assembly.h

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#ifndef ASSEMBLY_H
#define ASSEMBLY_H

#if defined(LIBMESH_HAVE_SLEPC) && defined(LIBMESH_HAVE_GLPK)

#include "libmesh/sparse_matrix.h"
#include "libmesh/numeric_vector.h"
#include "libmesh/dense_matrix.h"
#include "libmesh/dense_vector.h"
#include "libmesh/fe.h"
#include "libmesh/fe_interface.h"
#include "libmesh/fe_base.h"
#include "libmesh/elem_assembly.h"
#include "libmesh/quadrature_gauss.h"

// rbOOmit includes
#include "libmesh/rb_theta.h"
#include "libmesh/rb_assembly_expansion.h"

// Bring in bits from the libMesh namespace.
// Just the bits we're using, since this is a header.
using libMesh::ElemAssembly;
using libMesh::FEInterface;
using libMesh::FEMContext;
using libMesh::Number;
using libMesh::Point;
using libMesh::RBTheta;
using libMesh::Real;
using libMesh::RealGradient;
using libMesh::FEBase;

// Functors for the parameter-dependent part of the affine decomposition of the PDE
// The RHS and outputs just require a constant value of 1, so use a default RBTheta object there
struct ThetaA0 : RBTheta { virtual Number evaluate(const RBParameters & mu) { return mu.get_value("mu_0"); } };
struct ThetaA1 : RBTheta { virtual Number evaluate(const RBParameters & mu) { return mu.get_value("mu_1"); } };
struct ThetaA2 : RBTheta { virtual Number evaluate(const RBParameters & mu) { return mu.get_value("mu_2"); } };

struct B : ElemAssembly
{
  // Assemble the H1 inner product. This will be used as the inner product
  // for this problem.
  virtual void interior_assembly(FEMContext & c)
  {
    const unsigned int u_var = 0;

    FEBase * elem_fe = nullptr;
    c.get_element_fe(u_var, elem_fe);

    const std::vector<Real> & JxW = elem_fe->get_JxW();

    const std::vector<std::vector<Real>> & phi = elem_fe->get_phi();

    // The velocity shape function gradients at interior
    // quadrature points.
    const std::vector<std::vector<RealGradient>> & dphi = elem_fe->get_dphi();

    // The number of local degrees of freedom in each variable
    const unsigned int n_u_dofs = c.get_dof_indices(u_var).size();

    // Now we will build the affine operator
    unsigned int n_qpoints = c.get_element_qrule().n_points();

    for (unsigned int qp=0; qp != n_qpoints; qp++)
      for (unsigned int i=0; i != n_u_dofs; i++)
        for (unsigned int j=0; j != n_u_dofs; j++)
          c.get_elem_jacobian()(i,j) += JxW[qp] * (phi[j][qp]*phi[i][qp] + dphi[j][qp]*dphi[i][qp]);
  }
};


struct A0 : ElemAssembly
{
  // Assemble the Laplacian operator
  virtual void interior_assembly(FEMContext & c)
  {
    const unsigned int u_var = 0;

    FEBase * elem_fe = nullptr;
    c.get_element_fe(u_var, elem_fe);

    const std::vector<Real> & JxW = elem_fe->get_JxW();

    // The velocity shape function gradients at interior
    // quadrature points.
    const std::vector<std::vector<RealGradient>> & dphi = elem_fe->get_dphi();

    // The number of local degrees of freedom in each variable
    const unsigned int n_u_dofs = c.get_dof_indices(u_var).size();

    // Now we will build the affine operator
    unsigned int n_qpoints = c.get_element_qrule().n_points();

    Real
      min_x=0.,
      max_x=0.5;

    Point avg = c.get_elem().vertex_average();
    if ((min_x <= avg(0)) && (avg(0) < max_x))
      for (unsigned int qp=0; qp != n_qpoints; qp++)
        for (unsigned int i=0; i != n_u_dofs; i++)
          for (unsigned int j=0; j != n_u_dofs; j++)
            c.get_elem_jacobian()(i,j) += JxW[qp] * dphi[j][qp]*dphi[i][qp];
  }
};

struct A1 : ElemAssembly
{
  // Assemble the Laplacian operator
  virtual void interior_assembly(FEMContext & c)
  {
    const unsigned int u_var = 0;

    FEBase * elem_fe = nullptr;
    c.get_element_fe(u_var, elem_fe);

    const std::vector<Real> & JxW = elem_fe->get_JxW();

    // The velocity shape function gradients at interior
    // quadrature points.
    const std::vector<std::vector<RealGradient>> & dphi = elem_fe->get_dphi();

    // The number of local degrees of freedom in each variable
    const unsigned int n_u_dofs = c.get_dof_indices(u_var).size();

    // Now we will build the affine operator
    unsigned int n_qpoints = c.get_element_qrule().n_points();

    Real
      min_x=0.5,
      max_x=1.;

    Point avg = c.get_elem().vertex_average();
    if ((min_x <= avg(0)) && (avg(0) <= max_x))
      for (unsigned int qp=0; qp != n_qpoints; qp++)
        for (unsigned int i=0; i != n_u_dofs; i++)
          for (unsigned int j=0; j != n_u_dofs; j++)
            c.get_elem_jacobian()(i,j) += JxW[qp] * dphi[j][qp]*dphi[i][qp];
  }
};

struct A2 : ElemAssembly
{
  // Convection in the x-direction
  virtual void interior_assembly(FEMContext & c)
  {
    const unsigned int u_var = 0;

