void
InitialCondition::compute()
{
// -- NOTE ----
// The following code is a copy from libMesh project_vector.C plus it adds some features, so we can couple variable values
// and we also do not call any callbacks, but we use our initial condition system directly.
// ------------
// The element matrix and RHS for projections.
// Note that Ke is always real-valued, whereas Fe may be complex valued if complex number support is enabled
DenseMatrix<Real> Ke;
DenseVector<Number> Fe;
// The new element coefficients
DenseVector<Number> Ue;
const FEType & fe_type = _var.feType();
// The dimension of the current element
const unsigned int dim = _current_elem->dim();
// The element type
const ElemType elem_type = _current_elem->type();
// The number of nodes on the new element
const unsigned int n_nodes = _current_elem->n_nodes();
// The global DOF indices
std::vector<dof_id_type> dof_indices;
// Side/edge DOF indices
std::vector<unsigned int> side_dofs;
// Get FE objects of the appropriate type
// We cannot use the FE object in Assembly, since the following code is messing with the quadrature rules
// for projections and would screw it up. However, if we implement projections from one mesh to another,
// this code should use that implementation.
UniquePtr<FEBase> fe (FEBase::build(dim, fe_type));
// Prepare variables for projection
UniquePtr<QBase> qrule (fe_type.default_quadrature_rule(dim));
UniquePtr<QBase> qedgerule (fe_type.default_quadrature_rule(1));
UniquePtr<QBase> qsiderule (fe_type.default_quadrature_rule(dim-1));
// The values of the shape functions at the quadrature points
const std::vector<std::vector<Real> > & phi = fe->get_phi();
// The gradients of the shape functions at the quadrature points on the child element.
const std::vector<std::vector<RealGradient> > * dphi = NULL;
const FEContinuity cont = fe->get_continuity();
if (cont == C_ONE)
{
const std::vector<std::vector<RealGradient> > & ref_dphi = fe->get_dphi();
dphi = &ref_dphi;
}
// The Jacobian * quadrature weight at the quadrature points
const std::vector<Real> & JxW = fe->get_JxW();
// The XYZ locations of the quadrature points
const std::vector<Point>& xyz_values = fe->get_xyz();
// Update the DOF indices for this element based on the current mesh
_var.prepareIC();
dof_indices = _var.dofIndices();
// The number of DOFs on the element
const unsigned int n_dofs = dof_indices.size();
if (n_dofs == 0)
return;
// Fixed vs. free DoFs on edge/face projections
std::vector<char> dof_is_fixed(n_dofs, false); // bools
std::vector<int> free_dof(n_dofs, 0);
// Zero the interpolated values
Ue.resize (n_dofs);
Ue.zero();
// In general, we need a series of
// projections to ensure a unique and continuous
// solution. We start by interpolating nodes, then
// hold those fixed and project edges, then
// hold those fixed and project faces, then
// hold those fixed and project interiors
_fe_problem.sizeZeroes(n_nodes, _tid);
// Interpolate node values first
unsigned int current_dof = 0;
for (unsigned int n = 0; n != n_nodes; ++n)
{
// FIXME: this should go through the DofMap,
// not duplicate dof_indices code badly!
