OGS  master
NumLib::NonlinearSolver< NonlinearSolverTag::Picard > Class Referencefinal

Detailed Description

Find a solution to a nonlinear equation using the Picard fixpoint iteration method.

Definition at line 160 of file NonlinearSolver.h.

#include <NonlinearSolver.h>

Inheritance diagram for NumLib::NonlinearSolver< NonlinearSolverTag::Picard >:
[legend]
Collaboration diagram for NumLib::NonlinearSolver< NonlinearSolverTag::Picard >:
[legend]

Public Types

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

Public Member Functions

 NonlinearSolver (GlobalLinearSolver &linear_solver, const int maxiter)
 
 ~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
 
const int _maxiter
 maximum number of iterations More...
 
GlobalVector_r_neq = nullptr
 non-equilibrium initial residuum. More...
 
std::size_t _A_id = 0u
 ID of the \( A \) matrix. More...
 
std::size_t _rhs_id = 0u
 ID of the right-hand side vector. More...
 
std::size_t _x_new_id = 0u
 
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 165 of file NonlinearSolver.h.

Constructor & Destructor Documentation

◆ NonlinearSolver()

NumLib::NonlinearSolver< NonlinearSolverTag::Picard >::NonlinearSolver ( GlobalLinearSolver linear_solver,
const int  maxiter 
)
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.

Definition at line 173 of file NonlinearSolver.h.

175  : _linear_solver(linear_solver), _maxiter(maxiter)
176  {
177  }
const int _maxiter
maximum number of iterations

◆ ~NonlinearSolver()

Definition at line 457 of file NonlinearSolver.cpp.

458 {
459  if (_r_neq != nullptr)
460  {
462  }
463 }
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::Picard >::calculateNonEquilibriumInitialResiduum ( std::vector< GlobalVector * > const &  x,
std::vector< GlobalVector * > const &  x_prev,
int const  process_id 
)
overridevirtual

Implements NumLib::NonlinearSolverBase.

Definition at line 27 of file NonlinearSolver.cpp.

31 {
33  {
34  return;
35  }
36 
39  _equation_system->assemble(x, x_prev, process_id);
41  _equation_system->getRhs(*x_prev[process_id], rhs);
42 
43  // r_neq = A * x - rhs
45  MathLib::LinAlg::matMult(A, *x[process_id], *_r_neq);
46  MathLib::LinAlg::axpy(*_r_neq, -1.0, rhs); // res -= rhs
47 }
virtual GlobalMatrix & getMatrix(std::size_t &id)=0
Get an uninitialized matrix with the given id.
std::size_t _rhs_id
ID of the right-hand side vector.
virtual void getA(GlobalMatrix &A) const =0
virtual void assemble(std::vector< GlobalVector * > const &x, std::vector< GlobalVector * > const &x_prev, int const process_id)=0
virtual void getRhs(GlobalVector const &x_prev, GlobalVector &rhs) const =0
virtual GlobalVector & getVector(std::size_t &id)=0
Get an uninitialized vector with the given id.
void axpy(PETScVector &y, double const a, PETScVector const &x)
Definition: LinAlg.cpp:57
void matMult(PETScMatrix const &A, PETScVector const &x, PETScVector &y)
Definition: LinAlg.cpp:141
static NUMLIB_EXPORT MatrixProvider & provider

References MathLib::LinAlg::axpy(), NumLib::MatrixProvider::getMatrix(), NumLib::VectorProvider::getVector(), MathLib::LinAlg::matMult(), NumLib::GlobalVectorProvider::provider, and NumLib::GlobalMatrixProvider::provider.

◆ compensateNonEquilibriumInitialResiduum()

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

Definition at line 201 of file NonlinearSolver.h.

202  {
204  }

◆ setEquationSystem()

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

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

Definition at line 183 of file NonlinearSolver.h.

184  {
185  _equation_system = &eq;
186  _convergence_criterion = &conv_crit;
187  }

◆ solve()

NonlinearSolverStatus NumLib::NonlinearSolver< NonlinearSolverTag::Picard >::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 49 of file NonlinearSolver.cpp.

