Example #1
0
File: ASMs3DLag.C Project: OPM/IFEM
bool ASMs3DLag::integrate (Integrand& integrand,
			   GlobalIntegral& glInt,
			   const TimeDomain& time)
{
  if (!svol) return true; // silently ignore empty patches

  // Get Gaussian quadrature points and weights
  const double* xg = GaussQuadrature::getCoord(nGauss);
  const double* wg = GaussQuadrature::getWeight(nGauss);
  if (!xg || !wg) return false;

  // Get the reduced integration quadrature points, if needed
  const double* xr = nullptr;
  const double* wr = nullptr;
  int nRed = integrand.getReducedIntegration(nGauss);
  if (nRed > 0)
  {
    xr = GaussQuadrature::getCoord(nRed);
    wr = GaussQuadrature::getWeight(nRed);
    if (!xr || !wr) return false;
  }
  else if (nRed < 0)
    nRed = nGauss; // The integrand needs to know nGauss

  // Get parametric coordinates of the elements
  RealArray upar, vpar, wpar;
  this->getGridParameters(upar,0,1);
  this->getGridParameters(vpar,1,1);
  this->getGridParameters(wpar,2,1);

  // Number of elements in each direction
  const int nel1 = upar.size() - 1;
  const int nel2 = vpar.size() - 1;

  // Order of basis in the three parametric directions (order = degree + 1)
  const int p1 = svol->order(0);
  const int p2 = svol->order(1);
  const int p3 = svol->order(2);


  // === Assembly loop over all elements in the patch ==========================

  bool ok = true;
  for (size_t g = 0; g < threadGroupsVol.size() && ok; g++)
  {
#pragma omp parallel for schedule(static)
    for (size_t t = 0; t < threadGroupsVol[g].size(); t++)
    {
      FiniteElement fe(p1*p2*p3);
      Matrix dNdu, Xnod, Jac;
      Vec4   X;
      for (size_t l = 0; l < threadGroupsVol[g][t].size() && ok; l++)
      {
        int iel = threadGroupsVol[g][t][l];
        int i1  =  iel % nel1;
        int i2  = (iel / nel1) % nel2;
        int i3  =  iel / (nel1*nel2);

        // Set up nodal point coordinates for current element
        if (!this->getElementCoordinates(Xnod,++iel))
        {
          ok = false;
          break;
        }

        if (integrand.getIntegrandType() & Integrand::ELEMENT_CENTER)
        {
          // Compute the element "center" (average of element node coordinates)
          X = 0.0;
          for (size_t i = 1; i <= 3; i++)
            for (size_t j = 1; j <= Xnod.cols(); j++)
              X[i-1] += Xnod(i,j);

          X *= 1.0/(double)Xnod.cols();
        }

        // Initialize element quantities
        fe.iel = MLGE[iel-1];
        LocalIntegral* A = integrand.getLocalIntegral(fe.N.size(),fe.iel);
        if (!integrand.initElement(MNPC[iel-1],fe,X,nRed*nRed*nRed,*A))
        {
          A->destruct();
          ok = false;
          break;
        }

        if (xr)
        {
          // --- Selective reduced integration loop ----------------------------

          for (int k = 0; k < nRed; k++)
            for (int j = 0; j < nRed; j++)
              for (int i = 0; i < nRed; i++)
              {
                // Local element coordinates of current integration point
                fe.xi   = xr[i];
                fe.eta  = xr[j];
                fe.zeta = xr[k];

                // Parameter value of current integration point
                fe.u = 0.5*(upar[i1]*(1.0-xr[i]) + upar[i1+1]*(1.0+xr[i]));
                fe.v = 0.5*(vpar[i2]*(1.0-xr[j]) + vpar[i2+1]*(1.0+xr[j]));
                fe.w = 0.5*(wpar[i3]*(1.0-xr[k]) + wpar[i3+1]*(1.0+xr[k]));

                // Compute basis function derivatives at current point
                // using tensor product of one-dimensional Lagrange polynomials
                if (!Lagrange::computeBasis(fe.N,dNdu,
                                            p1,xr[i],p2,xr[j],p3,xr[k]))
                {
                  ok = false;
                  break;
                }