const unsigned int nc = FEInterface::n_dofs_at_node (dim, fe_type, elem_type, n);
if (!_current_elem->is_vertex(n))
{
current_dof += nc;
continue;
}
if (cont == DISCONTINUOUS)
{
libmesh_assert(nc == 0);
}
// Assume that C_ZERO elements have a single nodal
// value shape function
else if (cont == C_ZERO)
{
libmesh_assert(nc == 1);
_qp = n;
_current_node = _current_elem->get_node(n);
Ue(current_dof) = value(*_current_node);
dof_is_fixed[current_dof] = true;
current_dof++;
}
// The hermite element vertex shape functions are weird
else if (fe_type.family == HERMITE)
{
_qp = n;
_current_node = _current_elem->get_node(n);
Ue(current_dof) = value(*_current_node);
dof_is_fixed[current_dof] = true;
current_dof++;
Gradient grad = gradient(*_current_node);
// x derivative
Ue(current_dof) = grad(0);
dof_is_fixed[current_dof] = true;
current_dof++;
if (dim > 1)
{
// We'll finite difference mixed derivatives
Point nxminus = _current_elem->point(n),
nxplus = _current_elem->point(n);
nxminus(0) -= TOLERANCE;
nxplus(0) += TOLERANCE;
Gradient gxminus = gradient(nxminus);
Gradient gxplus = gradient(nxplus);
// y derivative
Ue(current_dof) = grad(1);
dof_is_fixed[current_dof] = true;
current_dof++;
// xy derivative
Ue(current_dof) = (gxplus(1) - gxminus(1)) / 2. / TOLERANCE;
dof_is_fixed[current_dof] = true;
current_dof++;
if (dim > 2)
{
// z derivative
Ue(current_dof) = grad(2);
dof_is_fixed[current_dof] = true;
current_dof++;
// xz derivative
Ue(current_dof) = (gxplus(2) - gxminus(2)) / 2. / TOLERANCE;
dof_is_fixed[current_dof] = true;
current_dof++;
// We need new points for yz
Point nyminus = _current_elem->point(n),
nyplus = _current_elem->point(n);
nyminus(1) -= TOLERANCE;
nyplus(1) += TOLERANCE;
Gradient gyminus = gradient(nyminus);
Gradient gyplus = gradient(nyplus);
// xz derivative
Ue(current_dof) = (gyplus(2) - gyminus(2)) / 2. / TOLERANCE;
dof_is_fixed[current_dof] = true;
current_dof++;
// Getting a 2nd order xyz is more tedious
Point nxmym = _current_elem->point(n),
nxmyp = _current_elem->point(n),
nxpym = _current_elem->point(n),
nxpyp = _current_elem->point(n);
nxmym(0) -= TOLERANCE;
nxmym(1) -= TOLERANCE;
nxmyp(0) -= TOLERANCE;
nxmyp(1) += TOLERANCE;
nxpym(0) += TOLERANCE;
nxpym(1) -= TOLERANCE;
nxpyp(0) += TOLERANCE;
nxpyp(1) += TOLERANCE;
Gradient gxmym = gradient(nxmym);
Gradient gxmyp = gradient(nxmyp);
Gradient gxpym = gradient(nxpym);
Gradient gxpyp = gradient(nxpyp);
Number gxzplus = (gxpyp(2) - gxmyp(2)) / 2. / TOLERANCE;
Number gxzminus = (gxpym(2) - gxmym(2)) / 2. / TOLERANCE;
// xyz derivative
Ue(current_dof) = (gxzplus - gxzminus) / 2. / TOLERANCE;
dof_is_fixed[current_dof] = true;
current_dof++;
}
}
}
// Assume that other C_ONE elements have a single nodal
// value shape function and nodal gradient component
// shape functions
else if (cont == C_ONE)
{
libmesh_assert(nc == 1 + dim);
_current_node = _current_elem->get_node(n);
Ue(current_dof) = value(*_current_node);
dof_is_fixed[current_dof] = true;
current_dof++;
Gradient grad = gradient(*_current_node);
for (unsigned int i=0; i != dim; ++i)
{
Ue(current_dof) = grad(i);
dof_is_fixed[current_dof] = true;
current_dof++;
}
}
else
libmesh_error();
} // loop over nodes
// From here on out we won't be sampling at nodes anymore
_current_node = NULL;
// In 3D, project any edge values next
if (dim > 2 && cont != DISCONTINUOUS)
