bool EulerSolver::element_residual (bool request_jacobian,
DiffContext &context)
{
unsigned int n_dofs = context.get_elem_solution().size();
// Local nonlinear solution at old timestep
DenseVector<Number> old_elem_solution(n_dofs);
for (unsigned int i=0; i != n_dofs; ++i)
old_elem_solution(i) =
old_nonlinear_solution(context.get_dof_indices()[i]);
// Local nonlinear solution at time t_theta
DenseVector<Number> theta_solution(context.get_elem_solution());
theta_solution *= theta;
theta_solution.add(1. - theta, old_elem_solution);
// Technically the elem_solution_derivative is either theta
// or -1.0 in this implementation, but we scale the former part
// ourselves
context.elem_solution_derivative = 1.0;
// Technically the fixed_solution_derivative is always theta,
// but we're scaling a whole jacobian by theta after these first
// evaluations
context.fixed_solution_derivative = 1.0;
// If a fixed solution is requested, we'll use theta_solution
if (_system.use_fixed_solution)
context.get_elem_fixed_solution() = theta_solution;
// Move theta_->elem_, elem_->theta_
context.get_elem_solution().swap(theta_solution);
// Move the mesh into place first if necessary
context.elem_reinit(theta);
// We're going to compute just the change in elem_residual
// (and possibly elem_jacobian), then add back the old values
DenseVector<Number> old_elem_residual(context.get_elem_residual());
DenseMatrix<Number> old_elem_jacobian;
if (request_jacobian)
{
old_elem_jacobian = context.get_elem_jacobian();
context.get_elem_jacobian().zero();
}
context.get_elem_residual().zero();
// Get the time derivative at t_theta
bool jacobian_computed =
_system.element_time_derivative(request_jacobian, context);
// For a moving mesh problem we may need the pseudoconvection term too
jacobian_computed =
_system.eulerian_residual(jacobian_computed, context) && jacobian_computed;
// Scale the time-dependent residual and jacobian correctly
context.get_elem_residual() *= _system.deltat;
if (jacobian_computed)
context.get_elem_jacobian() *= (theta * _system.deltat);
// The fixed_solution_derivative is always theta,
// and now we're done scaling jacobians
context.fixed_solution_derivative = theta;
// We evaluate mass_residual with the change in solution
// to get the mass matrix, reusing old_elem_solution to hold that
// delta_solution. We're solving dt*F(u) - du = 0, so our
// delta_solution is old_solution - new_solution.
// We're still keeping elem_solution in theta_solution for now
old_elem_solution -= theta_solution;
// Move old_->elem_, theta_->old_
context.get_elem_solution().swap(old_elem_solution);
// We do a trick here to avoid using a non-1
// elem_solution_derivative:
context.get_elem_jacobian() *= -1.0;
context.fixed_solution_derivative *= -1.0;
jacobian_computed = _system.mass_residual(jacobian_computed, context) &&
jacobian_computed;
context.get_elem_jacobian() *= -1.0;
context.fixed_solution_derivative *= -1.0;
// Move elem_->elem_, old_->theta_
context.get_elem_solution().swap(theta_solution);
// Restore the elem position if necessary
context.elem_reinit(1.);
// Add the constraint term
jacobian_computed = _system.element_constraint(jacobian_computed, context) &&
jacobian_computed;
// Add back the old residual and jacobian
context.get_elem_residual() += old_elem_residual;
if (request_jacobian)
{
if (jacobian_computed)
context.get_elem_jacobian() += old_elem_jacobian;
else
context.get_elem_jacobian().swap(old_elem_jacobian);
}
return jacobian_computed;
}
bool EulerSolver::_general_residual (bool request_jacobian,
DiffContext &context,
ResFuncType mass,
ResFuncType time_deriv,
ResFuncType constraint,
ReinitFuncType reinit_func)
{
unsigned int n_dofs = context.get_elem_solution().size();
// We might need to save the old jacobian in case one of our physics
// terms later is unable to update it analytically.
DenseMatrix<Number> old_elem_jacobian(n_dofs, n_dofs);
if (request_jacobian)
old_elem_jacobian.swap(context.get_elem_jacobian());
// Local nonlinear solution at old timestep
DenseVector<Number> old_elem_solution(n_dofs);
for (unsigned int i=0; i != n_dofs; ++i)
old_elem_solution(i) =
old_nonlinear_solution(context.get_dof_indices()[i]);
// Local time derivative of solution
context.get_elem_solution_rate() = context.get_elem_solution();
context.get_elem_solution_rate() -= old_elem_solution;
context.elem_solution_rate_derivative = 1 / _system.deltat;
context.get_elem_solution_rate() *=
context.elem_solution_rate_derivative;
// Local nonlinear solution at time t_theta
DenseVector<Number> theta_solution(context.get_elem_solution());
theta_solution *= theta;
theta_solution.add(1. - theta, old_elem_solution);
context.elem_solution_derivative = theta;
context.fixed_solution_derivative = theta;
// If a fixed solution is requested, we'll use theta_solution
if (_system.use_fixed_solution)
context.get_elem_fixed_solution() = theta_solution;
// Move theta_->elem_, elem_->theta_
context.get_elem_solution().swap(theta_solution);
// Move the mesh into place first if necessary
(context.*reinit_func)(theta);
// Get the time derivative at t_theta
bool jacobian_computed =
(_system.*time_deriv)(request_jacobian, context);
jacobian_computed = (_system.*mass)(jacobian_computed, context) &&
jacobian_computed;
// Restore the elem position if necessary
(context.*reinit_func)(1);
// Move elem_->elem_, theta_->theta_
context.get_elem_solution().swap(theta_solution);
context.elem_solution_derivative = 1;
// Add the constraint term
jacobian_computed = (_system.*constraint)(jacobian_computed, context) &&
jacobian_computed;
// Add back (or restore) the old jacobian
if (request_jacobian)
{
if (jacobian_computed)
context.get_elem_jacobian() += old_elem_jacobian;
else
context.get_elem_jacobian().swap(old_elem_jacobian);
}
return jacobian_computed;
}