OGS
NumLib::NonlinearSolver< NonlinearSolverTag::Newton > Class Referencefinal

Detailed Description

Find a solution to a nonlinear equation using the Newton-Raphson method.

Definition at line 76 of file NonlinearSolver.h.

#include <NonlinearSolver.h>

Inheritance diagram for NumLib::NonlinearSolver< NonlinearSolverTag::Newton >:
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Collaboration diagram for NumLib::NonlinearSolver< NonlinearSolverTag::Newton >:
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Public Types

using System = NonlinearSystem<NonlinearSolverTag::Newton>
 Type of the nonlinear equation system to be solved.
 

Public Member Functions

 NonlinearSolver (GlobalLinearSolver &linear_solver, int const maxiter, double const damping=1.0)
 
 ~NonlinearSolver ()
 
void setEquationSystem (System &eq, ConvergenceCriterion &conv_crit)
 
void calculateNonEquilibriumInitialResiduum (std::vector< GlobalVector * > const &x, std::vector< GlobalVector * > const &x_prev, int const process_id) override
 
NonlinearSolverStatus solve (std::vector< GlobalVector * > &x, std::vector< GlobalVector * > const &x_prev, std::function< void(int, std::vector< GlobalVector * > const &)> const &postIterationCallback, int const process_id) override
 
void compensateNonEquilibriumInitialResiduum (bool const value)
 
- Public Member Functions inherited from NumLib::NonlinearSolverBase
virtual ~NonlinearSolverBase ()=default
 

Private Attributes

GlobalLinearSolver_linear_solver
 
System_equation_system = nullptr
 
ConvergenceCriterion_convergence_criterion = nullptr
 
int const _maxiter
 maximum number of iterations
 
double const _damping
 
GlobalVector_r_neq = nullptr
 non-equilibrium initial residuum.
 
std::size_t _res_id = 0u
 ID of the residual vector.
 
std::size_t _J_id = 0u
 ID of the Jacobian matrix.
 
std::size_t _minus_delta_x_id = 0u
 ID of the \( -\Delta x\) vector.
 
std::size_t _x_new_id
 ID of the vector storing \( x - (-\Delta x) \).
 
std::size_t _r_neq_id = 0u
 
bool _compensate_non_equilibrium_initial_residuum = false
 

Member Typedef Documentation

◆ System

Type of the nonlinear equation system to be solved.

Definition at line 81 of file NonlinearSolver.h.

Constructor & Destructor Documentation

◆ NonlinearSolver()

NumLib::NonlinearSolver< NonlinearSolverTag::Newton >::NonlinearSolver ( GlobalLinearSolver & linear_solver,
int const maxiter,
double const damping = 1.0 )
inlineexplicit

Constructs a new instance.

Parameters
linear_solverthe linear solver used by this nonlinear solver.
maxiterthe maximum number of iterations used to solve the equation.
dampingA positive damping factor.
See also
_damping

Definition at line 91 of file NonlinearSolver.h.

94 : _linear_solver(linear_solver), _maxiter(maxiter), _damping(damping)
95 {
96 }
int const _maxiter
maximum number of iterations

◆ ~NonlinearSolver()

Definition at line 572 of file NonlinearSolver.cpp.

573{
574 if (_r_neq != nullptr)
575 {
577 }
578}
GlobalVector * _r_neq
non-equilibrium initial residuum.
virtual void releaseVector(GlobalVector const &x)=0
static NUMLIB_EXPORT VectorProvider & provider

References NumLib::GlobalVectorProvider::provider, and NumLib::VectorProvider::releaseVector().

Member Function Documentation

◆ calculateNonEquilibriumInitialResiduum()

void NumLib::NonlinearSolver< NonlinearSolverTag::Newton >::calculateNonEquilibriumInitialResiduum ( std::vector< GlobalVector * > const & x,
std::vector< GlobalVector * > const & x_prev,
int const process_id )
overridevirtual

Implements NumLib::NonlinearSolverBase.

Definition at line 302 of file NonlinearSolver.cpp.

