C++ BFPtr::testFunctional方法代码示例

//.........这里部分代码省略.........
  
  qoptIP = Teuchos::rcp(new IP());
      
  if (useCompliantGraphNorm) {
    qoptIP->addTerm( mu * v1->dx() + tau1->x() ); // sigma11
    qoptIP->addTerm( mu * v1->dy() + tau1->y() ); // sigma12
    qoptIP->addTerm( mu * v2->dx() + tau2->x() ); // sigma21
    qoptIP->addTerm( mu * v2->dy() + tau2->y() ); // sigma22
    qoptIP->addTerm( mu * v1->dx() + mu * v2->dy() );   // pressure
    qoptIP->addTerm( h * tau1->div() - h * q->dx() );   // u1
    qoptIP->addTerm( h * tau2->div() - h * q->dy());    // u2
    
    qoptIP->addTerm( (mu / h) * v1 );
    qoptIP->addTerm( (mu / h) * v2 );
    qoptIP->addTerm( q );
    qoptIP->addTerm( tau1 );
    qoptIP->addTerm( tau2 );
  } else { // standard graph norm, then
    qoptIP = stokesBF->graphNorm();
  }

  ip = qoptIP;
  
  if (rank==0) 
    ip->printInteractions();
  
  // aim is just to answer one simple question:
  // have I figured out a trial-space preimage for optimal test function (q=1, tau=0, v=0)?
  
  SolutionPtr soln = Teuchos::rcp(new Solution(mesh));
  
  FunctionPtr x = Function::xn();
  FunctionPtr y = Function::yn();
  
  // u1 = u1_hat = x / 2
  FunctionPtr u1_exact = x / 2;
  
  // u2 = u2_hat = y / 2
  FunctionPtr u2_exact = y / 2;
  
  // sigma = 0.5 * I
  FunctionPtr sigma11_exact = Function::constant(0.5);
  FunctionPtr sigma22_exact = Function::constant(0.5);
  
  // tn_hat = 0.5 * n
  FunctionPtr n = Function::normal();
  FunctionPtr t1n_exact = n->x() / 2;
  FunctionPtr t2n_exact = n->y() / 2;
  
  map<int, FunctionPtr > exact_soln;
  exact_soln[u1->ID()] = u1_exact;
  exact_soln[u1hat->ID()] = u1_exact;
  exact_soln[u2->ID()] = u2_exact;
  exact_soln[u2hat->ID()] = u2_exact;
  exact_soln[sigma11->ID()] = sigma11_exact;
  exact_soln[sigma22->ID()] = sigma22_exact;
  exact_soln[t1n->ID()] = t1n_exact;
  exact_soln[t2n->ID()] = t2n_exact;
  
  exact_soln[p->ID()] = Function::zero();
  exact_soln[sigma12->ID()] = Function::zero();
  exact_soln[sigma21->ID()] = Function::zero();
  
  soln->projectOntoMesh(exact_soln);
  
  LinearTermPtr soln_functional = stokesBF->testFunctional(soln);
  
  RieszRepPtr rieszRep = Teuchos::rcp( new RieszRep(mesh, ip, soln_functional) );
  
  rieszRep->computeRieszRep();
  
  // get test functions:
  FunctionPtr q_fxn = Teuchos::rcp( new RepFunction(q, rieszRep) );
  FunctionPtr v1_fxn = Teuchos::rcp( new RepFunction(v1, rieszRep) );
  FunctionPtr v2_fxn = Teuchos::rcp( new RepFunction(v2, rieszRep) );
  FunctionPtr tau1_fxn = Teuchos::rcp( new RepFunction(tau1, rieszRep) );
  FunctionPtr tau2_fxn = Teuchos::rcp( new RepFunction(tau2, rieszRep) );
  
  cout << "L2 norm of (q-1) : " << (q_fxn - 1)->l2norm(mesh) << endl;
  cout << "L2 norm of (v1) : " << (v1_fxn)->l2norm(mesh) << endl;
  cout << "L2 norm of (v2) : " << (v2_fxn)->l2norm(mesh) << endl;
  cout << "L2 norm of (tau1) : " << (tau1_fxn)->l2norm(mesh) << endl;
  cout << "L2 norm of (tau2) : " << (tau2_fxn)->l2norm(mesh) << endl;
  
  VTKExporter exporter(soln, mesh, varFactory);
  exporter.exportSolution("conservationPreimage", H1Order*2);

  cout << "Checking that the soln_functional is what I expect:\n";
  
  FunctionPtr xyVector = Function::vectorize(x, y);
  
  cout << "With v1 = x, integral: " << integralOverMesh(soln_functional, v1, x) << endl;
  cout << "With v2 = y, integral: " << integralOverMesh(soln_functional, v2, y) << endl;
  cout << "With tau1=(x,y), integral: " << integralOverMesh(soln_functional, tau1, xyVector) << endl;
  cout << "With tau2=(x,y), integral: " << integralOverMesh(soln_functional, tau2, xyVector) << endl;
  cout << "With q   =x, integral: " << integralOverMesh(soln_functional, q, x) << endl;
  
  cout << "(Expect 0s all around, except for q, where we expect (1,x) == 0.5.)\n";
  return 0;
}

