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Refactored line search functionality for do_one_defect_correction_Stokes_step in solver_schemes.cc #6772

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Refactored line search functionality for do_one_defect_correction_Stokes_step in solver_schemes.cc #6772

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10 changes: 10 additions & 0 deletions include/aspect/simulator.h
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Original file line number Diff line number Diff line change
Expand Up @@ -1337,6 +1337,16 @@ namespace aspect
void interpolate_onto_velocity_system(const TensorFunction<1,dim> &func,
LinearAlgebra::Vector &vec) const;

/**
* Perform a Newton line search to determine the optimal step length
* along the search direction.
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@bangerth bangerth Nov 11, 2025

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Also say that the result of the function is that current_linearization_point is set to the old current_linearization_point plus a suitable update in direction of search_direction.

*
* This function is implemented in
* <code>source/simulator/helper_functions.cc</code>
*/
double perform_line_search(const DefectCorrectionResiduals &dcr,
const bool use_picard,
LinearAlgebra::BlockVector &search_direction);

/**
* Add constraints to the given @p constraints object that are required
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89 changes: 89 additions & 0 deletions source/simulator/helper_functions.cc
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Original file line number Diff line number Diff line change
Expand Up @@ -2629,6 +2629,92 @@ namespace aspect
return initial_newton_residual;
}

/**
* Performs a Newton line search for the do_one_defect_correction_Stokes_step function
*/
template <int dim>
double Simulator<dim>::perform_line_search(const DefectCorrectionResiduals &dcr,
const bool use_picard,
LinearAlgebra::BlockVector &search_direction)
{
LinearAlgebra::BlockVector backup_linearization_point(introspection.index_sets.stokes_partitioning, mpi_communicator);
double step_length_factor = 1.0;
unsigned int line_search_iteration = 0;
// Many parts of the solver depend on the block layout (velocity = 0,
// pressure = 1). For example the linearized_stokes_initial_guess vector or the StokesBlock matrix
// wrapper. Let us make sure that this holds (and shorten their names):
const unsigned int pressure_block_index = (parameters.include_melt_transport) ?
introspection.variable("fluid pressure").block_index
: introspection.block_indices.pressure;
const unsigned int velocity_block_index = introspection.block_indices.velocities;
Assert(velocity_block_index == 0, ExcNotImplemented());
Assert(pressure_block_index == 1, ExcNotImplemented());
(void) pressure_block_index;
// Do the loop for the line search at least once with the full step length.
// If line search is disabled we will exit the loop in the first iteration.

do
{
if (line_search_iteration == 0)
{
// backup our starting point for the line search
backup_linearization_point.block(pressure_block_index) = current_linearization_point.block(pressure_block_index);
backup_linearization_point.block(velocity_block_index) = current_linearization_point.block(velocity_block_index);
}
else
{
// undo the last iteration and try again with smaller step length
current_linearization_point.block(pressure_block_index) = backup_linearization_point.block(pressure_block_index);
current_linearization_point.block(velocity_block_index) = backup_linearization_point.block(velocity_block_index);
search_direction.block(pressure_block_index) *= step_length_factor;
search_direction.block(velocity_block_index) *= step_length_factor;
}

// Update the current linearization point with the search direction
current_linearization_point.block(pressure_block_index) += search_direction.block(pressure_block_index);
current_linearization_point.block(velocity_block_index) += search_direction.block(velocity_block_index);

// Rebuild the rhs to determine the new residual.
assemble_newton_stokes_matrix = rebuild_stokes_preconditioner = false;
rebuild_stokes_matrix = !boundary_velocity_manager.get_prescribed_boundary_velocity_indicators().empty();

assemble_stokes_system();

const double test_velocity_residual = system_rhs.block(velocity_block_index).l2_norm();
const double test_pressure_residual = system_rhs.block(pressure_block_index).l2_norm();
const double test_residual = std::sqrt(test_velocity_residual * test_velocity_residual
+ test_pressure_residual * test_pressure_residual);

// Determine if the residual has decreased sufficiently.
const double alpha = 1e-4;
if (test_residual < (1.0 - alpha * step_length_factor) * dcr.residual
||
line_search_iteration >= newton_handler->parameters.max_newton_line_search_iterations
||
use_picard)
{
pcout << " Newton system information: Norm of the rhs: " << test_residual
<< ", Derivative scaling factor: " << newton_handler->parameters.newton_derivative_scaling_factor << std::endl;
return test_residual;
}
else
{
pcout << " Line search iteration " << line_search_iteration << ", with norm of the rhs "
<< test_residual << " and going to " << (1.0 - alpha * step_length_factor) * dcr.residual
<< ", relative residual: " << test_residual/dcr.initial_residual << std::endl;

// The current search direction has not decreased the residual
// enough, so we take a smaller step and try again.
// TODO: make a parameter out of this.
step_length_factor = 2.0/3.0;
}

