distance_function.C

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// GRINS - General Reacting Incompressible Navier-Stokes
//
// Copyright (C) 2014 Paul T. Bauman, Roy H. Stogner
// Copyright (C) 2010-2013 The PECOS Development Team

// This program is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public License
// as published by the Free Software Foundation; either version 2.1
// of the License, or (at your option) any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU Lesser General Public License for more details.

// You should have received a copy of the GNU Lesser General Public License
// along with this program; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.

// system
#include <limits>
#include <cmath>

// libmesh
#include "libmesh/libmesh_base.h"
#include "libmesh/libmesh_common.h"
#include "libmesh/mesh_base.h"
#include "libmesh/mesh_output.h" // for MeshSerializer
#include "libmesh/equation_systems.h"
#include "libmesh/explicit_system.h"
#include "libmesh/boundary_mesh.h"
#include "libmesh/node.h"
#include "libmesh/elem.h"
#include "libmesh/enum_order.h"
#include "libmesh/enum_elem_type.h"
#include "libmesh/numeric_vector.h"
#include "libmesh/auto_ptr.h"
#include "libmesh/dense_vector.h"
#include "libmesh/fe_base.h"
#include "libmesh/dof_map.h"
#include "libmesh/point.h"

// local
#include "grins/distance_function.h"


// anonymous namespace for implementation details -
// gives file scope and prevents symbol clashing at link time
// in case there is an e.g. "Line" declared somewhere else too.
namespace
{
  using namespace libMesh;

  //***************************************************
  // A helper data structure. Only used internally.
  //***************************************************
  struct Line
  {
    Point p0;
    Point p1;
  };



  //***************************************************
  // Some helper functions.  Only used internally.
  //***************************************************

  //---------------------------------------------------
  // Project pt onto line.
  //
  // Returns xi, the location of projected point in
  // the reference space of the line.
  //
  template<int dim>
  void ProjectPointToLine( Point pt, Line line, Real& xi )
  {
    libmesh_assert( (dim==2) || (dim==3) );

    Point& p0 = line.p0;
    Point& p1 = line.p1;

    Real dx[dim];
    Real xavg[dim];
    Real length2=0;
    for ( unsigned int ii=0; ii<dim; ii++ ) {
      dx[ii] = p1(ii) - p0(ii);
      length2 += dx[ii]*dx[ii];
      xavg[ii] = 0.5*( p1(ii) + p0(ii) );
    }

    // xi is the point in reference space that minimizes
    // the distance between the point pt and the line
    // defined by the points in the Line struct
    xi = 0.0;
    for ( unsigned int ii=0; ii<dim; ii++ ) {
      xi += 2.0*( pt(ii) - xavg[ii] )*dx[ii];
    }
    xi /= length2;
  }

  //---------------------------------------------------
  // Compute distance from pt to line segment
  //
  template<int dim>
  void
  DistanceToSegment( Point pt, Line line, Real& distance )
  {
    libmesh_assert( (dim==2) || (dim==3) );

    Real xi;
    ProjectPointToLine<dim> (pt, line, xi);

    // if xi is outside edge, bring to nearest node
    if( xi < -1.0 ) xi = -1.0;
    if( xi >  1.0 ) xi =  1.0;

    // interpolate between p0 and p1 to compute location in physical space
    Real xint[dim];
    for ( unsigned int ii=0; ii<dim; ii++ ) {
      xint[ii] = line.p0(ii)*(-0.5*(xi-1.0)) + line.p1(ii)*(0.5*(xi+1.0));
    }

    // compute distance
    distance = 0.0;
    for ( unsigned int ii=0; ii<dim; ii++ ) {
      distance += (pt(ii) - xint[ii])*(pt(ii) - xint[ii]);
    }
    distance = sqrt(distance);

    libmesh_assert( (std::isfinite(distance)) && (distance>=0.0) );
  }

} // end anonymous namespace



namespace GRINS {

  //***************************************************
  // DistanceFunction class functions
  //***************************************************

  //---------------------------------------------------
  // Constructor
  //
  //DistanceFunction::DistanceFunction (EquationSystems& equation_systems, const UnstructuredMesh& boundary_mesh)
  DistanceFunction::DistanceFunction (libMesh::EquationSystems &es_in, const libMesh::UnstructuredMesh &bm_in):
    _equation_systems (es_in),
    _boundary_mesh    (bm_in),
    _dist_fe          (libMesh::FEBase::build(_equation_systems.get_mesh().mesh_dimension(), libMesh::FEType(libMesh::FIRST, libMesh::LAGRANGE)))
  {
    // Ensure that libmesh is ready to roll
    libmesh_assert(libMesh::initialized());

