tribol or some other contact setting
*/

#include "mfem.hpp"
#include <fstream>
#include <iostream>

using namespace std;
using namespace mfem;

/**
   Given a vector space fespace, and the array constrained_att that
   includes the boundary *attributes* that are constrained to have normal
   component zero, this returns a SparseMatrix representing the
   constraints that need to be imposed.

   It also returns in x_dofs, y_dofs, z_dofs the partition of dofs
   invovled in constraints, which can be used in an elimination solver.

   @todo do this in parallel

   Probably the correct parallel algorithm is to build this on
   each processor, and then do a kind of RAP procedure, but without
   adding, as in ParDiscreteLinearOperator::ParallelAssemble()
*/
SparseMatrix * BuildNormalConstraints(FiniteElementSpace& fespace,
                                      Array<int> constrained_att,<commit_msg>Update todo list.<commit_after>//                       MFEM Example normal-bc - Parallel Version
//
// Compile with: make ex-normal
//
// Sample runs:  ex-normal
//               ex-normal --diffusion --boundary-attribute 1
//               ex-normal --mesh ../miniapps/meshing/icf.mesh
//               ex-normal --mesh sphere_hex27.mesh
//               ex-normal --elimination
//               ex-normal --penalty 1e+4
//
// Description:  Demonstrates solving a linear system subject to a linear
//               constraint, using the ConstrainedSolver object.
//
//               This particular example finds the global L2 projection of the
//               vector field (1, 0, 0) or (1, 0) onto the given mesh subject
//               to the constraint that the normal component of the vector
//               field vanishes on a particular (curved) boundary.
//
//               We recommend viewing example 2 before viewing this example.

/*
  todo:

  - timing / scaling of different solvers
  - parallel BuildNormalConstraints in this example
  - make sure curved mesh works (is this a real problem or just VisIt visualization?)
  - make elimination solver parallel
  - think about preconditioning interface; user may have good preconditioner
    for primal system that we could use in all three existing solvers?
  - improve Schur complement block in Schur solver (user-defined preconditioner, but
    different interface)
  - finer grained control of hypre rigid body modes, for example in elimination
    solver the numbering gets messed up, can we deal with that?
  - hook up to Smith or Tribol or some other contact setting
*/

#include "mfem.hpp"
#include <fstream>
#include <iostream>

using namespace std;
using namespace mfem;

/**
   Given a vector space fespace, and the array constrained_att that
   includes the boundary *attributes* that are constrained to have normal
   component zero, this returns a SparseMatrix representing the
   constraints that need to be imposed.

   It also returns in x_dofs, y_dofs, z_dofs the partition of dofs
   invovled in constraints, which can be used in an elimination solver.

   @todo do this in parallel

   Probably the correct parallel algorithm is to build this on
   each processor, and then do a kind of RAP procedure, but without
   adding, as in ParDiscreteLinearOperator::ParallelAssemble()
*/
SparseMatrix * BuildNormalConstraints(FiniteElementSpace& fespace,
                                      Array<int> constrained_att,
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