schur_complement.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_schur_complement_h
#define dealii_schur_complement_h

#include <deal.II/base/config.h>

#include <deal.II/base/exceptions.h>

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


DEAL_II_NAMESPACE_OPEN


template <typename Range_1,
          typename Domain_1,
          typename Range_2,
          typename Domain_2,
          typename Payload>
LinearOperator<Range_2, Domain_2, Payload>
schur_complement(const LinearOperator<Domain_1, Range_1, Payload> &A_inv,
                 const LinearOperator<Range_1, Domain_2, Payload> &B,
                 const LinearOperator<Range_2, Domain_1, Payload> &C,
                 const LinearOperator<Range_2, Domain_2, Payload> &D)
{
  // We return the result of the compound LinearOperator
  // directly, so as to ensure that the underlying Payload
  // definition aligns with the operations expressed here.
  // All of the memory allocations etc. are taken care of
  // internally.
  if (D.is_null_operator == false)
    return D - C * A_inv * B;
  else
    return -1.0 * C * A_inv * B;
}




template <typename Range_1,
          typename Domain_1,
          typename Range_2,
          typename Payload>
PackagedOperation<Range_2>
condense_schur_rhs(const LinearOperator<Range_1, Domain_1, Payload> &A_inv,
                   const LinearOperator<Range_2, Domain_1, Payload> &C,
                   const Range_1 &                                   f,
                   const Range_2 &                                   g)
{
  // We return the result of the compound PackagedOperation
  // directly, so as to ensure that the underlying Payload
  // definition aligns with the operations expressed here.
  // All of the memory allocations etc. are taken care of
  // internally.
  return g - C * A_inv * f;
}

template <typename Range_1,
          typename Domain_1,
          typename Domain_2,
          typename Payload>
PackagedOperation<Domain_1>
postprocess_schur_solution(
  const LinearOperator<Range_1, Domain_1, Payload> &A_inv,
  const LinearOperator<Range_1, Domain_2, Payload> &B,
  const Domain_2 &                                  y,
  const Range_1 &                                   f)
{
  // We return the result of the compound PackagedOperation
  // directly, so as to ensure that the underlying Payload
  // definition aligns with the operations expressed here.
  // All of the memory allocations etc. are taken care of
  // internally.
  return A_inv * (f - B * y);
}


DEAL_II_NAMESPACE_CLOSE

#endif