//.........这里部分代码省略.........
  ////////////////////////////////////////////////////////////////////
  // CREATE SOLUTION OBJECT
  ////////////////////////////////////////////////////////////////////

  Teuchos::RCP<Solution> solution = Teuchos::rcp(new Solution(mesh, inflowBC, rhs, ip));
  mesh->registerSolution(solution); solution->setCubatureEnrichmentDegree(10);

  ////////////////////////////////////////////////////////////////////
  // HESSIAN BIT + CHECKS ON GRADIENT + HESSIAN
  ////////////////////////////////////////////////////////////////////

  VarFactory hessianVars = varFactory.getBubnovFactory(VarFactory::BUBNOV_TRIAL);
  VarPtr du = hessianVars.test(u->ID());
  //  BFPtr hessianBF = Teuchos::rcp( new BF(hessianVars) ); // initialize bilinear form

  FunctionPtr du_current  = Teuchos::rcp( new PreviousSolutionFunction(solution, u) );

  FunctionPtr fnhat = Teuchos::rcp(new PreviousSolutionFunction(solution,fn));
  LinearTermPtr residual = Teuchos::rcp(new LinearTerm);// residual
  residual->addTerm(fnhat*v,true);
  residual->addTerm( - (e1 * (u_prev_squared_div2) + e2 * (u_prev)) * v->grad(),true);

  LinearTermPtr Bdu = Teuchos::rcp(new LinearTerm);// residual
  Bdu->addTerm( - du_current*(beta*v->grad()));

  Teuchos::RCP<RieszRep> riesz = Teuchos::rcp(new RieszRep(mesh, ip, residual));
  Teuchos::RCP<RieszRep> duRiesz = Teuchos::rcp(new RieszRep(mesh, ip, Bdu));
  riesz->computeRieszRep();
  FunctionPtr e_v = Teuchos::rcp(new RepFunction(v,riesz));
  e_v->writeValuesToMATLABFile(mesh, "e_v.m");
  FunctionPtr posErrPart = Teuchos::rcp(new PositivePart(e_v->dx()));
  //  hessianBF->addTerm(e_v->dx()*u,du); 
  //  hessianBF->addTerm(posErrPart*u,du); 
  //  Teuchos::RCP<NullFilter> nullFilter = Teuchos::rcp(new NullFilter);
  //  Teuchos::RCP<HessianFilter> hessianFilter = Teuchos::rcp(new HessianFilter(hessianBF));

  Teuchos::RCP< LineSearchStep > LS_Step = Teuchos::rcp(new LineSearchStep(riesz));

  double NL_residual = 9e99;
  for (int i = 0;i<numSteps;i++){
    // write matrix to file and then resollve without hessian
    /*
    solution->setFilter(hessianFilter);           
    stringstream oss;
    oss << "hessianMatrix" << i << ".dat";
    solution->setWriteMatrixToFile(true,oss.str());      
    solution->solve(false);

    solution->setFilter(nullFilter);
    oss.str(""); // clear
    oss << "stiffnessMatrix" << i << ".dat";
    solution->setWriteMatrixToFile(false,oss.str());      
    */

    solution->solve(false); // do one solve to initialize things...   
    double stepLength = 1.0;
    stepLength = LS_Step->stepSize(backgroundFlow,solution, NL_residual);

    //      solution->setWriteMatrixToFile(true,"stiffness.dat");    

    backgroundFlow->addSolution(solution,stepLength);
    NL_residual = LS_Step->getNLResidual();
    if (rank==0){
      cout << "NL residual after adding = " << NL_residual << " with step size " << stepLength << endl;    
    }

    double fd_gradient;
    for (int dofIndex = 0;dofIndex<mesh->numGlobalDofs();dofIndex++){
      TestingUtilities::initializeSolnCoeffs(solnPerturbation);
      TestingUtilities::setSolnCoeffForGlobalDofIndex(solnPerturbation,1.0,dofIndex);
      fd_gradient = FiniteDifferenceUtilities::finiteDifferenceGradient(mesh, riesz, backgroundFlow, dofIndex);
      
      // CHECK GRADIENT
      LinearTermPtr b_u =  bf->testFunctional(solnPerturbation);
      map<int,FunctionPtr> NL_err_rep_map;