55 {
56  namespace LinAlg = MathLib::LinAlg;
57  auto& sys = *_equation_system;
58 
61 
62  std::vector<GlobalVector*> x_new{x};
63  x_new[process_id] =
65  LinAlg::copy(*x[process_id], *x_new[process_id]); // set initial guess
66 
67  bool error_norms_met = false;
68 
70 
71  int iteration = 1;
72  for (; iteration <= _maxiter; ++iteration, _convergence_criterion->reset())
73  {
74  BaseLib::RunTime timer_dirichlet;
75  double time_dirichlet = 0.0;
76 
77  BaseLib::RunTime time_iteration;
78  time_iteration.start();
79 
80  timer_dirichlet.start();
81  sys.computeKnownSolutions(*x_new[process_id], process_id);
82  sys.applyKnownSolutions(*x_new[process_id]);
83  time_dirichlet += timer_dirichlet.elapsed();
84 
85  sys.preIteration(iteration, *x_new[process_id]);
86 
87  BaseLib::RunTime time_assembly;
88  time_assembly.start();
89  sys.assemble(x_new, x_prev, process_id);
90  sys.getA(A);
91  sys.getRhs(*x_prev[process_id], rhs);
92  INFO("[time] Assembly took {:g} s.", time_assembly.elapsed());
93 
94  // Subtract non-equilibrium initial residuum if set
95  if (_r_neq != nullptr)
96  {
97  LinAlg::axpy(rhs, -1, *_r_neq);
98  }
99 
100  timer_dirichlet.start();
101  sys.applyKnownSolutionsPicard(A, rhs, *x_new[process_id]);
102  time_dirichlet += timer_dirichlet.elapsed();
103  INFO("[time] Applying Dirichlet BCs took {:g} s.", time_dirichlet);
104 
105  if (!sys.isLinear() && _convergence_criterion->hasResidualCheck())
106  {
107  GlobalVector res;
108  LinAlg::matMult(A, *x_new[process_id], res); // res = A * x_new
109  LinAlg::axpy(res, -1.0, rhs); // res -= rhs
111  }
112 
113  BaseLib::RunTime time_linear_solver;
114  time_linear_solver.start();
115  bool iteration_succeeded =
116  _linear_solver.solve(A, rhs, *x_new[process_id]);
117  INFO("[time] Linear solver took {:g} s.", time_linear_solver.elapsed());
118 
119  if (!iteration_succeeded)
120  {
121  ERR("Picard: The linear solver failed.");
122  }
123  else
124  {
125  if (postIterationCallback)
126  {
127  postIterationCallback(iteration, x_new);
128  }
129 
130  switch (sys.postIteration(*x_new[process_id]))
131  {
133  // Don't copy here. The old x might still be used further
134  // below. Although currently it is not.
135  break;
137  ERR("Picard: The postIteration() hook reported a "
138  "non-recoverable error.");
139  iteration_succeeded = false;
140  // Copy new solution to x.
141  // Thereby the failed solution can be used by the caller for
142  // debugging purposes.
143  LinAlg::copy(*x_new[process_id], *x[process_id]);
144  break;
146  INFO(
147  "Picard: The postIteration() hook decided that this "
148  "iteration has to be repeated.");
149  LinAlg::copy(
150  *x[process_id],
151  *x_new[process_id]); // throw the iteration result away
152  continue;
153  }
154  }
155 
156  if (!iteration_succeeded)
157  {
158  // Don't compute error norms, break here.
159  error_norms_met = false;
160  break;
161  }
162 
163  if (sys.isLinear())
164  {
165  error_norms_met = true;
166  }
167  else
168  {
170  {
171  GlobalVector minus_delta_x(*x[process_id]);
172  LinAlg::axpy(minus_delta_x, -1.0,
173  *x_new[process_id]); // minus_delta_x = x - x_new
174  _convergence_criterion->checkDeltaX(minus_delta_x,
175  *x_new[process_id]);
176  }
177 
178  error_norms_met = _convergence_criterion->isSatisfied();
179  }
180 
181  // Update x s.t. in the next iteration we will compute the right delta x
182  LinAlg::copy(*x_new[process_id], *x[process_id]);
183 
184  INFO("[time] Iteration #{:d} took {:g} s.", iteration,
185  time_iteration.elapsed());
186 
187  if (error_norms_met)
188  {
189  break;
190  }
191 
192  // Avoid increment of the 'iteration' if the error norms are not met,
193  // but maximum number of iterations is reached.
194  if (iteration >= _maxiter)
195  {
196  break;
197  }
198  }
199 
200  if (iteration > _maxiter)
201  {
202  ERR("Picard: Could not solve the given nonlinear system within {:d} "
203  "iterations",
204  _maxiter);
205  }
206 
210 
211  return {error_norms_met, iteration};
212 }
void INFO(char const *fmt, Args const &... args)
Definition: Logging.h:32
void ERR(char const *fmt, Args const &... args)
Definition: Logging.h:42
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)
Global vector based on Eigen vector.
Definition: EigenVector.h:27
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
void copy(PETScVector const &x, PETScVector &y)
Definition: LinAlg.cpp:37

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

Member Data Documentation

◆ _A_id

std::size_t NumLib::NonlinearSolver< NonlinearSolverTag::Picard >::_A_id = 0u
private

ID of the \( A \) matrix.

Definition at line 215 of file NonlinearSolver.h.

◆ _compensate_non_equilibrium_initial_residuum

bool NumLib::NonlinearSolver< NonlinearSolverTag::Picard >::_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 224 of file NonlinearSolver.h.

◆ _convergence_criterion

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

Definition at line 211 of file NonlinearSolver.h.

◆ _equation_system

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

Definition at line 208 of file NonlinearSolver.h.

◆ _linear_solver

Definition at line 207 of file NonlinearSolver.h.

◆ _maxiter

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

maximum number of iterations

Definition at line 212 of file NonlinearSolver.h.

◆ _r_neq

non-equilibrium initial residuum.

Definition at line 214 of file NonlinearSolver.h.

◆ _r_neq_id

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

ID of the non-equilibrium initial residuum vector.

Definition at line 219 of file NonlinearSolver.h.

◆ _rhs_id

std::size_t NumLib::NonlinearSolver< NonlinearSolverTag::Picard >::_rhs_id = 0u
private

ID of the right-hand side vector.

Definition at line 216 of file NonlinearSolver.h.

◆ _x_new_id

std::size_t NumLib::NonlinearSolver< NonlinearSolverTag::Picard >::_x_new_id = 0u
private

ID of the vector storing the solution of the linearized equation.

Definition at line 217 of file NonlinearSolver.h.


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