void
MaxQpsThread::operator() (const ConstElemRange & range)
{
ParallelUniqueId puid;
_tid = puid.id;
// For short circuiting reinit
std::set<ElemType> seen_it;
for (ConstElemRange::const_iterator elem_it = range.begin() ; elem_it != range.end(); ++elem_it)
{
const Elem * elem = *elem_it;
// Only reinit if the element type has not previously been seen
if (seen_it.insert(elem->type()).second)
{
FEType fe_type(FIRST, LAGRANGE);
unsigned int dim = elem->dim();
unsigned int side = 0; // we assume that any element will have at least one side ;)
// We cannot mess with the FE objects in Assembly, because we might need to request second derivatives
// later on. If we used them, we'd call reinit on them, thus making the call to request second
// derivatives harmful (i.e. leading to segfaults/asserts). Thus, we have to use a locally allocated object here.
FEBase * fe = FEBase::build(dim, fe_type).release();
// figure out the number of qps for volume
QBase * qrule = QBase::build(_qtype, dim, _order).release();
fe->attach_quadrature_rule(qrule);
fe->reinit(elem);
if (qrule->n_points() > _max)
_max = qrule->n_points();
delete qrule;
// figure out the number of qps for the face
// NOTE: user might specify higher order rule for faces, thus possibly ending up with more qps than in the volume
QBase * qrule_face = QBase::build(_qtype, dim - 1, _face_order).release();
fe->attach_quadrature_rule(qrule_face);
fe->reinit(elem, side);
if (qrule_face->n_points() > _max)
_max = qrule_face->n_points();
delete qrule_face;
delete fe;
}
}
}
// This function assembles the system matrix and right-hand-side
// for the discrete form of our wave equation.
void assemble_wave(EquationSystems & es,
const std::string & system_name)
{
// It is a good idea to make sure we are assembling
// the proper system.
libmesh_assert_equal_to (system_name, "Wave");
#ifdef LIBMESH_ENABLE_INFINITE_ELEMENTS
// Get a constant reference to the mesh object.
const MeshBase & mesh = es.get_mesh();
// Get a reference to the system we are solving.
LinearImplicitSystem & system = es.get_system<LinearImplicitSystem>("Wave");
// A reference to the \p DofMap object for this system. The \p DofMap
// object handles the index translation from node and element numbers
// to degree of freedom numbers.
const DofMap & dof_map = system.get_dof_map();
// The dimension that we are running.
const unsigned int dim = mesh.mesh_dimension();
// Copy the speed of sound to a local variable.
const Real speed = es.parameters.get<Real>("speed");
// Get a constant reference to the Finite Element type
// for the first (and only) variable in the system.
const FEType & fe_type = dof_map.variable_type(0);
// Build a Finite Element object of the specified type. Since the
// \p FEBase::build() member dynamically creates memory we will
// store the object as an \p UniquePtr<FEBase>. Check ex5 for details.
UniquePtr<FEBase> fe (FEBase::build(dim, fe_type));
// Do the same for an infinite element.
UniquePtr<FEBase> inf_fe (FEBase::build_InfFE(dim, fe_type));
// A 2nd order Gauss quadrature rule for numerical integration.
QGauss qrule (dim, SECOND);
// Tell the finite element object to use our quadrature rule.
fe->attach_quadrature_rule (&qrule);
// Due to its internal structure, the infinite element handles
// quadrature rules differently. It takes the quadrature
// rule which has been initialized for the FE object, but
// creates suitable quadrature rules by @e itself. The user
// need not worry about this.
inf_fe->attach_quadrature_rule (&qrule);
// Define data structures to contain the element matrix
// and right-hand-side vector contribution. Following
// basic finite element terminology we will denote these
// "Ke", "Ce", "Me", and "Fe" for the stiffness, damping
// and mass matrices, and the load vector. Note that in
// Acoustics, these descriptors though do @e not match the
// true physical meaning of the projectors. The final
// overall system, however, resembles the conventional
// notation again.
DenseMatrix<Number> Ke;
DenseMatrix<Number> Ce;
DenseMatrix<Number> Me;
DenseVector<Number> Fe;
// This vector will hold the degree of freedom indices for
// the element. These define where in the global system
// the element degrees of freedom get mapped.
std::vector<dof_id_type> dof_indices;
// Now we will loop over all the elements in the mesh.
// We will compute the element matrix and right-hand-side
// contribution.
MeshBase::const_element_iterator el = mesh.active_local_elements_begin();
const MeshBase::const_element_iterator end_el = mesh.active_local_elements_end();
for ( ; el != end_el; ++el)
{
// Store a pointer to the element we are currently
// working on. This allows for nicer syntax later.
const Elem * elem = *el;
// Get the degree of freedom indices for the
// current element. These define where in the global
// matrix and right-hand-side this element will
// contribute to.
dof_map.dof_indices (elem, dof_indices);
// The mesh contains both finite and infinite elements. These
// elements are handled through different classes, namely
// \p FE and \p InfFE, respectively. However, since both
// are derived from \p FEBase, they share the same interface,
// and overall burden of coding is @e greatly reduced through
// using a pointer, which is adjusted appropriately to the
// current element type.