      NL_err_rep_map[v->ID()] = Teuchos::rcp(new RepFunction(v,riesz));
      FunctionPtr gradient = b_u->evaluate(NL_err_rep_map, TestingUtilities::isFluxOrTraceDof(mesh,dofIndex)); // use boundary part only if flux or trace
      double grad;
      if (TestingUtilities::isFluxOrTraceDof(mesh,dofIndex)){
	grad = gradient->integralOfJump(mesh,10);
      }else{
	grad = gradient->integrate(mesh,10);
      }
      double fdgrad = fd_gradient;
      double diff = grad-fdgrad;
      if (abs(diff)>1e-6 && i>0){
	cout << "Found difference of " << diff << ", " << " with fd val = " << fdgrad << " and gradient = " << grad << " in dof " << dofIndex << ", isTraceDof = " << TestingUtilities::isFluxOrTraceDof(mesh,dofIndex) << endl;
      }
    }
  }
  
  VTKExporter exporter(solution, mesh, varFactory);
  if (rank==0){
    exporter.exportSolution("qopt");
    cout << endl;
  }

  return 0;
}

//.........这里部分代码省略.........
    qoptIP->addTerm( h * beta_const * v->grad() - tau->div() );
    qoptIP->addTerm(v);
    qoptIP->addTerm(tau);
  }
  
  ////////////////////   SPECIFY RHS   ///////////////////////
  RHSPtr rhs = RHS::rhs();
  FunctionPtr f = Teuchos::rcp( new ConstantScalarFunction(0.0) );
  rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!

  ////////////////////   CREATE BCs   ///////////////////////
  BCPtr bc = BC::bc();
  SpatialFilterPtr inflowBoundary = Teuchos::rcp( new InflowSquareBoundary );
  SpatialFilterPtr outflowBoundary = Teuchos::rcp( new OutflowSquareBoundary );
  FunctionPtr u0 = Teuchos::rcp( new U0 );
  bc->addDirichlet(uhat, outflowBoundary, u0);

  bc->addDirichlet(uhat, inflowBoundary, u0);
  
//  Teuchos::RCP<PenaltyConstraints> pc = Teuchos::rcp(new PenaltyConstraints);
//  pc->addConstraint(uhat==u0,inflowBoundary);

  ////////////////////   BUILD MESH   ///////////////////////
  // create a new mesh on a single-cell, unit square domain
  Teuchos::RCP<Mesh> mesh = MeshFactory::quadMeshMinRule(confusionBF, H1Order, delta_k);
  
  ////////////////////   SOLVE & REFINE   ///////////////////////
  Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, qoptIP) );
//  solution->setFilter(pc);
  
  double energyThreshold = 0.2; // for mesh refinements
  
  bool useRieszRepBasedRefStrategy = true;
  
  if (rank==0) {
    if (useRieszRepBasedRefStrategy) {
      cout << "using RieszRep-based refinement strategy.\n";
    } else {
      cout << "using solution-based refinement strategy.\n";
    }
  }
  Teuchos::RCP<RefinementStrategy> refinementStrategy;
  if (!useRieszRepBasedRefStrategy) {
    refinementStrategy = Teuchos::rcp( new RefinementStrategy( solution, energyThreshold ) );
  } else {
    LinearTermPtr residual = confusionBF->testFunctional(solution) - rhs->linearTerm();
    refinementStrategy = Teuchos::rcp( new RefinementStrategy( mesh, residual, qoptIP, energyThreshold ) );
  }
  
  refinementStrategy->setReportPerCellErrors(true);
  refinementStrategy->setEnforceOneIrregularity(enforceOneIrregularity);
  
  for (int refIndex=0; refIndex<numRefs; refIndex++){
    if (writeStiffnessMatrices) {
      string stiffnessFile = fileNameForRefinement("confusion_stiffness", refIndex);
      solution->setWriteMatrixToFile(true, stiffnessFile);
    }
    solution->solve();
    if (writeWorstCaseGramMatrices) {
      string gramFile = fileNameForRefinement("confusion_gram", refIndex);
      bool jacobiScaling = true;
      double condNum = MeshUtilities::computeMaxLocalConditionNumber(qoptIP, mesh, jacobiScaling, gramFile);
      if (rank==0) {
        cout << "estimated worst-case Gram matrix condition number: " << condNum << endl;
        cout << "putative worst-case Gram matrix written to file " << gramFile << endl;
      }
    }
    if (refIndex == numRefs-1) { // write out second-to-last mesh
      if (rank==0)
        GnuPlotUtil::writeComputationalMeshSkeleton("confusionMesh", mesh, true);
    }
    refinementStrategy->refine(rank==0); // print to console on rank 0
  }
  if (writeStiffnessMatrices) {
    string stiffnessFile = fileNameForRefinement("confusion_stiffness", numRefs);
    solution->setWriteMatrixToFile(true, stiffnessFile);
  }
  if (writeWorstCaseGramMatrices) {
    string gramFile = fileNameForRefinement("confusion_gram", numRefs);
    bool jacobiScaling = true;
    double condNum = MeshUtilities::computeMaxLocalConditionNumber(qoptIP, mesh, jacobiScaling, gramFile);
    if (rank==0) {
      cout << "estimated worst-case Gram matrix condition number: " << condNum << endl;
      cout << "putative worst-case Gram matrix written to file " << gramFile << endl;
    }
  }
  // one more solve on the final refined mesh:
  solution->solve();
  
