MueLu_SchurComplementFactory_def.hpp

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#ifndef MUELU_SCHURCOMPLEMENTFACTORY_DEF_HPP_
#define MUELU_SCHURCOMPLEMENTFACTORY_DEF_HPP_

#include <Xpetra_BlockedCrsMatrix.hpp>
#include <Xpetra_MultiVectorFactory.hpp>
#include <Xpetra_VectorFactory.hpp>
#include <Xpetra_MatrixFactory.hpp>
#include <Xpetra_Matrix.hpp>
#include <Xpetra_MatrixMatrix.hpp>
#include <Xpetra_CrsMatrixWrap.hpp>
#include <Xpetra_BlockedCrsMatrix.hpp>
#include <Xpetra_CrsMatrix.hpp>
#include "MueLu_Level.hpp"
#include "MueLu_Monitor.hpp"
#include "MueLu_Utilities.hpp"
//#include "MueLu_HierarchyHelpers.hpp"

#include "MueLu_SchurComplementFactory.hpp"

namespace MueLu {

  template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
  RCP<const ParameterList> SchurComplementFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::GetValidParameterList() const {
    RCP<ParameterList> validParamList = rcp(new ParameterList());

    SC one = Teuchos::ScalarTraits<SC>::one();

    validParamList->set<RCP<const FactoryBase> >("A", NoFactory::getRCP()/*null*/, "Generating factory of the matrix A used for building Schur complement\n"
                                                                                   "(must be a 2x2 blocked operator)");
    validParamList->set<SC>                     ("omega",                     one, "Scaling parameter in S = A(1,1) - 1/omega A(1,0) diag{A(0,0)}^{-1} A(0,1)");
    validParamList->set<bool>                   ("lumping",                 false, "Use lumping to construct diag(A(0,0)), i.e. use row sum of the abs values on the diagonal "
                                                                                   "as approximation of A00 (and A00^{-1})");
    validParamList->set<bool>                   ("fixing",                  false, "Fix diagonal by replacing small entries with 1.0");

    return validParamList;
  }

  template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
  void SchurComplementFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::DeclareInput(Level& currentLevel) const {
    Input(currentLevel, "A");
  }

  template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
  void SchurComplementFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::Build(Level& currentLevel) const {
    FactoryMonitor m(*this, "Build", currentLevel);

    typedef Teuchos::ScalarTraits<SC> STS;
    SC zero = STS::zero(), one = STS::one();

    RCP<Matrix>            A = Get<RCP<Matrix> >(currentLevel, "A");
    RCP<BlockedCrsMatrix> bA = rcp_dynamic_cast<BlockedCrsMatrix>(A);
    TEUCHOS_TEST_FOR_EXCEPTION(bA.is_null(), Exceptions::BadCast,
                               "MueLu::SchurComplementFactory::Build: input matrix A is not of type BlockedCrsMatrix!");

    TEUCHOS_TEST_FOR_EXCEPTION(bA->Rows() != 2 || bA->Cols() != 2, Exceptions::RuntimeError,
                               "MueLu::SchurComplementFactory::Build: input matrix A is a " << bA->Rows() << "x" << bA->Cols() << " block matrix. We expect a 2x2 blocked operator.");

    RCP<Matrix> A00 = bA->getMatrix(0,0);
    RCP<Matrix> A01 = bA->getMatrix(0,1);
    RCP<Matrix> A10 = bA->getMatrix(1,0);
    RCP<Matrix> A11 = bA->getMatrix(1,1);

    RCP<BlockedCrsMatrix> bA01 = Teuchos::rcp_dynamic_cast<BlockedCrsMatrix>(A01);
    bool bIsBlocked = (bA01 == Teuchos::null ? false : true);

    const ParameterList& pL = GetParameterList();
    SC omega = pL.get<Scalar>("omega");

    TEUCHOS_TEST_FOR_EXCEPTION(omega == zero, Exceptions::RuntimeError,
                               "MueLu::SchurComplementFactory::Build: Scaling parameter omega must not be zero to avoid division by zero.");

    RCP<Matrix> S = Teuchos::null;
    // only if the off-diagonal blocks A10 and A01 are non-zero we have to do the MM multiplication
    if(A01.is_null() == false && A10.is_null() == false) {
      bool lumping = pL.get<bool>("lumping");
      bool fixing  = pL.get<bool>("fixing");
      RCP<Vector> diag = Teuchos::null;
      if (!lumping) {
        diag = VectorFactory::Build(A00->getRangeMap(), true);
        A00->getLocalDiagCopy(*diag);
      } else {
        RCP<BlockedCrsMatrix> bA00 = Teuchos::rcp_dynamic_cast<BlockedCrsMatrix>(A00);
        TEUCHOS_TEST_FOR_EXCEPTION(bA00.is_null()==false, MueLu::Exceptions::RuntimeError,"MueLu::SchurComplementFactory::Build: Mass lumping not implemented. Implement a mass lumping kernel!");
        diag = Utilities::GetLumpedMatrixDiagonal(A00);
      }
      // invert diagonal vector. Replace all entries smaller than 1e-4 by one!
      RCP<Vector> D = (!fixing ? Utilities::GetInverse(diag) : Utilities::GetInverse(diag, 1e-4, one));
      // scale with -1/omega
      D->scale(Teuchos::as<Scalar>(-one/omega));
      // left scale matrix T with (scaled) diagonal D
      // Copy the value of A01 so we can do the left scale.
      RCP<Matrix> T = MatrixFactory::BuildCopy(A01, false);
      T->leftScale(*D);

