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//
// Copyright (C) 2015 - 2016 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 at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------
#ifndef dealii__constrained_linear_operator_h
#define dealii__constrained_linear_operator_h
#include <deal.II/lac/linear_operator.h>
#include <deal.II/lac/packaged_operation.h>
#include <deal.II/lac/constraint_matrix.h>
#ifdef DEAL_II_WITH_CXX11
DEAL_II_NAMESPACE_OPEN
/**
* @name Indirectly applying constraints to LinearOperator
*/
//@{
/**
* This function takes a ConstraintMatrix @p constraint_matrix and an operator
* exemplar @p exemplar (this exemplar is usually a linear operator that
* describes the system matrix - it is only used to create domain and range
* vectors of appropriate sizes, its action <tt>vmult</tt> is never used). A
* LinearOperator object associated with the "homogeneous action" of the
* underlying ConstraintMatrix object is returned:
*
* Applying the LinearOperator object on a vector <code>u</code> results in a
* vector <code>v</code> that stores the result of calling
* ConstraintMatrix::distribute() on <code>u</code> - with one important
* difference: inhomogeneities are not applied, but always treated as 0
* instead.
*
* The LinearOperator object created by this function is primarily used
* internally in constrained_linear_operator() to build up a modified system
* of linear equations. How to solve a linear system of equations with this
* approach is explained in detail in the
* @ref constraints
* module.
*
* @author Mauro Bardelloni, Matthias Maier, 2015
*
* @note Currently, this function may not work correctly for distributed data
* structures.
*
* @relates LinearOperator
* @ingroup constraints
*/
template <typename Range, typename Domain>
LinearOperator<Range, Domain> distribute_constraints_linear_operator(
const ConstraintMatrix &constraint_matrix,
const LinearOperator<Range, Domain> &exemplar)
{
LinearOperator<Range, Domain> return_op = exemplar;
return_op.vmult_add = [&constraint_matrix](Range &v, const Domain &u)
{
Assert(!dealii::PointerComparison::equal(&v, &u),
dealii::ExcMessage("The domain and range vectors must be different "
"storage locations"));
for (auto i : v.locally_owned_elements())
{
if (constraint_matrix.is_constrained(i))
{
const auto *entries = constraint_matrix.get_constraint_entries(i);
for (types::global_dof_index j = 0; j < entries->size(); ++j)
{
const auto pos = (*entries)[j].first;
v(i) += u(pos) * (*entries)[j].second;
}
}
else
v(i) += u(i);
}
};
return_op.Tvmult_add = [&constraint_matrix](Domain &v, const Range &u)
{
Assert(!dealii::PointerComparison::equal(&v, &u),
dealii::ExcMessage("The domain and range vectors must be different "
"storage locations"));
for (auto i : v.locally_owned_elements())
{
if (constraint_matrix.is_constrained(i))
{
const auto *entries = constraint_matrix.get_constraint_entries(i);
for (types::global_dof_index j = 0; j < entries->size(); ++j)
{
const auto pos = (*entries)[j].first;
v(pos) += u(i) * (*entries)[j].second;
}
}
else
v(i)+=u(i);
}
};
// 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;
}
/**
* Given a ConstraintMatrix @p constraint_matrix and an operator exemplar @p
* exemplar, return a LinearOperator that is the projection to the subspace of
* constrained degrees of freedom, i.e. all entries of the result vector that
* correspond to unconstrained degrees of freedom are set to zero.