    // Add distance function system
    _equation_systems.add_system<libMesh::System>("distance_function");

    // Get reference to distance function system we just added
    libMesh::System& sys = _equation_systems.get_system<libMesh::System>("distance_function");

    // Add distance function variable
    sys.add_variable("distance", libMesh::FIRST);

    // Attach initialization function
    sys.attach_init_object(*this);

  }

  //---------------------------------------------------
  // Compute distance function
  //
  void DistanceFunction::initialize ()
  {
    // Call the compute function
    this->compute();
    return;
  }


  //---------------------------------------------------
  // Compute distance from input node to boundary_mesh
  //
  libMesh::Real DistanceFunction::node_to_boundary (const libMesh::Node* node)
  {
    // Ensure that node is not NULL
    libmesh_assert( node != NULL );

    // Initialize distance to infinity
    libMesh::Real distance = std::numeric_limits<libMesh::Real>::infinity();

    // Get dimension
    const unsigned int dim = _equation_systems.get_mesh().mesh_dimension();
    libmesh_assert( (dim==2) || (dim==3) );

    // Get coordinates of node
    std::vector<libMesh::Real> xnode(dim);
    for( unsigned int ii=0; ii<dim; ii++ ) xnode[ii] = (*node)(ii);

    // This function will work on a distributed interior mesh, but won't
    // give correct results on a distributed boundary mesh.
    libmesh_assert(_boundary_mesh.is_serial());

    // First loop over the boundary mesh and compute the distance to the
    // nodes.  This will give us an idea of what elements to check more
    // closely.

    libMesh::MeshBase::const_element_iterator       el     = _boundary_mesh.active_elements_begin();
    const libMesh::MeshBase::const_element_iterator end_el = _boundary_mesh.active_elements_end();

    if (el==end_el)
      {
        std::cout << "There are no elements to iterate through!!!  Returning..." << std::endl;
        return distance;
      }

    const libMesh::Elem* elem_containing_min = NULL;
    libMesh::Real dmin = std::numeric_limits<Real>::infinity();

    for ( ; el != end_el; ++el) {

      const libMesh::Elem* belem = *el;

      for (unsigned int bnode=0; bnode<belem->n_nodes(); ++bnode)
        {
          const libMesh::Point& pbndry = belem->point(bnode);

          libMesh::Real dnode = 0.0;
          for (unsigned int idim=0; idim<dim; ++idim)
            dnode += (xnode[idim] - pbndry(idim))*(xnode[idim] - pbndry(idim));

          dnode = std::sqrt(dnode);

          if (dnode<dmin)
            {
              dmin = dnode;
              elem_containing_min = belem;
            }
        }

    } // end element loop

    // grab the elements around the minimum
    std::set<const libMesh::Elem*> near_min_elems;
    elem_containing_min->find_point_neighbors (near_min_elems);

    // insert the element itself into the set... we must check it also
    near_min_elems.insert(elem_containing_min);

    std::set<const libMesh::Elem*>::iterator nm_el;

    // loop over the near_min_elems
    for (nm_el=near_min_elems.begin(); nm_el!=near_min_elems.end(); ++nm_el)
      {

        const libMesh::Elem* belem = *nm_el; //*el;

        // Ensure that elem defined by edge/face is linear
        libmesh_assert( belem->default_order() == FIRST );
        // For now we assume that the boundary_elems are linear, but give a warning
        //libmesh_warning( "Moving ahead, but need to make sure that the boundary elems are linear");

        // Initialize distance to this edge/face to infinity
        libMesh::Real dedge = std::numeric_limits<libMesh::Real>::infinity();

        if ( dim==2 )
          { // 2d

            // For 2d mesh, boundary elems must be 1d.  Due to the way
            // find_point_neighbors works, there may be some 2d elements
            // in the near_min_elems set.  These elements are clearly
            // not part of the boundary mesh, and thus we skip them.
            //
            if (belem->dim()!=1) continue;

            //std::cout<<"Number of nodes: "<<belem->n_nodes()<<std::endl;

            libmesh_assert( belem->n_nodes() == 2 );
            libmesh_assert( belem->type() == EDGE2 );

            // Points defining the edge
            const libMesh::Point& p0 = belem->point(0);
            const libMesh::Point& p1 = belem->point(1);

            Line line;
            line.p0 = p0;
            line.p1 = p1;

            DistanceToSegment<2>(*node, line, dedge);

            if ( dedge < distance ) distance = dedge;