    FEBase * elem_fe = nullptr;
    c.get_element_fe(u_var, elem_fe);

    const std::vector<Real> & JxW = elem_fe->get_JxW();

    const std::vector<std::vector<Real>> & phi = elem_fe->get_phi();

    const std::vector<std::vector<RealGradient>> & dphi = elem_fe->get_dphi();

    // The number of local degrees of freedom in each variable
    const unsigned int n_u_dofs = c.get_dof_indices(u_var).size();

    // Now we will build the affine operator
    unsigned int n_qpoints = c.get_element_qrule().n_points();

    for (unsigned int qp=0; qp != n_qpoints; qp++)
      for (unsigned int i=0; i != n_u_dofs; i++)
        for (unsigned int j=0; j != n_u_dofs; j++)
          c.get_elem_jacobian()(i,j) -= JxW[qp] * dphi[i][qp](0)*phi[j][qp];
  }
};


struct F0 : ElemAssembly
{
  // Source term, 1 throughout the domain
  virtual void interior_assembly(FEMContext & c)
  {
    const unsigned int u_var = 0;

    FEBase * elem_fe = nullptr;
    c.get_element_fe(u_var, elem_fe);

    const std::vector<Real> & JxW = elem_fe->get_JxW();

    const std::vector<std::vector<Real>> & phi = elem_fe->get_phi();

    // The number of local degrees of freedom in each variable
    const unsigned int n_u_dofs = c.get_dof_indices(u_var).size();

    // Now we will build the affine operator
    unsigned int n_qpoints = c.get_element_qrule().n_points();

    for (unsigned int qp=0; qp != n_qpoints; qp++)
      for (unsigned int i=0; i != n_u_dofs; i++)
        c.get_elem_residual()(i) += JxW[qp] * (1.*phi[i][qp]);
  }
};

struct OutputAssembly : ElemAssembly
{
  OutputAssembly(Real min_x_in, Real max_x_in,
                 Real min_y_in, Real max_y_in) :
    min_x(min_x_in),
    max_x(max_x_in),
    min_y(min_y_in),
    max_y(max_y_in)
  {}

  // Output: Average value over the region [min_x,max_x]x[min_y,max_y]
  virtual void interior_assembly(FEMContext & c)
  {
    const unsigned int u_var = 0;

    FEBase * elem_fe = nullptr;
    c.get_element_fe(u_var, elem_fe);

    const std::vector<Real> & JxW = elem_fe->get_JxW();

    const std::vector<std::vector<Real>> & phi = elem_fe->get_phi();

    // The number of local degrees of freedom in each variable
    const unsigned int n_u_dofs = c.get_dof_indices(u_var).size();

    // Now we will build the affine operator
    unsigned int n_qpoints = c.get_element_qrule().n_points();

    Real output_area = (max_x-min_x) * (max_y-min_y);

    Point avg = c.get_elem().vertex_average();
    if ((min_x <= avg(0)) && (avg(0) <= max_x) &&
        (min_y <= avg(1)) && (avg(1) <= max_y))
      for (unsigned int qp=0; qp != n_qpoints; qp++)
        for (unsigned int i=0; i != n_u_dofs; i++)
          c.get_elem_residual()(i) += JxW[qp] * (1.*phi[i][qp]) / output_area;
  }

  // Member variables that define the output region in 2D
  Real min_x, max_x, min_y, max_y;
};

// Define an RBThetaExpansion class for this PDE
struct Ex02RBThetaExpansion : RBThetaExpansion
{

  Ex02RBThetaExpansion()
  {
    // set up the RBThetaExpansion object
    attach_A_theta(&theta_a_0);   // Attach the lhs theta
    attach_A_theta(&theta_a_1);
    attach_A_theta(&theta_a_2);

    attach_F_theta(&rb_theta);    // Attach the rhs theta

    attach_output_theta(&rb_theta); // Attach output 0 theta
    attach_output_theta(&rb_theta); // Attach output 1 theta
    attach_output_theta(&rb_theta); // Attach output 2 theta
    attach_output_theta(&rb_theta); // Attach output 3 theta
  }

  // The RBTheta member variables
  ThetaA0 theta_a_0;
  ThetaA1 theta_a_1;
  ThetaA2 theta_a_2;
  RBTheta rb_theta; // Default RBTheta object, just returns 1.
};

// Define an RBAssemblyExpansion class for this PDE
struct Ex02RBAssemblyExpansion : RBAssemblyExpansion
{

  Ex02RBAssemblyExpansion()
    :
    L0(0.72, 0.88, 0.72, 0.88), // We make sure these output regions conform to the mesh
    L1(0.12, 0.28, 0.72, 0.88),
    L2(0.12, 0.28, 0.12, 0.28),
    L3(0.72, 0.88, 0.12, 0.28)
  {
    // And set up the RBAssemblyExpansion object
    attach_A_assembly(&A0_assembly); // Attach the lhs assembly
    attach_A_assembly(&A1_assembly);
    attach_A_assembly(&A2_assembly);

    attach_F_assembly(&F0_assembly); // Attach the rhs assembly

    attach_output_assembly(&L0);       // Attach output 0 assembly
    attach_output_assembly(&L1);       // Attach output 1 assembly
    attach_output_assembly(&L2);       // Attach output 2 assembly
    attach_output_assembly(&L3);       // Attach output 3 assembly
  }

  // The ElemAssembly objects
  B B_assembly;
  A0 A0_assembly;
  A1 A1_assembly;
  A2 A2_assembly;
  F0 F0_assembly;
  OutputAssembly L0;
  OutputAssembly L1;
  OutputAssembly L2;
  OutputAssembly L3;
};

#endif // LIBMESH_HAVE_SLEPC && LIBMESH_HAVE_GLPK

#endif