      // build Schur complement operator
      if (!bIsBlocked) {
        TEUCHOS_TEST_FOR_EXCEPTION(T->getRangeMap()->isSameAs(*(A10->getDomainMap())) == false, Exceptions::RuntimeError,
                                   "MueLu::SchurComplementFactory::Build: RangeMap of A01 and domain map of A10 are not the same.");
        RCP<ParameterList> myparams = rcp(new ParameterList);
        S = Xpetra::MatrixMatrix<Scalar, LocalOrdinal, GlobalOrdinal, Node>::Multiply(*A10, false, *T, false, GetOStream(Statistics2),true,true,std::string("SchurComplementFactory"),myparams);

      } else {
        // nested blocking
        RCP<BlockedCrsMatrix> bA10 = Teuchos::rcp_dynamic_cast<BlockedCrsMatrix>(A10);
        RCP<BlockedCrsMatrix> bT   = Teuchos::rcp_dynamic_cast<BlockedCrsMatrix>(T);

        TEUCHOS_TEST_FOR_EXCEPTION(bA01->Rows() != bA10->Cols(), Exceptions::RuntimeError,
                                   "MueLu::SchurComplementFactory::Build: Block rows and cols of A01 and A10 are not compatible.");
        TEUCHOS_TEST_FOR_EXCEPTION(bA01->Rows() != bT->Rows() || bA01->Cols() != bT->Cols(), Exceptions::RuntimeError,
                                   "MueLu::SchurComplementFactory::Build: The scaled A01 operator has " << bT->Rows() << "x" << bT->Cols() << " blocks, "
                                   "but should have " << bA01->Rows() << "x" << bA01->Cols() << " blocks.");
        TEUCHOS_TEST_FOR_EXCEPTION(bA01->Cols() != bA10->Rows(), Exceptions::RuntimeError,
                                   "MueLu::SchurComplementFactory::Build: Block rows and cols of A01 and A10 are not compatible.");

        S = Xpetra::MatrixMatrix<Scalar, LocalOrdinal, GlobalOrdinal, Node>::TwoMatrixMultiplyBlock(*bA10, false, *bT, false, GetOStream(Statistics2));
      }

      if (!A11.is_null()) {
        T = Teuchos::null;
        Xpetra::MatrixMatrix<Scalar, LocalOrdinal, GlobalOrdinal, Node>::TwoMatrixAdd(*A11, false, one, *S, false, one, T, GetOStream(Statistics2));
        T->fillComplete();
        S.swap(T);

        TEUCHOS_TEST_FOR_EXCEPTION(A11->getRangeMap()->isSameAs(*(S->getRangeMap())) == false, Exceptions::RuntimeError,
                                   "MueLu::SchurComplementFactory::Build: RangeMap of A11 and S are not the same.");
        TEUCHOS_TEST_FOR_EXCEPTION(A11->getDomainMap()->isSameAs(*(S->getDomainMap())) == false, Exceptions::RuntimeError,
                                   "MueLu::SchurComplementFactory::Build: DomainMap of A11 and S are not the same.");
      }

    }
    else {
      if (!A11.is_null()) {
        S = MatrixFactory::BuildCopy(A11);
      } else {
        S = MatrixFactory::Build(A11->getRowMap(), 10 /*A11->getNodeMaxNumRowEntries()*/);
        S->fillComplete(A11->getDomainMap(),A11->getRangeMap());
      }
    }

    // Check whether Schur complement operator is a 1x1 block matrix.
    // If so, unwrap it and return the CrsMatrix based Matrix object
    // We need this, as single-block smoothers expect it this way.
    // In case of Thyra GIDs we obtain a Schur complement operator in Thyra GIDs
    // This may make some special handling in feeding the SchurComplement solver Apply routine
    // necessary!
    if (bIsBlocked) {
      RCP<BlockedCrsMatrix> bS = Teuchos::rcp_dynamic_cast<BlockedCrsMatrix>(S);

      if (bS != Teuchos::null && bS->Rows() == 1 && bS->Cols() == 1) {
        RCP<Matrix> temp = bS->getCrsMatrix();
        S.swap(temp);
      }
    }
    // NOTE: "A" generated by this factory is actually the Schur complement
    // matrix, but it is required as all smoothers expect "A"
    Set(currentLevel, "A", S);
  }

} // namespace MueLu

#endif /* MUELU_SCHURCOMPLEMENTFACTORY_DEF_HPP_ */