306{
308 {
309 return;
310 }
311
312 INFO("Calculate non-equilibrium initial residuum.");
313
314 _equation_system->assemble(x, x_prev, process_id);
316 _equation_system->getResidual(*x[process_id], *x_prev[process_id], *_r_neq);
317
318 // Set the values of the selected entries of _r_neq, which are associated
319 // with the equations that do not need initial residual compensation, to
320 // zero.
321 const auto selected_global_indices =
323 std::vector<double> zero_entries(selected_global_indices.size(), 0.0);
324
325 _r_neq->set(selected_global_indices, zero_entries);
326
328}
void INFO(fmt::format_string< Args... > fmt, Args &&... args)
Definition Logging.h:35
void set(IndexType rowId, double v)
set entry
Definition EigenVector.h:73
virtual std::vector< GlobalIndexType > getIndicesOfResiduumWithoutInitialCompensation() const =0
virtual void assemble(std::vector< GlobalVector * > const &x, std::vector< GlobalVector * > const &x_prev, int const process_id)=0
virtual void getResidual(GlobalVector const &x, GlobalVector const &x_prev, GlobalVector &res) const =0
virtual GlobalVector & getVector(std::size_t &id)=0
Get an uninitialized vector with the given id.
void finalizeAssembly(PETScMatrix &A)
Definition LinAlg.cpp:198

References MathLib::LinAlg::finalizeAssembly(), NumLib::VectorProvider::getVector(), INFO(), and NumLib::GlobalVectorProvider::provider.

◆ compensateNonEquilibriumInitialResiduum()

void NumLib::NonlinearSolver< NonlinearSolverTag::Newton >::compensateNonEquilibriumInitialResiduum ( bool const value)
inline

Definition at line 120 of file NonlinearSolver.h.

◆ setEquationSystem()

void NumLib::NonlinearSolver< NonlinearSolverTag::Newton >::setEquationSystem ( System & eq,
ConvergenceCriterion & conv_crit )
inline

Set the nonlinear equation system that will be solved. TODO doc

Definition at line 102 of file NonlinearSolver.h.

103 {
104 _equation_system = &eq;
105 _convergence_criterion = &conv_crit;
106 }

◆ solve()

NonlinearSolverStatus NumLib::NonlinearSolver< NonlinearSolverTag::Newton >::solve ( std::vector< GlobalVector * > & x,
std::vector< GlobalVector * > const & x_prev,
std::function< void(int, std::vector< GlobalVector * > const &)> const & postIterationCallback,
int const process_id )
overridevirtual

Assemble and solve the equation system.

Parameters
xin: the initial guess, out: the solution.
x_prevprevious time step solution.
postIterationCallbackcalled after each iteration if set.
process_idusually used in staggered schemes.
Return values
trueif the equation system could be solved
falseotherwise

Implements NumLib::NonlinearSolverBase.

Definition at line 330 of file NonlinearSolver.cpp.

