constrained_linear_operator.h

// ---------------------------------------------------------------------
//
// Copyright (C) 2015 - 2018 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE.md at
// the top level directory of deal.II.
//
// ---------------------------------------------------------------------

#ifndef dealii_constrained_linear_operator_h
#define dealii_constrained_linear_operator_h

#include <deal.II/lac/affine_constraints.h>
#include <deal.II/lac/linear_operator.h>
#include <deal.II/lac/packaged_operation.h>


DEAL_II_NAMESPACE_OPEN




template <typename Range, typename Domain, typename Payload>
LinearOperator<Range, Domain, Payload>
distribute_constraints_linear_operator(
  const AffineConstraints<typename Range::value_type> &constraints,
  const LinearOperator<Range, Domain, Payload> &       exemplar)
{
  LinearOperator<Range, Domain, Payload> return_op = exemplar;

  return_op.vmult_add = [&constraints](Range &v, const Domain &u) {
    Assert(!::PointerComparison::equal(&v, &u),
           ::ExcMessage("The domain and range vectors must be different "
                              "storage locations"));

    // First, add vector u to v unconditionally and clean up constrained
    // degrees of freedom later.
    v += u;

    const auto &locally_owned_elements = v.locally_owned_elements();
    for (const auto &line : constraints.get_lines())
      {
        const auto i = line.index;
        if (locally_owned_elements.is_element(i))
          {
            v(i) -= u(i);
            const auto &entries = line.entries;
            for (types::global_dof_index j = 0; j < entries.size(); ++j)
              {
                const auto pos = entries[j].first;
                v(i) += u(pos) * entries[j].second;
              }
          }
      }

    v.compress(VectorOperation::add);
  };

  return_op.Tvmult_add = [&constraints](Domain &v, const Range &u) {
    Assert(!::PointerComparison::equal(&v, &u),
           ::ExcMessage("The domain and range vectors must be different "
                              "storage locations"));

    // First, add vector u to v unconditionally and clean up constrained
    // degrees of freedom later.
    v += u;

    const auto &locally_owned_elements = v.locally_owned_elements();
    for (const auto &line : constraints.get_lines())
      {
        const auto i = line.index;

        if (locally_owned_elements.is_element(i))
          {
            v(i) -= u(i);
          }

        const auto &entries = line.entries;
        for (types::global_dof_index j = 0; j < entries.size(); ++j)
          {
            const auto pos = entries[j].first;
            if (locally_owned_elements.is_element(pos))
              v(pos) += u(i) * entries[j].second;
          }
      }

    v.compress(VectorOperation::add);
  };

  // lambda capture expressions are a C++14 feature...
  const auto vmult_add = return_op.vmult_add;
  return_op.vmult      = [vmult_add](Range &v, const Domain &u) {
    v = 0.;
    vmult_add(v, u);
  };

  // lambda capture expressions are a C++14 feature...
  const auto Tvmult_add = return_op.Tvmult_add;
  return_op.Tvmult      = [Tvmult_add](Domain &v, const Range &u) {
    v = 0.;
    Tvmult_add(v, u);
  };

  return return_op;
}


template <typename Range, typename Domain, typename Payload>
LinearOperator<Range, Domain, Payload>
project_to_constrained_linear_operator(
  const AffineConstraints<typename Range::value_type> &constraints,
  const LinearOperator<Range, Domain, Payload> &       exemplar)
{
  LinearOperator<Range, Domain, Payload> return_op = exemplar;

  return_op.vmult_add = [&constraints](Range &v, const Domain &u) {
    const auto &locally_owned_elements = v.locally_owned_elements();
    for (const auto &line : constraints.get_lines())
      {
        const auto i = line.index;
        if (locally_owned_elements.is_element(i))
          {
            v(i) += u(i);
          }
      }

    v.compress(VectorOperation::add);
  };

  return_op.Tvmult_add = [&constraints](Domain &v, const Range &u) {
    const auto &locally_owned_elements = v.locally_owned_elements();
    for (const auto &line : constraints.get_lines())
      {
        const auto i = line.index;
        if (locally_owned_elements.is_element(i))
          {
            v(i) += u(i);
          }
      }

    v.compress(VectorOperation::add);
  };

  // lambda capture expressions are a C++14 feature...
  const auto vmult_add = return_op.vmult_add;
  return_op.vmult      = [vmult_add](Range &v, const Domain &u) {
    v = 0.;
    vmult_add(v, u);
  };

  // lambda capture expressions are a C++14 feature...
  const auto Tvmult_add = return_op.Tvmult_add;
  return_op.Tvmult      = [Tvmult_add](Domain &v, const Range &u) {
    v = 0.;
    Tvmult_add(v, u);
  };

  return return_op;
}


template <typename Range, typename Domain, typename Payload>
LinearOperator<Range, Domain, Payload>
constrained_linear_operator(
  const AffineConstraints<typename Range::value_type> &constraints,
  const LinearOperator<Range, Domain, Payload> &       linop)
{
  const auto C    = distribute_constraints_linear_operator(constraints, linop);
  const auto Ct   = transpose_operator(C);
  const auto Id_c = project_to_constrained_linear_operator(constraints, linop);
  return Ct * linop * C + Id_c;
}


template <typename Range, typename Domain, typename Payload>
PackagedOperation<Range>
constrained_right_hand_side(
  const AffineConstraints<typename Range::value_type> &constraints,
  const LinearOperator<Range, Domain, Payload> &       linop,
  const Range &                                        right_hand_side)
{
  PackagedOperation<Range> return_comp;

  return_comp.reinit_vector = linop.reinit_range_vector;

  return_comp.apply_add = [&constraints, &linop, &right_hand_side](Range &v) {
    const auto C  = distribute_constraints_linear_operator(constraints, linop);
    const auto Ct = transpose_operator(C);

    GrowingVectorMemory<Domain>            vector_memory;
    typename VectorMemory<Domain>::Pointer k(vector_memory);
    linop.reinit_domain_vector(*k, /*bool fast=*/false);
    constraints.distribute(*k);

    v += Ct * (right_hand_side - linop * *k);
  };

  // lambda capture expressions are a C++14 feature...
  const auto apply_add = return_comp.apply_add;
  return_comp.apply    = [apply_add](Range &v) {
    v = 0.;
    apply_add(v);
  };

  return return_comp;
}


DEAL_II_NAMESPACE_CLOSE

#endif