for (unsigned int e=0; e != _current_elem->n_edges(); ++e)
{
FEInterface::dofs_on_edge(_current_elem, dim, fe_type, e, side_dofs);
// Some edge dofs are on nodes and already
// fixed, others are free to calculate
unsigned int free_dofs = 0;
for (unsigned int i=0; i != side_dofs.size(); ++i)
if (!dof_is_fixed[side_dofs[i]])
free_dof[free_dofs++] = i;
// There may be nothing to project
if (!free_dofs)
continue;
Ke.resize (free_dofs, free_dofs); Ke.zero();
Fe.resize (free_dofs); Fe.zero();
// The new edge coefficients
DenseVector<Number> Uedge(free_dofs);
// Initialize FE data on the edge
fe->attach_quadrature_rule (qedgerule.get());
fe->edge_reinit (_current_elem, e);
const unsigned int n_qp = qedgerule->n_points();
_fe_problem.sizeZeroes(n_qp, _tid);
// Loop over the quadrature points
for (unsigned int qp = 0; qp < n_qp; qp++)
{
// solution at the quadrature point
Number fineval = value(xyz_values[qp]);
// solution grad at the quadrature point
Gradient finegrad;
if (cont == C_ONE)
finegrad = gradient(xyz_values[qp]);
// Form edge projection matrix
for (unsigned int sidei = 0, freei = 0; sidei != side_dofs.size(); ++sidei)
{
unsigned int i = side_dofs[sidei];
// fixed DoFs aren't test functions
if (dof_is_fixed[i])
continue;
for (unsigned int sidej = 0, freej = 0; sidej != side_dofs.size(); ++sidej)
{
unsigned int j = side_dofs[sidej];
if (dof_is_fixed[j])
Fe(freei) -= phi[i][qp] * phi[j][qp] * JxW[qp] * Ue(j);
else
Ke(freei,freej) += phi[i][qp] * phi[j][qp] * JxW[qp];
if (cont == C_ONE)
{
if (dof_is_fixed[j])
Fe(freei) -= ((*dphi)[i][qp] * (*dphi)[j][qp]) * JxW[qp] * Ue(j);
else
Ke(freei,freej) += ((*dphi)[i][qp] * (*dphi)[j][qp]) * JxW[qp];
}
if (!dof_is_fixed[j])
freej++;
}
Fe(freei) += phi[i][qp] * fineval * JxW[qp];
if (cont == C_ONE)
Fe(freei) += (finegrad * (*dphi)[i][qp]) * JxW[qp];
freei++;
}
}
Ke.cholesky_solve(Fe, Uedge);
// Transfer new edge solutions to element
for (unsigned int i=0; i != free_dofs; ++i)
{
Number &ui = Ue(side_dofs[free_dof[i]]);
libmesh_assert(std::abs(ui) < TOLERANCE || std::abs(ui - Uedge(i)) < TOLERANCE);
ui = Uedge(i);
dof_is_fixed[side_dofs[free_dof[i]]] = true;
}
}
// Project any side values (edges in 2D, faces in 3D)
if (dim > 1 && cont != DISCONTINUOUS)
for (unsigned int s=0; s != _current_elem->n_sides(); ++s)
{
FEInterface::dofs_on_side(_current_elem, dim, fe_type, s, side_dofs);
// Some side dofs are on nodes/edges and already
// fixed, others are free to calculate
unsigned int free_dofs = 0;
for (unsigned int i=0; i != side_dofs.size(); ++i)
if (!dof_is_fixed[side_dofs[i]])
free_dof[free_dofs++] = i;
// There may be nothing to project
if (!free_dofs)
continue;
Ke.resize (free_dofs, free_dofs); Ke.zero();
Fe.resize (free_dofs); Fe.zero();
// The new side coefficients
DenseVector<Number> Uside(free_dofs);
// Initialize FE data on the side
fe->attach_quadrature_rule (qsiderule.get());
fe->reinit (_current_elem, s);
const unsigned int n_qp = qsiderule->n_points();
_fe_problem.sizeZeroes(n_qp, _tid);
// Loop over the quadrature points
for (unsigned int qp = 0; qp < n_qp; qp++)
{
// solution at the quadrature point
Number fineval = value(xyz_values[qp]);
// solution grad at the quadrature point
Gradient finegrad;
if (cont == C_ONE)
finegrad = gradient(xyz_values[qp]);
// Form side projection matrix
for (unsigned int sidei = 0, freei = 0; sidei != side_dofs.size(); ++sidei)