#ifdef HAVE_EPETRAEXT_HDF5
  ostringstream dir_name;
  dir_name << "confusion_eps" << eps;
  HDF5Exporter exporter(mesh,dir_name.str());
  exporter.exportSolution(solution, varFactory, 0);
  if (rank==0) cout << "wrote solution to " << dir_name.str() << endl;
#endif

  
  return 0;
}

//.........这里部分代码省略.........
  SolutionPtr backgroundFlow = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );  
  mesh->registerSolution(backgroundFlow); // to trigger issue with p-refinements
  map<int, Teuchos::RCP<Function> > functionMap; functionMap[u->ID()] = Function::constant(3.14);
  backgroundFlow->projectOntoMesh(functionMap);

  // lower p to p = 1 at SINGULARITY only
  vector<int> ids;
  /*
  for (int i = 0;i<mesh->numActiveElements();i++){
    bool cellIDset = false;
    int cellID = mesh->activeElements()[i]->cellID();
    int elemOrder = mesh->cellPolyOrder(cellID)-1;
    FieldContainer<double> vv(4,2); mesh->verticesForCell(vv, cellID);
    bool vertexOnWall = false; bool vertexAtSingularity = false;
    for (int j = 0;j<4;j++){
      if ((abs(vv(j,0)-.5) + abs(vv(j,1)))<1e-10){
	vertexAtSingularity = true;     
	cellIDset = true;
      }
    }	
    if (!vertexAtSingularity && elemOrder<2 && !cellIDset ){
      ids.push_back(cellID);
      cout << "celliD = " << cellID << endl;
    }
  }
  */
  ids.push_back(1);
  ids.push_back(3);
  mesh->pRefine(ids); // to put order = 1

  return 0;
  
  LinearTermPtr residual = rhs->linearTermCopy();
  residual->addTerm(-confusionBF->testFunctional(solution));  
  RieszRepPtr rieszResidual = Teuchos::rcp(new RieszRep(mesh, ip, residual));
  rieszResidual->computeRieszRep();
  FunctionPtr e_v = Teuchos::rcp(new RepFunction(v,rieszResidual));
  FunctionPtr e_tau = Teuchos::rcp(new RepFunction(tau,rieszResidual));
  map<int,FunctionPtr> errRepMap;
  errRepMap[v->ID()] = e_v;
  errRepMap[tau->ID()] = e_tau;
  FunctionPtr errTau = tauVecLT->evaluate(errRepMap,false);
  FunctionPtr errV = vVecLT->evaluate(errRepMap,false);
  FunctionPtr errRest = restLT->evaluate(errRepMap,false);
  FunctionPtr xErr = (errTau->x())*(errTau->x()) + (errV->dx())*(errV->dx());
  FunctionPtr yErr = (errTau->y())*(errTau->y()) + (errV->dy())*(errV->dy());
  FunctionPtr restErr = errRest*errRest;

  RefinementStrategy refinementStrategy( solution, energyThreshold );    

  ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
  //                     PRE REFINEMENTS 
  ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////  

  if (rank==0){
    cout << "Number of pre-refinements = " << numPreRefs << endl;
  }
  for (int i =0;i<=numPreRefs;i++){   
    vector<ElementPtr> elems = mesh->activeElements();
    vector<ElementPtr>::iterator elemIt;
    vector<int> wallCells;    
    for (elemIt=elems.begin();elemIt != elems.end();elemIt++){
      int cellID = (*elemIt)->cellID();
      int numSides = mesh->getElement(cellID)->numSides();
      FieldContainer<double> vertices(numSides,2); //for quads

//.........这里部分代码省略.........

  //  SpatialFilterPtr inflowBoundary = Teuchos::rcp( new InflowSquareBoundary );
  //  SpatialFilterPtr outflowBoundary = Teuchos::rcp( new OutflowSquareBoundary);
  //  bc->addDirichlet(beta_n_u_minus_sigma_n, inflowBoundary, zero);
  //  bc->addDirichlet(uhat, outflowBoundary, zero);

  SpatialFilterPtr rampInflow = Teuchos::rcp(new LeftInflow);
  SpatialFilterPtr rampBoundary = MeshUtilities::rampBoundary(rampHeight);
  SpatialFilterPtr freeStream = Teuchos::rcp(new FreeStreamBoundary);
  SpatialFilterPtr outflowBoundary = Teuchos::rcp(new OutflowBoundary);
  bc->addDirichlet(uhat, rampBoundary, one);
  //  bc->addDirichlet(uhat, outflowBoundary, one);
  bc->addDirichlet(beta_n_u_minus_sigma_n, rampInflow, zero);
  bc->addDirichlet(beta_n_u_minus_sigma_n, freeStream, zero);

  ////////////////////   BUILD MESH   ///////////////////////
  // define nodes for mesh
  int H1Order = order+1;
  int pToAdd = 2;