                // Compute Jacobian inverse and derivatives
                fe.detJxW = utl::Jacobian(Jac,fe.dNdX,Xnod,dNdu);

                // Cartesian coordinates of current integration point
                X = Xnod * fe.N;
                X.t = time.t;

                // Compute the reduced integration terms of the integrand
                fe.detJxW *= wr[i]*wr[j]*wr[k];
                if (!integrand.reducedInt(*A,fe,X))
                  ok = false;
              }
        }


        // --- Integration loop over all Gauss points in each direction --------

        int jp = ((i3*nel2 + i2)*nel1 + i1)*nGauss*nGauss*nGauss;
        fe.iGP = firstIp + jp; // Global integration point counter

        for (int k = 0; k < nGauss; k++)
          for (int j = 0; j < nGauss; j++)
            for (int i = 0; i < nGauss; i++, fe.iGP++)
            {
              // Local element coordinates of current integration point
              fe.xi   = xg[i];
              fe.eta  = xg[j];
              fe.zeta = xg[k];

              // Parameter value of current integration point
              fe.u = 0.5*(upar[i1]*(1.0-xg[i]) + upar[i1+1]*(1.0+xg[i]));
              fe.v = 0.5*(vpar[i2]*(1.0-xg[j]) + vpar[i2+1]*(1.0+xg[j]));
              fe.w = 0.5*(wpar[i3]*(1.0-xg[k]) + wpar[i3+1]*(1.0+xg[k]));

              // Compute basis function derivatives at current integration point
              // using tensor product of one-dimensional Lagrange polynomials
              if (!Lagrange::computeBasis(fe.N,dNdu,p1,xg[i],p2,xg[j],p3,xg[k]))
                ok = false;

              // Compute Jacobian inverse of coordinate mapping and derivatives
              fe.detJxW = utl::Jacobian(Jac,fe.dNdX,Xnod,dNdu);
              if (fe.detJxW == 0.0) continue; // skip singular points

              // Cartesian coordinates of current integration point
              X = Xnod * fe.N;
              X.t = time.t;

              // Evaluate the integrand and accumulate element contributions
              fe.detJxW *= wg[i]*wg[j]*wg[k];
              if (!integrand.evalInt(*A,fe,time,X))
                ok = false;
            }

        // Finalize the element quantities
        if (ok && !integrand.finalizeElement(*A,time,firstIp+jp))
          ok = false;

        // Assembly of global system integral
        if (ok && !glInt.assemble(A->ref(),fe.iel))
          ok = false;

        A->destruct();
      }
    }
  }

  return ok;
}
Example #2
0
File: ASMs1D.C Project: OPM/IFEM
bool ASMs1D::integrate (Integrand& integrand,
			GlobalIntegral& glInt,
			const TimeDomain& time)
{
  if (!curv) return true; // silently ignore empty patches

  // Get Gaussian quadrature points and weights
  const double* xg = GaussQuadrature::getCoord(nGauss);
  const double* wg = GaussQuadrature::getWeight(nGauss);
  if (!xg || !wg) return false;

  // Get the reduced integration quadrature points, if needed
  const double* xr = nullptr;
  const double* wr = nullptr;
  int nRed = integrand.getReducedIntegration(nGauss);
  if (nRed > 0)
  {
    xr = GaussQuadrature::getCoord(nRed);
    wr = GaussQuadrature::getWeight(nRed);
    if (!xr || !wr) return false;
  }
  else if (nRed < 0)
    nRed = nGauss; // The integrand needs to know nGauss

  if (integrand.getIntegrandType() & Integrand::SECOND_DERIVATIVES)
    if (curv->rational())
    {
      std::cerr <<" *** ASMs1D::integrate: Second-derivatives of NURBS "
                <<" is not implemented yet, sorry..."<< std::endl;
      return false;
    }

  // Compute parameter values of the Gauss points over the whole patch
  Matrix gpar, redpar;
  this->getGaussPointParameters(gpar,nGauss,xg);
  if (xr)
    this->getGaussPointParameters(redpar,nRed,xr);

  const int p1 = curv->order();