{
unsigned int i = side_dofs[sidei];
// fixed DoFs aren't test functions
if (dof_is_fixed[i])
continue;
for (unsigned int sidej = 0, freej = 0; sidej != side_dofs.size(); ++sidej)
{
unsigned int j = side_dofs[sidej];
if (dof_is_fixed[j])
Fe(freei) -= phi[i][qp] * phi[j][qp] * JxW[qp] * Ue(j);
else
Ke(freei,freej) += phi[i][qp] * phi[j][qp] * JxW[qp];
if (cont == C_ONE)
{
if (dof_is_fixed[j])
Fe(freei) -= ((*dphi)[i][qp] * (*dphi)[j][qp]) * JxW[qp] * Ue(j);
else
Ke(freei,freej) += ((*dphi)[i][qp] * (*dphi)[j][qp]) * JxW[qp];
}
if (!dof_is_fixed[j])
freej++;
}
Fe(freei) += (fineval * phi[i][qp]) * JxW[qp];
if (cont == C_ONE)
Fe(freei) += (finegrad * (*dphi)[i][qp]) * JxW[qp];
freei++;
}
}
Ke.cholesky_solve(Fe, Uside);
// Transfer new side solutions to element
for (unsigned int i=0; i != free_dofs; ++i)
{
Number &ui = Ue(side_dofs[free_dof[i]]);
libmesh_assert(std::abs(ui) < TOLERANCE || std::abs(ui - Uside(i)) < TOLERANCE);
ui = Uside(i);
dof_is_fixed[side_dofs[free_dof[i]]] = true;
}
}
// Project the interior values, finally
// Some interior dofs are on nodes/edges/sides and
// already fixed, others are free to calculate
unsigned int free_dofs = 0;
for (unsigned int i=0; i != n_dofs; ++i)
if (!dof_is_fixed[i])
free_dof[free_dofs++] = i;
// There may be nothing to project
if (free_dofs)
{
Ke.resize (free_dofs, free_dofs); Ke.zero();
Fe.resize (free_dofs); Fe.zero();
// The new interior coefficients
DenseVector<Number> Uint(free_dofs);
// Initialize FE data
fe->attach_quadrature_rule (qrule.get());
fe->reinit (_current_elem);
const unsigned int n_qp = qrule->n_points();
_fe_problem.sizeZeroes(n_qp, _tid);
// Loop over the quadrature points
for (unsigned int qp=0; qp<n_qp; qp++)
{
// solution at the quadrature point
Number fineval = value(xyz_values[qp]);
// solution grad at the quadrature point
Gradient finegrad;
if (cont == C_ONE)
finegrad = gradient(xyz_values[qp]);
// Form interior projection matrix
for (unsigned int i=0, freei=0; i != n_dofs; ++i)
{
// fixed DoFs aren't test functions
if (dof_is_fixed[i])
continue;
for (unsigned int j=0, freej=0; j != n_dofs; ++j)
{
if (dof_is_fixed[j])
Fe(freei) -= phi[i][qp] * phi[j][qp] * JxW[qp] * Ue(j);
else
Ke(freei,freej) += phi[i][qp] * phi[j][qp] * JxW[qp];
if (cont == C_ONE)
{
if (dof_is_fixed[j])
Fe(freei) -= ((*dphi)[i][qp] * (*dphi)[j][qp]) * JxW[qp] * Ue(j);
else
Ke(freei,freej) += ((*dphi)[i][qp] * (*dphi)[j][qp]) * JxW[qp];
}
if (!dof_is_fixed[j])
freej++;
}
Fe(freei) += phi[i][qp] * fineval * JxW[qp];
if (cont == C_ONE)
Fe(freei) += (finegrad * (*dphi)[i][qp]) * JxW[qp];
freei++;
}
}
Ke.cholesky_solve(Fe, Uint);
// Transfer new interior solutions to element
for (unsigned int i=0; i != free_dofs; ++i)
{
Number &ui = Ue(free_dof[i]);
libmesh_assert(std::abs(ui) < TOLERANCE || std::abs(ui - Uint(i)) < TOLERANCE);
ui = Uint(i);
dof_is_fixed[free_dof[i]] = true;
}
} // if there are free interior dofs
// Make sure every DoF got reached!
for (unsigned int i=0; i != n_dofs; ++i)
libmesh_assert(dof_is_fixed[i]);
NumericVector<Number> & solution = _var.sys().solution();
// 'first' and 'last' are no longer used, see note about subdomain-restricted variables below
// const dof_id_type
// first = solution.first_local_index(),
// last = solution.last_local_index();
// Lock the new_vector since it is shared among threads.