          }
        else
          { // 3d

            // For 3d mesh, boundary elems must be 2d.  Due to the way
            // find_point_neighbors works, there may be some 3d elements
            // in the near_min_elems set.  These elements are clearly
            // not part of the boundary mesh, and thus we skip them.
            //
            if (belem->dim()!=2) continue;

            libmesh_assert( (belem->type() == TRI3) || (belem->type() == QUAD4) );

            if ( belem->type() == TRI3 )
              { // triangular boundary faces

                // Find the point in the plane defined by the boundary nodes that
                // minimizes the distance between the plane and the input node.
                //
                // Done in terms of the reference coordinates of the boundary element.
                //
                const libMesh::Point& p0 = belem->point(0);
                const libMesh::Point& p1 = belem->point(1);
                const libMesh::Point& p2 = belem->point(2);

                const libMesh::Real x_xi = (p1(0) - p0(0)), x_et = (p2(0) - p0(0));
                const libMesh::Real y_xi = (p1(1) - p0(1)), y_et = (p2(1) - p0(1));
                const libMesh::Real z_xi = (p1(2) - p0(2)), z_et = (p2(2) - p0(2));

                libMesh::Real A[2][2], b[2];

                A[0][0] = x_xi*x_xi + y_xi*y_xi + z_xi*z_xi;
                A[0][1] = x_xi*x_et + y_xi*y_et + z_xi*z_et;
                A[1][0] = x_xi*x_et + y_xi*y_et + z_xi*z_et;
                A[1][1] = x_et*x_et + y_et*y_et + z_et*z_et;

                b[0] = (xnode[0] - p0(0))*x_xi + (xnode[1] - p0(1))*y_xi + (xnode[2] - p0(2))*z_xi;
                b[1] = (xnode[0] - p0(0))*x_et + (xnode[1] - p0(1))*y_et + (xnode[2] - p0(2))*z_et;

                const libMesh::Real detA = A[0][0]*A[1][1] - A[1][0]*A[0][1];
                libmesh_assert( fabs(detA) > 0.0 ); // assert that A is not singular

                const libMesh::Real xi = ( A[1][1]*b[0] - A[0][1]*b[1])/detA;
                const libMesh::Real et = (-A[1][0]*b[0] + A[0][0]*b[1])/detA;


                // If projection of node onto plane defined by boundary face
                // (i.e., what we just computed) is not inside boundary face
                // then we need to figure out closest point that is inside the
                // boundary face
                //
                if ( (xi<0.0) || (et<0.0) || (et>1.0-xi) ) {

                  libMesh::Real dtmp = std::numeric_limits<libMesh::Real>::infinity();

                  // for each edge of boundary face, find distance from
                  // input node to the segment defined by that edge
                  //
                  // the minimum of these distances minimizes the distance
                  // to the node over the points in the boundary face
                  //
                  for ( unsigned int iedge=0; iedge<3; iedge++ ){

                    Line line;

                    // Get the endpoints of this edge
                    if      (iedge==0) { line.p0 = p1; line.p1 = p2; }
                    else if (iedge==1) { line.p0 = p0; line.p1 = p2; }
                    else   /*iedge==2*/{ line.p0 = p0; line.p1 = p1; }

                    DistanceToSegment<3>(*node, line, dtmp);

                    if( dtmp < dedge ) dedge = dtmp;

                  }

                } else { // projection is inside face, so we're good to go

                  // Map from reference to physical space
                  libMesh::Real xint[3];
                  for ( unsigned int ii=0; ii<3; ii++ ) {
                    xint[ii] = p0(ii)*(1.0 - xi - et) + p1(ii)*xi + p2(ii)*et;
                  }

                  // compute distance
                  dedge = 0.0;
                  for ( unsigned int ii=0; ii<3; ii++ ) {
                    dedge += (xnode[ii] - xint[ii])*(xnode[ii] - xint[ii]);
                  }
                  dedge = sqrt(dedge);

                }

              }
            else if ( belem->type() == QUAD4 )
              {
                //std::cout << "WARNING: this functionality is not well-tested.  Sorry." << std::endl;

                libMesh::Real RTOL = 1e-10;
                libMesh::Real ATOL = 1e-20;
                const unsigned int ITER_MAX=1000;
                unsigned int iter=0;

                ComputeDistanceResidual res(belem, node);

                ComputeDistanceJacobian jac;

                libMesh::DenseVector<libMesh::Real> X(2); X(0) = X(1) = 0.0;
                libMesh::DenseVector<libMesh::Real> dX(2);
                libMesh::Real det;

                libMesh::DenseVector<libMesh::Real> R(2);
                libMesh::DenseMatrix<libMesh::Real> dRdX(2,2);
                libMesh::DenseMatrix<libMesh::Real> dRdXinv(2,2);