  FiniteElement fe(p1);
  Matrix   dNdu, Jac;
  Matrix3D d2Ndu2, Hess;
  Vec4     X;

  if (nsd > 1 && (integrand.getIntegrandType() & Integrand::SECOND_DERIVATIVES))
    fe.G.resize(nsd,2); // For storing d{X}/du and d2{X}/du2


  // === Assembly loop over all elements in the patch ==========================

  for (size_t iel = 0; iel < nel; iel++)
  {
    fe.iel = MLGE[iel];
    if (fe.iel < 1) continue; // zero-length element

    // Check that the current element has nonzero length
    double dL = this->getParametricLength(1+iel);
    if (dL < 0.0) return false; // topology error (probably logic error)

    // Set up control point coordinates for current element
    if (!this->getElementCoordinates(fe.Xn,1+iel)) return false;

    if (integrand.getIntegrandType() & Integrand::ELEMENT_CORNERS)
      this->getElementEnds(p1+iel,fe.XC);

    if (integrand.getIntegrandType() & Integrand::NODAL_ROTATIONS)
    {
      this->getElementNodalRotations(fe.Tn,iel);
      if (!elmCS.empty()) fe.Te = elmCS[iel];
    }

    // Initialize element matrices
    LocalIntegral* A = integrand.getLocalIntegral(fe.N.size(),fe.iel);
    bool ok = integrand.initElement(MNPC[iel],fe,X,nRed,*A);

    if (xr)
    {
      // --- Selective reduced integration loop --------------------------------

      for (int i = 0; i < nRed && ok; i++)
      {
	// Local element coordinates of current integration point
	fe.xi = xr[i];

	// Parameter values of current integration point
	fe.u = redpar(1+i,1+iel);

        if (integrand.getIntegrandType() & Integrand::NO_DERIVATIVES)
          this->extractBasis(fe.u,fe.N);
        else
        {
          // Fetch basis function derivatives at current point
          this->extractBasis(fe.u,fe.N,dNdu);
          // Compute Jacobian inverse and derivatives
          dNdu.multiply(0.5*dL); // Derivatives w.r.t. xi=[-1,1]
          fe.detJxW = utl::Jacobian(Jac,fe.dNdX,fe.Xn,dNdu)*wr[i];
        }

	// Cartesian coordinates of current integration point
	X = fe.Xn * fe.N;
	X.t = time.t;

	// Compute the reduced integration terms of the integrand
	ok = integrand.reducedInt(*A,fe,X);
      }
    }


    // --- Integration loop over all Gauss points in current element -----------

    int jp = iel*nGauss;
    fe.iGP = firstIp + jp; // Global integration point counter

    for (int i = 0; i < nGauss && ok; i++, fe.iGP++)
    {
      // Local element coordinate of current integration point
      fe.xi = xg[i];

      // Parameter value of current integration point
      fe.u = gpar(1+i,1+iel);

      // Compute basis functions and derivatives
      if (integrand.getIntegrandType() & Integrand::NO_DERIVATIVES)
        this->extractBasis(fe.u,fe.N);
      else if (integrand.getIntegrandType() & Integrand::SECOND_DERIVATIVES)
        this->extractBasis(fe.u,fe.N,dNdu,d2Ndu2);
      else
        this->extractBasis(fe.u,fe.N,dNdu);

      if (!dNdu.empty())
      {
        // Compute derivatives in terms of physical coordinates
        dNdu.multiply(0.5*dL); // Derivatives w.r.t. xi=[-1,1]
        fe.detJxW = utl::Jacobian(Jac,fe.dNdX,fe.Xn,dNdu)*wg[i];
        if (fe.detJxW == 0.0) continue; // skip singular points

        // Compute Hessian of coordinate mapping and 2nd order derivatives
        if (integrand.getIntegrandType() & Integrand::SECOND_DERIVATIVES)
        {
          d2Ndu2.multiply(0.25*dL*dL); // 2nd derivatives w.r.t. xi=[-1,1]
          if (!utl::Hessian(Hess,fe.d2NdX2,Jac,fe.Xn,d2Ndu2,fe.dNdX))
            ok = false;
          else if (fe.G.cols() == 2)
          {
            // Store the first and second derivatives of {X} w.r.t.
            // the parametric coordinate (xi), in the G-matrix
            fe.G.fillColumn(1,Jac.ptr());
            fe.G.fillColumn(2,Hess.ptr());
          }
        }
      }