*
* @author Mauro Bardelloni, Matthias Maier, 2015
*
* @relates LinearOperator
* @ingroup constraints
*/
template <typename Range, typename Domain>
LinearOperator<Range, Domain> project_to_constrained_linear_operator(
const ConstraintMatrix &constraint_matrix,
const LinearOperator<Range, Domain> &exemplar)
{
LinearOperator<Range, Domain> return_op = exemplar;
return_op.vmult_add = [&constraint_matrix](Range &v, const Domain &u)
{
for (auto i : v.locally_owned_elements())
if (constraint_matrix.is_constrained(i))
v(i) += u(i);
};
return_op.Tvmult_add = [&constraint_matrix](Domain &v, const Range &u)
{
for (auto i : v.locally_owned_elements())
if (constraint_matrix.is_constrained(i))
v(i) += u(i);
};
return_op.vmult = [&constraint_matrix](Range &v, const Domain &u)
{
Assert(!dealii::PointerComparison::equal(&v, &u),
dealii::ExcMessage("The domain and range vectors must be different "
"storage locations"));
v = 0.;
for (auto i : v.locally_owned_elements())
if (constraint_matrix.is_constrained(i))
v(i) = u(i);
};
return_op.Tvmult = [&constraint_matrix](Domain &v, const Range &u)
{
Assert(!dealii::PointerComparison::equal(&v, &u),
dealii::ExcMessage("The domain and range vectors must be different "
"storage locations"));
v = 0.;
for (auto i : v.locally_owned_elements())
if (constraint_matrix.is_constrained(i))
v(i) = u(i);
};
return return_op;
}
/**
* Given a ConstraintMatrix object @p constraint_matrix and a LinearOperator
* @p linop, this function creates a LinearOperator object consisting of the
* composition of three operations and a regularization:
* @code
* Ct * linop * C + Id_c;
* @endcode
* with
* @code
* C = distribute_constraints_linear_operator(constraint_matrix, linop);
* Ct = transpose_operator(C);
* Id_c = project_to_constrained_linear_operator(constraint_matrix, linop);
* @endcode
* and <code>Id_c</code> is the projection to the subspace consisting of all
* vector entries associated with constrained degrees of freedoms.
*
* This LinearOperator object is used together with
* constrained_right_hand_side() to build up the following modified system of
* linear equations:
* @f[
* (C^T A C + Id_c) x = C^T (b - A\,k)
* @f]
* with a given (unconstrained) system matrix $A$, right hand side $b$, and
* linear constraints $C$ with inhomogeneities $k$.
*
* A detailed explanation of this approach is given in the
* @ref constraints
* module.
*
* @author Mauro Bardelloni, Matthias Maier, 2015
*
* @note Currently, this function may not work correctly for distributed data
* structures.
*
* @relates LinearOperator
* @ingroup constraints
*/
template <typename Range, typename Domain>
LinearOperator<Range, Domain>
constrained_linear_operator(const ConstraintMatrix &constraint_matrix,
const LinearOperator<Range, Domain> &linop)
{
const auto C =
distribute_constraints_linear_operator(constraint_matrix, linop);
const auto Ct = transpose_operator(C);
const auto Id_c =
project_to_constrained_linear_operator(constraint_matrix, linop);
return Ct * linop * C + Id_c;
}
/**
* Given a ConstraintMatrix object @p constraint_matrix, a LinearOperator @p
* linop and a right-hand side @p right_hand_side, this function creates a
* PackagedOperation that stores the following computation:
* @code
* Ct * (right_hand_side - linop * k)
* @endcode
* with
* @code
* C = distribute_constraints_linear_operator(constraint_matrix, linop);
* Ct = transpose_operator(C);
* @endcode
*
* This LinearOperator object is used together with
* constrained_right_hand_side() to build up the following modified system of
* linear equations:
* @f[
* (C^T A C + Id_c) x = C^T (b - A\,k)
* @f]
* with a given (unconstrained) system matrix $A$, right hand side $b$, and
* linear constraints $C$ with inhomogeneities $k$.
*
* A detailed explanation of this approach is given in the
* @ref constraints
* module.
*
* @author Mauro Bardelloni, Matthias Maier, 2015
*
* @note Currently, this function may not work correctly for distributed data
* structures.
*
* @relates LinearOperator
* @ingroup constraints
*/
template <typename Range, typename Domain>
PackagedOperation<Range>
constrained_right_hand_side(const ConstraintMatrix &constraint_matrix,
const LinearOperator<Range, Domain> &linop,
const Range &right_hand_side)
{
PackagedOperation<Range> return_comp;
return_comp.reinit_vector = linop.reinit_range_vector;
return_comp.apply_add =
[&constraint_matrix, &linop, &right_hand_side](Range &v)
{
const auto C =
distribute_constraints_linear_operator(constraint_matrix, linop);
const auto Ct = transpose_operator(C);
static GrowingVectorMemory<Domain> vector_memory;
Domain *k = vector_memory.alloc();
linop.reinit_domain_vector(*k, /*bool fast=*/ false);
constraint_matrix.distribute(*k);
v += Ct * (right_hand_side - linop **k);
vector_memory.free(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 // DEAL_II_WITH_CXX11
#endif
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