                // evaluate residual... maybe we don't have to iterate
                res(X,R);

                libMesh::Real R0 = R.l2_norm();

                // iterate
                while ( (R.l2_norm() > ATOL) && (R.l2_norm()/R0 > RTOL) && (iter<ITER_MAX) )
                  {
                    // compute jacobian
                    jac(X, R, res, dRdX);

                    // invert jacobian
                    det = dRdX(0,0)*dRdX(1,1) - dRdX(0,1)*dRdX(1,0);

                    // protect against divide by zero
                    if(std::abs(det)<=1e-20)
                      {
                        std::cout << "WARNING: about to divide by zero." << std::endl;
                      }

                    dRdXinv(0,0) =  dRdX(1,1)/det;
                    dRdXinv(0,1) = -dRdX(0,1)/det;
                    dRdXinv(1,0) = -dRdX(1,0)/det;
                    dRdXinv(1,1) =  dRdX(0,0)/det;

                    // compute delta
                    dX(0) = -( dRdXinv(0,0)*R(0) + dRdXinv(0,1)*R(1) );
                    dX(1) = -( dRdXinv(1,0)*R(0) + dRdXinv(1,1)*R(1) );

                    // update
                    X += dX;

                    // if ( std::abs(X(0)) > 1.0 || std::abs(X(1)) > 1.0 )
                    //   {
                    //     std::cout << "WARNING: on iter = " << iter << ", xi is leaving the element!" << std::endl;
                    //   }

                    // recompute Residual
                    res(X,R);

                    // increment counter
                    iter++;
                  }

                // check that we converged
                if (iter==ITER_MAX)
                  {
                    // std::cerr << "Failed to converge distance function!!!" << std::endl;
                    // std::cerr << "Started with ||R|| = " << R0 << std::endl;
                    // std::cerr << "Finished " << iter << " iterations with ||R|| = " << R.l2_norm() << std::endl;
                    // std::cout << "Final location was xi = (" << X(0) << ", " << X(1) << ")." << std::endl;
                    // libmesh_error();

                    std::cout << "WARNING: Failed to converge distance function iteration.  Assuming that min is outside this face.  Use closest distance to edges to proceed." << std::endl;
                  }
                else
                  {
                    //std::cout << "Converged!" << std::endl;
                  }


                if ( std::abs(X(0)) > 1.0 || std::abs(X(1)) > 1.0 )
                  {
                    // converged to point outside the face... so min must
                    // be on edge, and luckily the edges are linear

                    libMesh::Real dtmp = std::numeric_limits<libMesh::Real>::infinity();

                    // for each edge of boundary face, find distance from
                    // input node to the segment defined by that edge
                    //
                    // the minimum of these distances minimizes the distance
                    // to the node over the points in the boundary face
                    //
                    for ( unsigned int iedge=0; iedge<4; iedge++ ){

                      Line line;

                      // Get the endpoints of this edge
                      if      (iedge==0) { line.p0 = belem->point(0); line.p1 = belem->point(1); }
                      else if (iedge==1) { line.p0 = belem->point(1); line.p1 = belem->point(2); }
                      else if (iedge==2) { line.p0 = belem->point(2); line.p1 = belem->point(3); }
                      else   /*iedge==3*/{ line.p0 = belem->point(3); line.p1 = belem->point(0); }

                      DistanceToSegment<3>(*node, line, dtmp);

                      if( dtmp < dedge ) dedge = dtmp;
                    }
                  }
                else
                  {
                    // converged to point inside, so compute point in
                    // physical space and use it to evaluate the distance

                    // assuming first order lagrange basis here
                    libMesh::UniquePtr<libMesh::FEBase> fe( libMesh::FEBase::build(2, libMesh::FEType(libMesh::FIRST, libMesh::LAGRANGE)) );

                    std::vector<libMesh::Point> xi(1);
                    xi[0](0) = X(0);
                    xi[0](1) = X(1);

                    // grab basis functions (evaluated at qpts)
                    const std::vector<std::vector<libMesh::Real> > &basis = fe->get_phi();

                    // reinitialize finite element data at xi
                    fe->reinit(belem, &xi);

                    // interpolate location
                    libMesh::DenseVector<libMesh::Real> xx(3);
                    xx.zero();

                    for (unsigned int inode=0; inode<belem->n_nodes(); ++inode)
                      for (unsigned int idim=0; idim<3; ++idim)
                        xx(idim) += belem->point(inode)(idim) * basis[inode][0];