FEBase * cfe = libmesh_nullptr;
// This here is almost the only place where we need to
// distinguish between finite and infinite elements.
// For faster computation, however, different approaches
// may be feasible.
//
// Up to now, we do not know what kind of element we
// have. Aske the element of what type it is:
if (elem->infinite())
{
// We have an infinite element. Let \p cfe point
// to our \p InfFE object. This is handled through
// an UniquePtr. Through the \p UniquePtr::get() we "borrow"
// the pointer, while the \p UniquePtr \p inf_fe is
// still in charge of memory management.
cfe = inf_fe.get();
}
else
{
// This is a conventional finite element. Let \p fe handle it.
cfe = fe.get();
// Boundary conditions.
// Here we just zero the rhs-vector. For natural boundary
// conditions check e.g. previous examples.
{
// Zero the RHS for this element.
Fe.resize (dof_indices.size());
system.rhs->add_vector (Fe, dof_indices);
} // end boundary condition section
} // else if (elem->infinite())
// This is slightly different from the Poisson solver:
// Since the finite element object may change, we have to
// initialize the constant references to the data fields
// each time again, when a new element is processed.
//
// The element Jacobian * quadrature weight at each integration point.
const std::vector<Real> & JxW = cfe->get_JxW();
// The element shape functions evaluated at the quadrature points.
const std::vector<std::vector<Real> > & phi = cfe->get_phi();
// The element shape function gradients evaluated at the quadrature
// points.
const std::vector<std::vector<RealGradient> > & dphi = cfe->get_dphi();
// The infinite elements need more data fields than conventional FE.
// These are the gradients of the phase term \p dphase, an additional
// radial weight for the test functions \p Sobolev_weight, and its
// gradient.
//
// Note that these data fields are also initialized appropriately by
// the \p FE method, so that the weak form (below) is valid for @e both
// finite and infinite elements.
const std::vector<RealGradient> & dphase = cfe->get_dphase();
const std::vector<Real> & weight = cfe->get_Sobolev_weight();
const std::vector<RealGradient> & dweight = cfe->get_Sobolev_dweight();
// Now this is all independent of whether we use an \p FE
// or an \p InfFE. Nice, hm? ;-)
//
// Compute the element-specific data, as described
// in previous examples.
cfe->reinit (elem);
// Zero the element matrices. Boundary conditions were already
// processed in the \p FE-only section, see above.
Ke.resize (dof_indices.size(), dof_indices.size());
Ce.resize (dof_indices.size(), dof_indices.size());
Me.resize (dof_indices.size(), dof_indices.size());
// The total number of quadrature points for infinite elements
// @e has to be determined in a different way, compared to
// conventional finite elements. This type of access is also
// valid for finite elements, so this can safely be used
// anytime, instead of asking the quadrature rule, as
// seen in previous examples.
unsigned int max_qp = cfe->n_quadrature_points();
// Loop over the quadrature points.
for (unsigned int qp=0; qp<max_qp; qp++)
{
// Similar to the modified access to the number of quadrature
// points, the number of shape functions may also be obtained
// in a different manner. This offers the great advantage
// of being valid for both finite and infinite elements.
const unsigned int n_sf = cfe->n_shape_functions();
// Now we will build the element matrices. Since the infinite
// elements are based on a Petrov-Galerkin scheme, the
// resulting system matrices are non-symmetric. The additional
// weight, described before, is part of the trial space.
//
// For the finite elements, though, these matrices are symmetric
// just as we know them, since the additional fields \p dphase,
// \p weight, and \p dweight are initialized appropriately.
//
// test functions: weight[qp]*phi[i][qp]
// trial functions: phi[j][qp]
// phase term: phase[qp]
//
// derivatives are similar, but note that these are of type
// Point, not of type Real.
for (unsigned int i=0; i<n_sf; i++)
for (unsigned int j=0; j<n_sf; j++)
{
// (ndt*Ht + nHt*d) * nH
Ke(i,j) +=
(
(dweight[qp] * phi[i][qp] // Point * Real = Point
+ // +
dphi[i][qp] * weight[qp] // Point * Real = Point
) * dphi[j][qp]
) * JxW[qp];
// (d*Ht*nmut*nH - ndt*nmu*Ht*H - d*nHt*nmu*H)
Ce(i,j) +=
(
(dphase[qp] * dphi[j][qp]) // (Point * Point) = Real
* weight[qp] * phi[i][qp] // * Real * Real = Real
- // -
(dweight[qp] * dphase[qp]) // (Point * Point) = Real
* phi[i][qp] * phi[j][qp] // * Real * Real = Real
- // -
(dphi[i][qp] * dphase[qp]) // (Point * Point) = Real
* weight[qp] * phi[j][qp] // * Real * Real = Real
) * JxW[qp];
// (d*Ht*H * (1 - nmut*nmu))
Me(i,j) +=
(
(1. - (dphase[qp] * dphase[qp])) // (Real - (Point * Point)) = Real
* phi[i][qp] * phi[j][qp] * weight[qp] // * Real * Real * Real = Real
) * JxW[qp];
} // end of the matrix summation loop
} // end of quadrature point loop
// The element matrices are now built for this element.