  // create a pointer to a new mesh:
  //  Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells,confusionBF, H1Order, H1Order+pToAdd);
  Teuchos::RCP<Mesh> mesh = MeshUtilities::buildRampMesh(rampHeight,confusionBF, H1Order, H1Order+pToAdd);
  mesh->setPartitionPolicy(Teuchos::rcp(new ZoltanMeshPartitionPolicy("HSFC")));

  ////////////////////   SOLVE & REFINE   ///////////////////////

  Teuchos::RCP<Solution> solution;
  solution = Teuchos::rcp( new Solution(mesh, bc, rhs, robIP) );
  //  solution->solve(false);
  solution->condensedSolve();

  LinearTermPtr residual = rhs->linearTermCopy();
  residual->addTerm(-confusionBF->testFunctional(solution));
  RieszRepPtr rieszResidual = Teuchos::rcp(new RieszRep(mesh, robIP, residual));
  rieszResidual->computeRieszRep();
  FunctionPtr e_v = Teuchos::rcp(new RepFunction(v,rieszResidual));
  FunctionPtr e_tau = Teuchos::rcp(new RepFunction(tau,rieszResidual));
  map<int,FunctionPtr> errRepMap;
  errRepMap[v->ID()] = e_v;
  errRepMap[tau->ID()] = e_tau;
  FunctionPtr errTau = tauVecLT->evaluate(errRepMap,false);
  FunctionPtr errV = vVecLT->evaluate(errRepMap,false);
  FunctionPtr errRest = restLT->evaluate(errRepMap,false);
  FunctionPtr xErr = (errTau->x())*(errTau->x()) + (errV->dx())*(errV->dx());
  FunctionPtr yErr = (errTau->y())*(errTau->y()) + (errV->dy())*(errV->dy());
  FunctionPtr restErr = errRest*errRest;

  RefinementStrategy refinementStrategy( solution, energyThreshold );

  ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
  //                     PRE REFINEMENTS
  ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

  if (rank==0)
  {
    cout << "Number of pre-refinements = " << numPreRefs << endl;
  }
  for (int i =0; i<=numPreRefs; i++)
  {
    vector<ElementPtr> elems = mesh->activeElements();
    vector<ElementPtr>::iterator elemIt;
    vector<int> wallCells;
    for (elemIt=elems.begin(); elemIt != elems.end(); elemIt++)
    {
      int cellID = (*elemIt)->cellID();

//.........这里部分代码省略.........
  // make residual for riesz representation function
  LinearTermPtr residual = Teuchos::rcp(new LinearTerm);// residual
  FunctionPtr parity = Function::sideParity();
  residual->addTerm(-fnhatFxn*v + (beta*uFxn)*v->grad());
  Teuchos::RCP<RieszRep> riesz = Teuchos::rcp(new RieszRep(mesh, ip, residual));
  riesz->computeRieszRep();
  map<int,FunctionPtr> err_rep_map;
  err_rep_map[v->ID()] = RieszRep::repFunction(v,riesz);

  ////////////////////   GET BOUNDARY CONDITION DATA    ///////////////////////

  FieldContainer<GlobalIndexType> bcGlobalIndices;
  FieldContainer<double> bcGlobalValues;
  mesh->boundary().bcsToImpose(bcGlobalIndices,bcGlobalValues,*(solution->bc()), NULL);
  set<int> bcInds;
  for (int i=0; i<bcGlobalIndices.dimension(0); i++)
  {
    bcInds.insert(bcGlobalIndices(i));
  }

  ////////////////////   CHECK GALERKIN ORTHOGONALITY   ///////////////////////

  BCPtr nullBC;
  RHSPtr nullRHS;
  IPPtr nullIP;
  SolutionPtr solnPerturbation = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );

  map< int, vector<DofInfo> > infoMap = constructGlobalDofToLocalDofInfoMap(mesh);

  for (map< int, vector<DofInfo> >::iterator mapIt = infoMap.begin();
       mapIt != infoMap.end(); mapIt++)
  {
    int dofIndex = mapIt->first;
    vector< DofInfo > dofInfoVector = mapIt->second; // all the local dofs that map to dofIndex
    // create perturbation in direction du
    solnPerturbation->clear(); // clear all solns
    // set each corresponding local dof to 1.0
    for (vector< DofInfo >::iterator dofInfoIt = dofInfoVector.begin();
         dofInfoIt != dofInfoVector.end(); dofInfoIt++)
    {
      DofInfo info = *dofInfoIt;
      FieldContainer<double> solnCoeffs(info.basisCardinality);
      solnCoeffs(info.basisOrdinal) = 1.0;
      solnPerturbation->setSolnCoeffsForCellID(solnCoeffs, info.cellID, info.trialID, info.sideIndex);
    }
    //    solnPerturbation->setSolnCoeffForGlobalDofIndex(1.0,dofIndex);