      // Cartesian coordinates of current integration point
      X = fe.Xn * fe.N;
      X.t = time.t;

      // Evaluate the integrand and accumulate element contributions
      if (ok && !integrand.evalInt(*A,fe,time,X))
        ok = false;
    }

    // Finalize the element quantities
    if (ok && !integrand.finalizeElement(*A,fe,time,firstIp+jp))
      ok = false;

    // Assembly of global system integral
    if (ok && !glInt.assemble(A->ref(),fe.iel))
      ok = false;

    A->destruct();

    if (!ok) return false;
  }

  return true;
}
Example #3
0
bool ASMs2DLag::integrate (Integrand& integrand,
			   GlobalIntegral& glInt,
			   const TimeDomain& time)
{
  if (this->empty()) return true; // silently ignore empty patches

  // Get Gaussian quadrature points and weights
  std::array<int,2> ng;
  std::array<const double*,2> xg, wg;
  for (int d = 0; d < 2; d++)
  {
    ng[d] = this->getNoGaussPt(d == 0 ? p1 : p2);
    xg[d] = GaussQuadrature::getCoord(ng[d]);
    wg[d] = GaussQuadrature::getWeight(ng[d]);
    if (!xg[d] || !wg[d]) return false;
  }

  // Get the reduced integration quadrature points, if needed
  const double* xr = nullptr;
  const double* wr = nullptr;
  int nRed = integrand.getReducedIntegration(ng[0]);
  if (nRed > 0)
  {
    xr = GaussQuadrature::getCoord(nRed);
    wr = GaussQuadrature::getWeight(nRed);
    if (!xr || !wr) return false;
  }
  else if (nRed < 0)
    nRed = ng[0]; // The integrand needs to know nGauss

  // Get parametric coordinates of the elements
  RealArray upar, vpar;
  this->getGridParameters(upar,0,1);
  this->getGridParameters(vpar,1,1);

  // Number of elements in each direction
  const int nelx = upar.empty() ? 0 : upar.size() - 1;


  // === Assembly loop over all elements in the patch ==========================

  bool ok = true;
  for (size_t g = 0; g < threadGroups.size() && ok; g++)
  {
#pragma omp parallel for schedule(static)
    for (size_t t = 0; t < threadGroups[g].size(); t++)
    {
      FiniteElement fe(p1*p2);
      Matrix dNdu, Xnod, Jac;
      Vec4   X;
      for (size_t i = 0; i < threadGroups[g][t].size() && ok; i++)
      {
        int iel = threadGroups[g][t][i];
        int i1  = nelx > 0 ? iel % nelx : 0;
        int i2  = nelx > 0 ? iel / nelx : 0;

        // Set up nodal point coordinates for current element
        if (!this->getElementCoordinates(Xnod,1+iel))
        {
          ok = false;
          break;
        }

        if (integrand.getIntegrandType() & Integrand::ELEMENT_CENTER)
        {
          // Compute the element "center" (average of element node coordinates)
          X = 0.0;
          for (size_t i = 1; i <= nsd; i++)
            for (size_t j = 1; j <= Xnod.cols(); j++)
              X[i-1] += Xnod(i,j);

          X *= 1.0/(double)Xnod.cols();
        }

        // Initialize element quantities
        fe.iel = MLGE[iel];
        LocalIntegral* A = integrand.getLocalIntegral(fe.N.size(),fe.iel);
        if (!integrand.initElement(MNPC[iel],fe,X,nRed*nRed,*A))
        {
          A->destruct();
          ok = false;
          break;
        }

        if (xr)
        {
          // --- Selective reduced integration loop ----------------------------

          for (int j = 0; j < nRed; j++)
            for (int i = 0; i < nRed; i++)
            {
              // Local element coordinates of current integration point
              fe.xi  = xr[i];
              fe.eta = xr[j];