// Collect them in Ke, and then add them to the global matrix.
// The \p SparseMatrix::add_matrix() member does this for us.
Ke.add(1./speed , Ce);
Ke.add(1./(speed*speed), Me);
// If this assembly program were to be used on an adaptive mesh,
// we would have to apply any hanging node constraint equations
dof_map.constrain_element_matrix(Ke, dof_indices);
system.matrix->add_matrix (Ke, dof_indices);
} // end of element loop
// Note that we have not applied any boundary conditions so far.
// Here we apply a unit load at the node located at (0,0,0).
{
// Iterate over local nodes
MeshBase::const_node_iterator nd = mesh.local_nodes_begin();
const MeshBase::const_node_iterator nd_end = mesh.local_nodes_end();
for (; nd != nd_end; ++nd)
{
// Get a reference to the current node.
const Node & node = **nd;
// Check the location of the current node.
if (std::abs(node(0)) < TOLERANCE &&
std::abs(node(1)) < TOLERANCE &&
std::abs(node(2)) < TOLERANCE)
{
// The global number of the respective degree of freedom.
unsigned int dn = node.dof_number(0,0,0);
system.rhs->add (dn, 1.);
}
}
}
#else
// dummy assert
libmesh_assert_not_equal_to (es.get_mesh().mesh_dimension(), 1);
#endif //ifdef LIBMESH_ENABLE_INFINITE_ELEMENTS
}
void
Assembly::reinitFE(const Elem * elem)
{
unsigned int dim = elem->dim();
std::map<FEType, FEBase *>::iterator it = _fe[dim].begin();
std::map<FEType, FEBase *>::iterator end = _fe[dim].end();
ElementFEShapeData * efesd = NULL;
// Whether or not we're going to do FE caching this time through
bool do_caching = _should_use_fe_cache && _currently_fe_caching;
if (do_caching)
{
efesd = _element_fe_shape_data_cache[elem->id()];
if (!efesd)
{
efesd = new ElementFEShapeData;
_element_fe_shape_data_cache[elem->id()] = efesd;
efesd->_invalidated = true;
}
}
for (; it != end; ++it)
{
FEBase * fe = it->second;
const FEType & fe_type = it->first;
_current_fe[fe_type] = fe;
FEShapeData * fesd = _fe_shape_data[fe_type];
FEShapeData * cached_fesd = NULL;
if (do_caching)
cached_fesd = efesd->_shape_data[fe_type];
if (!cached_fesd || efesd->_invalidated)
{
fe->reinit(elem);
fesd->_phi.shallowCopy(const_cast<std::vector<std::vector<Real> > &>(fe->get_phi()));
fesd->_grad_phi.shallowCopy(const_cast<std::vector<std::vector<RealGradient> > &>(fe->get_dphi()));
if (_need_second_derivative[fe_type])
fesd->_second_phi.shallowCopy(const_cast<std::vector<std::vector<RealTensor> > &>(fe->get_d2phi()));
if (do_caching)
{
if (!cached_fesd)
{
cached_fesd = new FEShapeData;
efesd->_shape_data[fe_type] = cached_fesd;
}
*cached_fesd = *fesd;
}
}
else // This means we have valid cached shape function values for this element / fe_type combo
{
fesd->_phi.shallowCopy(cached_fesd->_phi);
fesd->_grad_phi.shallowCopy(cached_fesd->_grad_phi);
if (_need_second_derivative[fe_type])
fesd->_second_phi.shallowCopy(cached_fesd->_second_phi);
}
}
// During that last loop the helper objects will have been reinitialized as well
// We need to dig out the q_points and JxW from it.
if (!do_caching || efesd->_invalidated)
{
_current_q_points.shallowCopy(const_cast<std::vector<Point> &>((*_holder_fe_helper[dim])->get_xyz()));
_current_JxW.shallowCopy(const_cast<std::vector<Real> &>((*_holder_fe_helper[dim])->get_JxW()));
if (do_caching)
{
efesd->_q_points = _current_q_points;
efesd->_JxW = _current_JxW;
}
}
else // Use cached values
{
_current_q_points.shallowCopy(efesd->_q_points);
_current_JxW.shallowCopy(efesd->_JxW);
}
if (do_caching)
efesd->_invalidated = false;
}