schur_complement.h

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// -----------------------------------------------------------------------------
//
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception OR LGPL-2.1-or-later
// Copyright (C) 2016 - 2025 by the deal.II authors
//
// This file is part of the deal.II library.
//
// Detailed license information governing the source code and contributions
// can be found in LICENSE.md and CONTRIBUTING.md at the top level directory.
//
// -----------------------------------------------------------------------------
 
#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