              // Parameter value of current integration point
              if (!upar.empty())
                fe.u = 0.5*(upar[i1]*(1.0-xr[i]) + upar[i1+1]*(1.0+xr[i]));
              if (!vpar.empty())
                fe.v = 0.5*(vpar[i2]*(1.0-xr[j]) + vpar[i2+1]*(1.0+xr[j]));

              // Compute basis function derivatives at current point
              // using tensor product of one-dimensional Lagrange polynomials
              if (!Lagrange::computeBasis(fe.N,dNdu,p1,xr[i],p2,xr[j]))
                ok = false;

              // Compute Jacobian inverse and derivatives
              fe.detJxW = utl::Jacobian(Jac,fe.dNdX,Xnod,dNdu);

              // Cartesian coordinates of current integration point
              X = Xnod * fe.N;
              X.t = time.t;

              // Compute the reduced integration terms of the integrand
              fe.detJxW *= wr[i]*wr[j];
              if (!integrand.reducedInt(*A,fe,X))
                ok = false;
            }
        }


        // --- Integration loop over all Gauss points in each direction --------

        int jp = iel*ng[0]*ng[1];
        fe.iGP = firstIp + jp; // Global integration point counter

        for (int j = 0; j < ng[1]; j++)
          for (int i = 0; i < ng[0]; i++, fe.iGP++)
          {
            // Local element coordinates of current integration point
            fe.xi  = xg[0][i];
            fe.eta = xg[1][j];

            // Parameter value of current integration point
            if (!upar.empty())
              fe.u = 0.5*(upar[i1]*(1.0-xg[0][i]) + upar[i1+1]*(1.0+xg[0][i]));
            if (!vpar.empty())
              fe.v = 0.5*(vpar[i2]*(1.0-xg[1][j]) + vpar[i2+1]*(1.0+xg[1][j]));

            // Compute basis function derivatives at current integration point
            // using tensor product of one-dimensional Lagrange polynomials
            if (!Lagrange::computeBasis(fe.N,dNdu,p1,xg[0][i],p2,xg[1][j]))
              ok = false;

            // Compute Jacobian inverse of coordinate mapping and derivatives
            fe.detJxW = utl::Jacobian(Jac,fe.dNdX,Xnod,dNdu);
            if (fe.detJxW == 0.0) continue; // skip singular points

            // Cartesian coordinates of current integration point
            X = Xnod * fe.N;
            X.t = time.t;

            // Evaluate the integrand and accumulate element contributions
            fe.detJxW *= wg[0][i]*wg[1][j];
            if (!integrand.evalInt(*A,fe,time,X))
              ok = false;
          }

        // Finalize the element quantities
        if (ok && !integrand.finalizeElement(*A,time,firstIp+jp))
          ok = false;

        // Assembly of global system integral
        if (ok && !glInt.assemble(A->ref(),fe.iel))
          ok = false;

        A->destruct();
      }
    }
  }

  return ok;
}
Example #4
0
bool ASMs1DSpec::integrate (Integrand& integrand,
			    GlobalIntegral& glInt,
			    const TimeDomain& time)
{
  if (!curv) return true; // silently ignore empty patches

  // Order of basis (order = degree + 1)
  const int p1 = curv->order();
  const int n1 = nGauss < 1 ? p1 : nGauss;

  // Evaluate integration points and weights

  Vector wg1, xg1, points1;
  if (!Legendre::GLL(wg1,points1,p1))
    return false;

  Matrix D1;
  if (nGauss < 1)
  {
    // We are using the nodal points themselves as integration points
    if (!Legendre::basisDerivatives(n1,D1))
      return false;
  }
  else
    // Using Gauss-Legendre scheme with nGauss points
    if (!Legendre::GL(wg1,xg1,n1))
      return false;

  FiniteElement fe(p1);
  Matrix dNdu, Xnod, Jac;
  Vec4   X;


  // === Assembly loop over all elements in the patch ==========================

  const int nel = this->getNoElms();
  for (int iel = 1; iel <= nel; iel++)
  {
    // Set up control point coordinates for current element
    if (!this->getElementCoordinates(Xnod,iel)) return false;