                    // compute distance
                    dedge = 0.0;
                    for ( unsigned int ii=0; ii<3; ii++ ) {
                      dedge += (xnode[ii] - xx(ii))*(xnode[ii] - xx(ii));
                    }
                    dedge = sqrt(dedge);

                  }

              }
            else
              { // higher-order faces not supported yet
                std::cout << "My type is " << belem->type() << std::endl;
                libmesh_not_implemented();
              }

            if ( dedge < distance ) distance = dedge;

          } // end if(2d)

      } // end loop over elements

    // make sure we are returning valid distance---i.e., 0 <= distance < infinity
    // But this may fail if we try to get the distance on a mesh with no
    // boundary
    //  libmesh_assert( (std::isfinite(distance)) && (distance>=0.0) );

    return distance;
  }


  //---------------------------------------------------
  // Fill distance function data at mesh nodes
  //
  void DistanceFunction::compute ()
  {
    // Get mesh
    const libMesh::MeshBase& mesh = _equation_systems.get_mesh();

    // Get reference to system and system number
    libMesh::System& system = _equation_systems.get_system<libMesh::System>("distance_function");
    const unsigned int sys_num = system.number();

    //Debugging code
    //system.print_info();
    //_equation_systems.print_info();
    //End debugging

    // The boundary mesh needs to all be on this processor for us to
    // calculate a correct distance function.  Since we don't need it to
    // be serial afterwards, we use a temporary serializer.
    {
      libMesh::MeshSerializer serialize(const_cast<libMesh::UnstructuredMesh&>(_boundary_mesh));

      // Loop over nodes in mesh
      libMesh::MeshBase::const_node_iterator node_it  = mesh.local_nodes_begin();
      const libMesh::MeshBase::const_node_iterator node_end = mesh.local_nodes_end();

      //Debugging code
      //const libMesh::Elem *elem = *mesh.elements_begin();
      //if (elem->default_order() == libMesh::FIRST)
      // std::cout<<"Mesh is using FIRST order elements."<<std::endl;
      //End debugging


      for ( ; node_it != node_end; ++node_it) {

        // Grab node
        const libMesh::Node* node = *node_it;

        // Compute distance to nearest point in boundary_mesh
        const libMesh::Real distance = DistanceFunction::node_to_boundary (node);

        // Stuff data into appropriate place in the system solution
        const unsigned int dof = node->dof_number(sys_num,0,0);
        system.solution->set (dof, distance);

      } // end loop over nodes

    } // end boundary mesh serialization

    system.solution->close();
    system.update();

    std::cout << "Distance Function computed." << std::endl;
  }


  //---------------------------------------------------
  // Interpolate nodal data
  //
  libMesh::UniquePtr< libMesh::DenseVector<libMesh::Real> >
  DistanceFunction::interpolate (const libMesh::Elem* elem, const std::vector<libMesh::Point>& qpts) const
  {
    libmesh_assert( elem != NULL );    // can't interpolate in NULL elem
    libmesh_assert( qpts.size() > 0 ); // can't interpolate if no points requested

    // grab basis functions (evaluated at qpts)
    const std::vector<std::vector<libMesh::Real> > &phi = _dist_fe->get_phi();

    // reinitialize finite element data at qpts
    _dist_fe->reinit(elem, &qpts);

    // number of basis functions
    const unsigned int n_dofs = phi.size();

    // number of points
    const unsigned int n_pts = qpts.size();

    // instantiate auto_ptr to dense vector to hold results
    libMesh::UniquePtr< DenseVector<libMesh::Real> > ap( new libMesh::DenseVector<libMesh::Real>(qpts.size()) );
    (*ap).zero();

    // pull off distance function at nodes on this element
    libMesh::System& sys = _equation_systems.get_system<libMesh::System>("distance_function");
    const libMesh::DofMap& dof_map = sys.get_dof_map();

    std::vector<unsigned int> dof_ind;
    dof_map.dof_indices(elem, dof_ind);

    libMesh::DenseVector<libMesh::Real> nodal_dist;
    nodal_dist.resize(n_dofs);
    //dof_map.extract_local_vector( *(sys.solution), dof_ind, nodal_dist);
    dof_map.extract_local_vector( *(sys.current_local_solution), dof_ind, nodal_dist);

    for ( unsigned int idof=0; idof<n_dofs; idof++ ) {
      for ( unsigned int iqpt=0; iqpt<n_pts; iqpt++ ) {
        (*ap)(iqpt) += nodal_dist(idof) * phi[idof][iqpt];
      }
    }

    return ap;
  }


} // end namespace GRINS