    LinearTermPtr b_du =  convectionBF->testFunctional(solnPerturbation);
    FunctionPtr gradient = b_du->evaluate(err_rep_map, TestingUtilities::isFluxOrTraceDof(mesh,dofIndex)); // use boundary part only if flux
    double grad = gradient->integrate(mesh,10);
    if (!TestingUtilities::isFluxOrTraceDof(mesh,dofIndex) && abs(grad)>tol)  // if we're not single-precision zero FOR FIELDS
    {
      //      int cellID = mesh->getGlobalToLocalMap()[dofIndex].first;
      cout << "Failed testGalerkinOrthogonality() for fields with diff " << abs(grad) << " at dof " << dofIndex << "; info:" << endl;
      cout << dofInfoString(infoMap[dofIndex]);
      success = false;
    }
  }
  FieldContainer<double> errorJumps(mesh->numGlobalDofs()); //initialized to zero
  // just test fluxes ON INTERNAL SKELETON here
  set<GlobalIndexType> activeCellIDs = mesh->getActiveCellIDsGlobal();
  for (GlobalIndexType activeCellID : activeCellIDs)
  {
    ElementPtr elem = mesh->getElement(activeCellID);
    for (int sideIndex = 0; sideIndex < 4; sideIndex++)
    {
      ElementTypePtr elemType = elem->elementType();
      vector<int> localDofIndices = elemType->trialOrderPtr->getDofIndices(beta_n_u->ID(), sideIndex);
      for (int i = 0; i<localDofIndices.size(); i++)
      {
        int globalDofIndex = mesh->globalDofIndex(elem->cellID(), localDofIndices[i]);
        vector< DofInfo > dofInfoVector = infoMap[globalDofIndex];

        solnPerturbation->clear();
        TestingUtilities::setSolnCoeffForGlobalDofIndex(solnPerturbation,1.0,globalDofIndex);
        // also add in BCs
        for (int i = 0; i<bcGlobalIndices.dimension(0); i++)
        {
          TestingUtilities::setSolnCoeffForGlobalDofIndex(solnPerturbation,bcGlobalValues(i),bcGlobalIndices(i));
        }

        LinearTermPtr b_du =  convectionBF->testFunctional(solnPerturbation);
        FunctionPtr gradient = b_du->evaluate(err_rep_map, TestingUtilities::isFluxOrTraceDof(mesh,globalDofIndex)); // use boundary part only if flux
        double jump = gradient->integrate(mesh,10);
        errorJumps(globalDofIndex) += jump;
      }
    }
  }
  for (int i = 0; i<mesh->numGlobalDofs(); i++)
  {
    if (abs(errorJumps(i))>tol)
    {
      cout << "Failing Galerkin orthogonality test for fluxes with diff " << errorJumps(i) << " at dof " << i << endl;
      cout << dofInfoString(infoMap[i]);
      success = false;
    }
  }

  return success;
}

bool ScratchPadTests::testResidualMemoryError()
{

  int rank = Teuchos::GlobalMPISession::getRank();

  double tol = 1e-11;
  bool success = true;

  int nCells = 2;
  double eps = 1e-2;

  ////////////////////   DECLARE VARIABLES   ///////////////////////
  // define test variables
  VarFactoryPtr varFactory = VarFactory::varFactory();
  VarPtr tau = varFactory->testVar("\\tau", HDIV);
  VarPtr v = varFactory->testVar("v", HGRAD);

  // define trial variables
  VarPtr uhat = varFactory->traceVar("\\widehat{u}");
  VarPtr beta_n_u_minus_sigma_n = varFactory->fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
  VarPtr u = varFactory->fieldVar("u");
  VarPtr sigma1 = varFactory->fieldVar("\\sigma_1");
  VarPtr sigma2 = varFactory->fieldVar("\\sigma_2");

  vector<double> beta;
  beta.push_back(1.0);
  beta.push_back(0.0);

  ////////////////////   DEFINE BILINEAR FORM   ///////////////////////

  BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
  // tau terms:
  confusionBF->addTerm(sigma1 / eps, tau->x());
  confusionBF->addTerm(sigma2 / eps, tau->y());
  confusionBF->addTerm(u, tau->div());
  confusionBF->addTerm(uhat, -tau->dot_normal());

  // v terms:
  confusionBF->addTerm( sigma1, v->dx() );
  confusionBF->addTerm( sigma2, v->dy() );
  confusionBF->addTerm( -u, beta * v->grad() );
  confusionBF->addTerm( beta_n_u_minus_sigma_n, v);

  ////////////////////   DEFINE INNER PRODUCT(S)   ///////////////////////

  // robust test norm
  IPPtr robIP = Teuchos::rcp(new IP);
  robIP->addTerm(tau);
  robIP->addTerm(tau->div());
  robIP->addTerm(v->grad());
  robIP->addTerm(v);

  ////////////////////   SPECIFY RHS   ///////////////////////

  FunctionPtr zero = Function::constant(0.0);
  FunctionPtr one = Function::constant(1.0);
  RHSPtr rhs = RHS::rhs();
  FunctionPtr f = zero;
  //  FunctionPtr f = one;
  rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!