    // Initialize element quantities
    fe.iel = MLGE[iel-1];
    LocalIntegral* A = integrand.getLocalIntegral(p1,fe.iel);
    if (!integrand.initElement(MNPC[iel-1],*A)) return false;

    // --- Integration loop over integration points ----------------------------

    for (int i = 0; i < n1; i++)
    {
      // Compute basis function derivatives at current integration point
      if (nGauss < 1)
      {
	fe.N.fill(0.0);
	fe.N(i+1) = 1.0;
	dNdu.fillColumn(1,D1.getRow(i+1));
      }
      else
	if (!Lagrange::computeBasis(fe.N,&dNdu,points1,xg1[i]))
	  return false;

      // Compute Jacobian inverse of coordinate mapping and derivatives
      fe.detJxW = utl::Jacobian(Jac,fe.dNdX,Xnod,dNdu);

      // Cartesian coordinates of current integration point
      X = Xnod*fe.N;
      X.t = time.t;

      // Evaluate the integrand and accumulate element contributions
      fe.detJxW *= wg1[i];
      if (!integrand.evalInt(*A,fe,time,X))
	return false;
    }

    // Assembly of global system integral
    if (!glInt.assemble(A->ref(),fe.iel))
      return false;

    A->destruct();
  }

  return true;
}
Example #5
0
bool ASMs2DSpec::integrate (Integrand& integrand,
			    GlobalIntegral& glInt,
			    const TimeDomain& time)
{
  if (this->empty()) return true; // silently ignore empty patches

  // Evaluate integration points (= nodal points) and weights
  Vector wg1,xg1,wg2,xg2;
  if (!Legendre::GLL(wg1,xg1,p1)) return false;
  if (!Legendre::GLL(wg2,xg2,p2)) return false;

  Matrix D1, D2;
  if (!Legendre::basisDerivatives(p1,D1)) return false;
  if (!Legendre::basisDerivatives(p2,D2)) return false;


  // === Assembly loop over all elements in the patch ==========================

  bool ok = true;
  for (size_t g = 0; g < threadGroups.size() && ok; g++)
  {
#pragma omp parallel for schedule(static)
    for (size_t t = 0; t < threadGroups[g].size(); t++)
    {
      FiniteElement fe(p1*p2);
      Matrix dNdu(p1*p2,2), Xnod, Jac;
      Vec4   X;
      for (size_t e = 0; e < threadGroups[g][t].size(); e++)
      {
        int iel = threadGroups[g][t][e]+1;

        // Set up control point coordinates for current element
        if (!this->getElementCoordinates(Xnod,iel))
        {
          ok = false;
          break;
        }

        // Initialize element quantities
        fe.iel = MLGE[iel-1];
        LocalIntegral* A = integrand.getLocalIntegral(fe.N.size(),fe.iel);
        if (!integrand.initElement(MNPC[iel-1],*A))
        {
          A->destruct();
          ok = false;
          break;
        }


        // --- Integration loop over all Gauss points in each direction --------

        int count = 1;
        for (int j = 1; j <= p2; j++)
          for (int i = 1; i <= p1; i++, count++)
          {
            // Evaluate the basis functions and gradients using
            // tensor product of one-dimensional Lagrange polynomials
            evalBasis(i,j,p1,p2,D1,D2,fe.N,dNdu);

            // Compute Jacobian inverse of coordinate mapping and derivatives
            fe.detJxW = utl::Jacobian(Jac,fe.dNdX,Xnod,dNdu);
            if (fe.detJxW == 0.0) continue; // skip singular points

            // Cartesian coordinates of current integration point
            X.x = Xnod(1,count);
            X.y = Xnod(2,count);
            X.t = time.t;

            // Evaluate the integrand and accumulate element contributions
            fe.detJxW *= wg1(i)*wg2(j);
            if (!integrand.evalInt(*A,fe,time,X))
              ok = false;
          }

        // Assembly of global system integral
        if (ok && !glInt.assemble(A->ref(),fe.iel))
          ok = false;

        A->destruct();
      }
    }
  }

  return ok;
}