++line_search_iteration;
Assert(line_search_iteration <= newton_handler->parameters.max_newton_line_search_iterations,
ExcInternalError());
}
while (true);
}


template <int dim>
Expand Down Expand Up @@ -2779,6 +2865,9 @@ namespace aspect
template void Simulator<dim>::restore_outflow_boundary_ids(const unsigned int boundary_id_offset); \
template void Simulator<dim>::check_consistency_of_boundary_conditions() const; \
template double Simulator<dim>::compute_initial_newton_residual(); \
template double Simulator<dim>::perform_line_search(const DefectCorrectionResiduals &dcr, \
const bool use_picard, \
LinearAlgebra::BlockVector &search_direction); \
template double Simulator<dim>::compute_Eisenstat_Walker_linear_tolerance(const bool EisenstatWalkerChoiceOne, \
const double maximum_linear_stokes_solver_tolerance, \
const double linear_stokes_solver_tolerance, \
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77 changes: 6 additions & 71 deletions source/simulator/solver_schemes.cc
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Original file line number Diff line number Diff line change
Expand Up @@ -530,6 +530,7 @@ namespace aspect
}



template <int dim>
void Simulator<dim>::do_one_defect_correction_Stokes_step(DefectCorrectionResiduals &dcr,
const bool use_picard)
Expand Down Expand Up @@ -702,7 +703,9 @@ namespace aspect
dcr.residual,
dcr.residual_old);

pcout << " The linear solver tolerance is set to " << parameters.linear_stokes_solver_tolerance << std::endl;
pcout << " The linear solver tolerance is set to "
<< parameters.linear_stokes_solver_tolerance
<< ". ";
}
}

Expand Down Expand Up @@ -737,79 +740,11 @@ namespace aspect
dcr.residual_old = dcr.residual;

// We have computed an update. Prepare for a line search.
LinearAlgebra::BlockVector backup_linearization_point(introspection.index_sets.stokes_partitioning, mpi_communicator);

double step_length_factor = 1.0;
unsigned int line_search_iteration = 0;

// Do the loop for the line search at least once with the full step length.
// If line search is disabled we will exit the loop in the first iteration.
do
{
if (line_search_iteration == 0)
{
// backup our starting point for the line search
backup_linearization_point.block(pressure_block_index) = current_linearization_point.block(pressure_block_index);
backup_linearization_point.block(velocity_block_index) = current_linearization_point.block(velocity_block_index);
}
else
{
// undo the last iteration and try again with smaller step length
current_linearization_point.block(pressure_block_index) = backup_linearization_point.block(pressure_block_index);
current_linearization_point.block(velocity_block_index) = backup_linearization_point.block(velocity_block_index);
search_direction.block(pressure_block_index) *= step_length_factor;
search_direction.block(velocity_block_index) *= step_length_factor;
}

// Update the current linearization point with the search direction
current_linearization_point.block(pressure_block_index) += search_direction.block(pressure_block_index);
current_linearization_point.block(velocity_block_index) += search_direction.block(velocity_block_index);

// Rebuild the rhs to determine the new residual.
assemble_newton_stokes_matrix = rebuild_stokes_preconditioner = false;
rebuild_stokes_matrix = !boundary_velocity_manager.get_prescribed_boundary_velocity_indicators().empty();

assemble_stokes_system();

const double test_velocity_residual = system_rhs.block(velocity_block_index).l2_norm();
const double test_pressure_residual = system_rhs.block(pressure_block_index).l2_norm();
const double test_residual = std::sqrt(test_velocity_residual * test_velocity_residual
+ test_pressure_residual * test_pressure_residual);

// Determine if the residual has decreased sufficiently.
const double alpha = 1e-4;
if (test_residual < (1.0 - alpha * step_length_factor) * dcr.residual
||
line_search_iteration >= newton_handler->parameters.max_newton_line_search_iterations
||
use_picard)
{
pcout << " Newton system information: Norm of the rhs: " << test_residual
<< ", Derivative scaling factor: " << newton_handler->parameters.newton_derivative_scaling_factor << std::endl;
dcr.residual = test_residual;
break;
}
else
{
pcout << " Line search iteration " << line_search_iteration << ", with norm of the rhs "
<< test_residual << " and going to " << (1.0 - alpha * step_length_factor) * dcr.residual
<< ", relative residual: " << test_residual/dcr.initial_residual << std::endl;

// The current search direction has not decreased the residual
// enough, so we take a smaller step and try again.
// TODO: make a parameter out of this.
step_length_factor = 2.0/3.0;
}

++line_search_iteration;
Assert(line_search_iteration <= newton_handler->parameters.max_newton_line_search_iterations,
ExcInternalError());
}
while (true);
dcr.residual = perform_line_search(dcr, use_picard, search_direction);
}


if (use_picard == true)
if (use_picard)
{
// When we are using (defect corrected) Picard, keep the
// newton_derivative_scaling_factor at zero. The newton_derivative_scaling_factor
Expand Down