  ////////////////////   CREATE BCs   ///////////////////////
  BCPtr bc = BC::bc();
  SpatialFilterPtr inflowBoundary = Teuchos::rcp( new LRInflowSquareBoundary );
  SpatialFilterPtr outflowBoundary = Teuchos::rcp( new LROutflowSquareBoundary);

  FunctionPtr n = Function::normal();

  vector<double> e1,e2;
  e1.push_back(1.0);
  e1.push_back(0.0);
  e2.push_back(0.0);
  e2.push_back(1.0);

  bc->addDirichlet(beta_n_u_minus_sigma_n, inflowBoundary, beta*n*one);
  bc->addDirichlet(uhat, outflowBoundary, zero);

  ////////////////////   BUILD MESH   ///////////////////////
  // define nodes for mesh
  int order = 2;
  int H1Order = order+1;
  int pToAdd = 2;

  // create a pointer to a new mesh:
  Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells,confusionBF, H1Order, H1Order+pToAdd);
  //  mesh->setPartitionPolicy(Teuchos::rcp(new ZoltanMeshPartitionPolicy("HSFC")));

  ////////////////////   SOLVE & REFINE   ///////////////////////

  Teuchos::RCP<Solution> solution;
  solution = Teuchos::rcp( new Solution(mesh, bc, rhs, robIP) );
  solution->solve(false);
  mesh->registerSolution(solution);
  double energyErr1 = solution->energyErrorTotal();

  LinearTermPtr residual = rhs->linearTermCopy();
  residual->addTerm(-confusionBF->testFunctional(solution));
  RieszRepPtr rieszResidual = Teuchos::rcp(new RieszRep(mesh, robIP, residual));
  rieszResidual->computeRieszRep();
  FunctionPtr e_v = RieszRep::repFunction(v,rieszResidual);
//.........这里部分代码省略.........

// tests to make sure the energy error calculated thru direct integration works for vector valued test functions too
bool ScratchPadTests::testLTResidual()
{
  double tol = 1e-11;
  int rank = Teuchos::GlobalMPISession::getRank();

  bool success = true;

  int nCells = 2;
  double eps = .1;

  ////////////////////   DECLARE VARIABLES   ///////////////////////

  // define test variables
  VarFactoryPtr varFactory = VarFactory::varFactory();
  VarPtr tau = varFactory->testVar("\\tau", HDIV);
  VarPtr v = varFactory->testVar("v", HGRAD);

  // define trial variables
  VarPtr uhat = varFactory->traceVar("\\widehat{u}");
  VarPtr beta_n_u_minus_sigma_n = varFactory->fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
  VarPtr u = varFactory->fieldVar("u");
  VarPtr sigma1 = varFactory->fieldVar("\\sigma_1");
  VarPtr sigma2 = varFactory->fieldVar("\\sigma_2");

  vector<double> beta;
  beta.push_back(1.0);
  beta.push_back(0.0);

  ////////////////////   DEFINE BILINEAR FORM   ///////////////////////

  BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
  // tau terms:
  confusionBF->addTerm(sigma1 / eps, tau->x());
  confusionBF->addTerm(sigma2 / eps, tau->y());
  confusionBF->addTerm(u, tau->div());
  confusionBF->addTerm(uhat, -tau->dot_normal());

  // v terms:
  confusionBF->addTerm( sigma1, v->dx() );
  confusionBF->addTerm( sigma2, v->dy() );
  confusionBF->addTerm( -u, beta * v->grad() );
  confusionBF->addTerm( beta_n_u_minus_sigma_n, v);

  ////////////////////   DEFINE INNER PRODUCT(S)   ///////////////////////

  // robust test norm
  IPPtr ip = Teuchos::rcp(new IP);

  // choose the mesh-independent norm even though it may have boundary layers
  ip->addTerm(v->grad());
  ip->addTerm(v);
  ip->addTerm(tau);
  ip->addTerm(tau->div());

  ////////////////////   SPECIFY RHS AND HELPFUL FUNCTIONS   ///////////////////////

  FunctionPtr n = Function::normal();
  vector<double> e1,e2;
  e1.push_back(1.0);
  e1.push_back(0.0);
  e2.push_back(0.0);
  e2.push_back(1.0);
  FunctionPtr one = Function::constant(1.0);

  FunctionPtr zero = Function::constant(0.0);
  RHSPtr rhs = RHS::rhs();
  FunctionPtr f = one; // if this is set to zero instead, we pass the test (a clue?)
  rhs->addTerm( f * v );

  ////////////////////   CREATE BCs   ///////////////////////
  BCPtr bc = BC::bc();
  SpatialFilterPtr squareBoundary = Teuchos::rcp( new SquareBoundary );

  bc->addDirichlet(uhat, squareBoundary, one);