{
Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
for (unsigned int i = 0; i < n_dofs; i++)
// We may be projecting a new zero value onto
// an old nonzero approximation - RHS
// if (Ue(i) != 0.)
// This is commented out because of subdomain restricted variables.
// It can be the case that if a subdomain restricted variable's boundary
// aligns perfectly with a processor boundary that the variable will get
// no value. To counteract this we're going to let every processor set a
// value at every node and then let PETSc figure it out.
// Later we can choose to do something different / better.
// if ((dof_indices[i] >= first) && (dof_indices[i] < last))
{
solution.set(dof_indices[i], Ue(i));
if (cont == C_ZERO)
_var.setNodalValue(Ue(i), i);
}
}
}
void
InitialConditionTempl<T>::setHermiteVertices()
{
// The hermite element vertex shape functions are weird
_qp = _n;
_current_node = _current_elem->node_ptr(_n);
_Ue(_current_dof) = value(*_current_node);
_dof_is_fixed[_current_dof] = true;
_current_dof++;
Gradient grad = gradient(*_current_node);
// x derivative
_Ue(_current_dof) = grad(0);
_dof_is_fixed[_current_dof] = true;
_current_dof++;
if (_dim > 1)
{
// We'll finite difference mixed derivatives
Point nxminus = _current_elem->point(_n), nxplus = _current_elem->point(_n);
nxminus(0) -= TOLERANCE;
nxplus(0) += TOLERANCE;
Gradient gxminus = gradient(nxminus);
Gradient gxplus = gradient(nxplus);
// y derivative
_Ue(_current_dof) = grad(1);
_dof_is_fixed[_current_dof] = true;
_current_dof++;
// xy derivative
_Ue(_current_dof) = (gxplus(1) - gxminus(1)) / 2. / TOLERANCE;
_dof_is_fixed[_current_dof] = true;
_current_dof++;
if (_dim > 2)
{
// z derivative
_Ue(_current_dof) = grad(2);
_dof_is_fixed[_current_dof] = true;
_current_dof++;
// xz derivative
_Ue(_current_dof) = (gxplus(2) - gxminus(2)) / 2. / TOLERANCE;
_dof_is_fixed[_current_dof] = true;
_current_dof++;
// We need new points for yz
Point nyminus = _current_elem->point(_n), nyplus = _current_elem->point(_n);
nyminus(1) -= TOLERANCE;
nyplus(1) += TOLERANCE;
Gradient gyminus = gradient(nyminus);
Gradient gyplus = gradient(nyplus);
// xz derivative
_Ue(_current_dof) = (gyplus(2) - gyminus(2)) / 2. / TOLERANCE;
_dof_is_fixed[_current_dof] = true;
_current_dof++;
// Getting a 2nd order xyz is more tedious
Point nxmym = _current_elem->point(_n), nxmyp = _current_elem->point(_n),
nxpym = _current_elem->point(_n), nxpyp = _current_elem->point(_n);
nxmym(0) -= TOLERANCE;
nxmym(1) -= TOLERANCE;
nxmyp(0) -= TOLERANCE;
nxmyp(1) += TOLERANCE;
nxpym(0) += TOLERANCE;
nxpym(1) -= TOLERANCE;
nxpyp(0) += TOLERANCE;
nxpyp(1) += TOLERANCE;
Gradient gxmym = gradient(nxmym);
Gradient gxmyp = gradient(nxmyp);
Gradient gxpym = gradient(nxpym);
Gradient gxpyp = gradient(nxpyp);
Number gxzplus = (gxpyp(2) - gxmyp(2)) / 2. / TOLERANCE;
Number gxzminus = (gxpym(2) - gxmym(2)) / 2. / TOLERANCE;
// xyz derivative
_Ue(_current_dof) = (gxzplus - gxzminus) / 2. / TOLERANCE;
_dof_is_fixed[_current_dof] = true;
_current_dof++;
}
}
}