336{
337 namespace LinAlg = MathLib::LinAlg;
338 auto& sys = *_equation_system;
339
341 auto& minus_delta_x =
344
345 bool error_norms_met = false;
346
347 // TODO be more efficient
348 // init minus_delta_x to the right size
349 LinAlg::copy(*x[process_id], minus_delta_x);
350
352
353 int iteration = 1;
354 for (; iteration <= _maxiter; ++iteration, _convergence_criterion->reset())
355 {
356 BaseLib::RunTime timer_dirichlet;
357 double time_dirichlet = 0.0;
358
359 BaseLib::RunTime time_iteration;
360 time_iteration.start();
361
362 timer_dirichlet.start();
363 sys.computeKnownSolutions(*x[process_id], process_id);
364 time_dirichlet += timer_dirichlet.elapsed();
365
366 sys.preIteration(iteration, *x[process_id]);
367
368 BaseLib::RunTime time_assembly;
369 time_assembly.start();
370 int mpi_rank_assembly_ok = 1;
371 int mpi_all_assembly_ok = 0;
372 try
373 {
374 sys.assemble(x, x_prev, process_id);
375 }
376 catch (AssemblyException const& e)
377 {
378 ERR("Abort nonlinear iteration. Repeating timestep. Reason: {:s}",
379 e.what());
380 error_norms_met = false;
381 iteration = _maxiter;
382 mpi_rank_assembly_ok = 0;
383 }
384 mpi_all_assembly_ok = BaseLib::MPI::reduceMin(mpi_rank_assembly_ok);
385 if (mpi_all_assembly_ok == 0)
386 {
387 break;
388 }
389 sys.getResidual(*x[process_id], *x_prev[process_id], res);
390 sys.getJacobian(J);
391 INFO("[time] Assembly took {:g} s.", time_assembly.elapsed());
392
393 // Subtract non-equilibrium initial residuum if set
394 if (_r_neq != nullptr)
395 LinAlg::axpy(res, -1, *_r_neq);
396
397 minus_delta_x.setZero();
398
399 timer_dirichlet.start();
400 sys.applyKnownSolutionsNewton(J, res, *x[process_id], minus_delta_x);
401 time_dirichlet += timer_dirichlet.elapsed();
402 INFO("[time] Applying Dirichlet BCs took {:g} s.", time_dirichlet);
403
404 if (!sys.isLinear() && _convergence_criterion->hasResidualCheck())
405 {
407 }
408
409 BaseLib::RunTime time_linear_solver;
410 time_linear_solver.start();
411 bool iteration_succeeded = _linear_solver.solve(J, res, minus_delta_x);
412 INFO("[time] Linear solver took {:g} s.", time_linear_solver.elapsed());
413
414 if (!iteration_succeeded)
415 {
416 ERR("Newton: The linear solver failed.");
417 }
418 else
419 {
420 // TODO could be solved in a better way
421 // cf.
422 // https://petsc.org/release/manualpages/Vec/VecWAXPY
423
424 // Copy pointers, replace the one for the given process id.
425 std::vector<GlobalVector*> x_new{x};
426 x_new[process_id] =
428 *x[process_id], _x_new_id);
429 LinAlg::axpy(*x_new[process_id], -_damping, minus_delta_x);
430
431 if (postIterationCallback)
432 {
433 postIterationCallback(iteration, x_new);
434 }
435
436 switch (sys.postIteration(*x_new[process_id]))
437 {
439 break;
441 ERR("Newton: The postIteration() hook reported a "
442 "non-recoverable error.");
443 iteration_succeeded = false;
444 break;
446 INFO(
447 "Newton: The postIteration() hook decided that this "
448 "iteration has to be repeated.");
449 // TODO introduce some onDestroy hook.
451 *x_new[process_id]);
452 continue; // That throws the iteration result away.
453 }
454
455 LinAlg::copy(*x_new[process_id],
456 *x[process_id]); // copy new solution to x
458 *x_new[process_id]);
459 }
460
461 if (!iteration_succeeded)
462 {
463 // Don't compute further error norms, but break here.
464 error_norms_met = false;
465 break;
466 }
467
468 if (sys.isLinear())
469 {
470 error_norms_met = true;
471 }
472 else
473 {
475 {
476 // Note: x contains the new solution!
477 _convergence_criterion->checkDeltaX(minus_delta_x,
478 *x[process_id]);
479 }
480
481 error_norms_met = _convergence_criterion->isSatisfied();
482 }
483
484 INFO("[time] Iteration #{:d} took {:g} s.", iteration,
485 time_iteration.elapsed());
486
487 if (error_norms_met)
488 {
489 break;
490 }
491
492 // Avoid increment of the 'iteration' if the error norms are not met,
493 // but maximum number of iterations is reached.
494 if (iteration >= _maxiter)
495 {
496 break;
497 }
498 }
499
500 if (iteration > _maxiter)
501 {
502 ERR("Newton: Could not solve the given nonlinear system within {:d} "
503 "iterations",
504 _maxiter);
505 }
506
510
511 return {error_norms_met, iteration};
512}
void ERR(fmt::format_string< Args... > fmt, Args &&... args)
Definition Logging.h:45
Count the running time.
Definition RunTime.h:29
double elapsed() const
Get the elapsed time in seconds.
Definition RunTime.h:42
void start()
Start the timer.
Definition RunTime.h:32
bool solve(EigenMatrix &A, EigenVector &b, EigenVector &x)
virtual void checkResidual(GlobalVector const &residual)=0
Check if the residual satisfies the convergence criterion.
virtual bool hasResidualCheck() const =0
virtual bool isSatisfied() const
Tell if the convergence criterion is satisfied.
virtual void checkDeltaX(GlobalVector const &minus_delta_x, GlobalVector const &x)=0
virtual bool hasDeltaXCheck() const =0
virtual void releaseMatrix(GlobalMatrix const &A)=0
virtual GlobalMatrix & getMatrix(std::size_t &id)=0
Get an uninitialized matrix with the given id.
std::size_t _J_id
ID of the Jacobian matrix.
std::size_t _x_new_id
ID of the vector storing .
std::size_t _res_id
ID of the residual vector.
static int reduceMin(int const val)
Definition MPI.h:191
void copy(PETScVector const &x, PETScVector &y)
Definition LinAlg.cpp:37
void axpy(PETScVector &y, PetscScalar const a, PETScVector const &x)
Definition LinAlg.cpp:57
static NUMLIB_EXPORT MatrixProvider & provider