  ////////////////////   BUILD MESH   ///////////////////////
  // define nodes for mesh
  int order = 2;
  int H1Order = order+1;
  int pToAdd = 2;

  // create a pointer to a new mesh:
  Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells,confusionBF, H1Order, H1Order+pToAdd);

  ////////////////////   SOLVE & REFINE   ///////////////////////

  Teuchos::RCP<Solution> solution;
  solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
  solution->solve(false);
  double energyError = solution->energyErrorTotal();

  LinearTermPtr residual = rhs->linearTermCopy();
  residual->addTerm(-confusionBF->testFunctional(solution),true);

//  FunctionPtr uh = Function::solution(uhat,solution);
//  FunctionPtr fn = Function::solution(beta_n_u_minus_sigma_n,solution);
//  FunctionPtr uF = Function::solution(u,solution);
//  FunctionPtr sigma = e1*Function::solution(sigma1,solution)+e2*Function::solution(sigma2,solution);
//  residual->addTerm(- (fn*v - uh*tau->dot_normal()));
//.........这里部分代码省略.........

// tests residual computation on simple convection
bool ScratchPadTests::testLTResidualSimple()
{
  double tol = 1e-11;
  int rank = Teuchos::GlobalMPISession::getRank();

  bool success = true;

  int nCells = 2;

  ////////////////////   DECLARE VARIABLES   ///////////////////////

  // define test variables
  VarFactoryPtr varFactory = VarFactory::varFactory();
  VarPtr v = varFactory->testVar("v", HGRAD);

  // define trial variables
  VarPtr beta_n_u = varFactory->fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
  VarPtr u = varFactory->fieldVar("u");

  vector<double> beta;
  beta.push_back(1.0);
  beta.push_back(1.0);

  ////////////////////   DEFINE BILINEAR FORM   ///////////////////////

  BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
  // v terms:
  confusionBF->addTerm( -u, beta * v->grad() );
  confusionBF->addTerm( beta_n_u, v);

  ////////////////////   DEFINE INNER PRODUCT(S)   ///////////////////////

  // robust test norm
  IPPtr ip = Teuchos::rcp(new IP);

  // choose the mesh-independent norm even though it may have BLs
  ip->addTerm(v->grad());
  ip->addTerm(v);

  ////////////////////   SPECIFY RHS AND HELPFUL FUNCTIONS   ///////////////////////

  FunctionPtr n = Function::normal();
  vector<double> e1,e2;
  e1.push_back(1.0);
  e1.push_back(0.0);
  e2.push_back(0.0);
  e2.push_back(1.0);
  FunctionPtr one = Function::constant(1.0);

  FunctionPtr zero = Function::constant(0.0);
  RHSPtr rhs = RHS::rhs();
  FunctionPtr f = one;
  rhs->addTerm( f * v );

  ////////////////////   CREATE BCs   ///////////////////////
  BCPtr bc = BC::bc();
  SpatialFilterPtr boundary = Teuchos::rcp( new InflowSquareBoundary );
  FunctionPtr u_in = Teuchos::rcp(new Uinflow);
  bc->addDirichlet(beta_n_u, boundary, beta*n*u_in);

  ////////////////////   BUILD MESH   ///////////////////////
  // define nodes for mesh
  int order = 2;
  int H1Order = order+1;
  int pToAdd = 2;

  // create a pointer to a new mesh:
  Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells,confusionBF, H1Order, H1Order+pToAdd);

  ////////////////////   SOLVE & REFINE   ///////////////////////

  int cubEnrich = 0;

  Teuchos::RCP<Solution> solution;
  solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
  solution->solve(false);
  double energyError = solution->energyErrorTotal();

  LinearTermPtr residual = rhs->linearTermCopy();
  residual->addTerm(-confusionBF->testFunctional(solution),true);

  Teuchos::RCP<RieszRep> rieszResidual = Teuchos::rcp(new RieszRep(mesh, ip, residual));
  rieszResidual->computeRieszRep(cubEnrich);
  double energyErrorLT = rieszResidual->getNorm();

  bool testVsTest = true;
  FunctionPtr e_v = RieszRep::repFunction(v,rieszResidual);
  map<int,FunctionPtr> errFxns;
  errFxns[v->ID()] = e_v;
  FunctionPtr err = (ip->evaluate(errFxns,false))->evaluate(errFxns,false); // don't need boundary terms unless they're in IP
  double energyErrorIntegrated = sqrt(err->integrate(mesh,cubEnrich,testVsTest));
  // check that energy error computed thru Solution and through rieszRep are the same
  success = abs(energyError-energyErrorLT) < tol;
  if (success==false)
  {
    if (rank==0)
      cout << "Failed testLTResidualSimple; energy error = " << energyError << ", while linearTerm error is computed to be " << energyErrorLT << endl;
    return success;
  }
//.........这里部分代码省略.........