References MathLib::LinAlg::axpy(), MathLib::LinAlg::copy(), BaseLib::RunTime::elapsed(), ERR(), NumLib::FAILURE, NumLib::MatrixProvider::getMatrix(), NumLib::VectorProvider::getVector(), INFO(), NumLib::GlobalMatrixProvider::provider, NumLib::GlobalVectorProvider::provider, BaseLib::MPI::reduceMin(), NumLib::MatrixProvider::releaseMatrix(), NumLib::VectorProvider::releaseVector(), NumLib::REPEAT_ITERATION, BaseLib::RunTime::start(), and NumLib::SUCCESS.

Member Data Documentation

◆ _compensate_non_equilibrium_initial_residuum

bool NumLib::NonlinearSolver< NonlinearSolverTag::Newton >::_compensate_non_equilibrium_initial_residuum = false
private

Enables computation of the non-equilibrium initial residuum \( r_{\rm neq} \) before the first time step. The forces are zero if the external forces are in equilibrium with the initial state/initial conditions. During the simulation the new residuum reads \( \tilde r = r - r_{\rm neq} \).

Definition at line 153 of file NonlinearSolver.h.

◆ _convergence_criterion

ConvergenceCriterion* NumLib::NonlinearSolver< NonlinearSolverTag::Newton >::_convergence_criterion = nullptr
private

Definition at line 130 of file NonlinearSolver.h.

◆ _damping

double const NumLib::NonlinearSolver< NonlinearSolverTag::Newton >::_damping
private

A positive damping factor. The default value 1.0 gives a non-damped Newton method. Common values are in the range 0.5 to 0.7 for somewhat conservative method and seldom become smaller than 0.2 for very conservative approach.

Definition at line 137 of file NonlinearSolver.h.

◆ _equation_system

System* NumLib::NonlinearSolver< NonlinearSolverTag::Newton >::_equation_system = nullptr
private

Definition at line 127 of file NonlinearSolver.h.

◆ _J_id

std::size_t NumLib::NonlinearSolver< NonlinearSolverTag::Newton >::_J_id = 0u
private

ID of the Jacobian matrix.

Definition at line 141 of file NonlinearSolver.h.

◆ _linear_solver

Definition at line 126 of file NonlinearSolver.h.

◆ _maxiter

int const NumLib::NonlinearSolver< NonlinearSolverTag::Newton >::_maxiter
private

maximum number of iterations

Definition at line 131 of file NonlinearSolver.h.

◆ _minus_delta_x_id

std::size_t NumLib::NonlinearSolver< NonlinearSolverTag::Newton >::_minus_delta_x_id = 0u
private

ID of the \( -\Delta x\) vector.

Definition at line 142 of file NonlinearSolver.h.

◆ _r_neq

non-equilibrium initial residuum.

Definition at line 139 of file NonlinearSolver.h.

◆ _r_neq_id

std::size_t NumLib::NonlinearSolver< NonlinearSolverTag::Newton >::_r_neq_id = 0u
private

ID of the non-equilibrium initial residuum vector.

Definition at line 145 of file NonlinearSolver.h.

◆ _res_id

std::size_t NumLib::NonlinearSolver< NonlinearSolverTag::Newton >::_res_id = 0u
private

ID of the residual vector.

Definition at line 140 of file NonlinearSolver.h.

◆ _x_new_id

std::size_t NumLib::NonlinearSolver< NonlinearSolverTag::Newton >::_x_new_id
private
Initial value:
=
0u

ID of the vector storing \( x - (-\Delta x) \).

Definition at line 143 of file NonlinearSolver.h.


The documentation for this class was generated from the following files: