OGS 6.2.0-97-g4a610c866
ODE Solver Library

Detailed Description

This ODE solver library has been designed with an implicit first-order quasilinear ODE in mind. However, it is in principle not restricted to such a kind of equation, but can be extended to also solve other equation types. In particular it is possible to introduce equation types that are no ODEs, but are nonlinear equations without time derivative terms.

The aim of the library's design is being able to formulate FEM processes without having to care which time discretization scheme and which nonlinear iteration method will be used to solve it.

The library offers different time discretization schemes, cf. the conceputal remarks on them, namely the forward and backward Euler and Crank-Nicolson methods and Backward Differentiation Formulas. The design follows Gear's method, which also underlies the DASSL algorithm of Petzold et al., cf. Differential-algebraic equations article, section Numerical methods/Direct discretization [2].

A rough overview over the interplay between the various parts of this library is given in the image below. Therein red symbols indicate which classes own which matrices or vectors (for the meaning of the different symbols refer to the documentation of the respective classes). The word own should not be taken too strict in the sense of C++ member ownership, although currently it is implemented as such; but in the future this implementation detail might change. Rather own means that the class is in charge of the respective matrix or vector, i.e., it can read from and write to it or pass it on to functions; or in other words: The class knows about the meaning of that matrix/vector. Note that only matrices and vectors that describe some proper state of the respective classes are shown; those storing only intermediate computations have been omitted from the image.

ode-solver-concept.png
Interplay of the different parts of the ODE solver library at the example of a first-order implicit quasilinear ODE.
In the ODE solver library the instances of some classes can work together with several instances of other classes throughout there lifetime, whereas they have a strict one-to-one correspondence to objects of some different type. Those relations are given in the following table.

Class 1 Class 2 Relation Remarks
TimeDiscretizedODESystem ODESystem 1:1 the ODESystem represents part of the state of the TimeDiscretizedODESystem
TimeDiscretizedODESystem TimeDiscretization 1:1 analogous for the TimeDiscretization
TimeDiscretizedODESystem MatrixTranslator 1:1 analogous for the MatrixTranslator
NonlinearSolver NonlinearSystem 1:n a nonlinear solver can solve various equations, one after the other
LinearSolver NonlinearSolver 1:n various NonlinearSolver's can share the same LinearSolver

Classes

class  NumLib::EquationSystem
 
class  NumLib::MatrixTranslator< ODETag >
 
class  NumLib::MatrixTranslator< ODESystemTag::FirstOrderImplicitQuasilinear >
 
class  NumLib::MatrixTranslatorGeneral< ODETag >
 
class  NumLib::MatrixTranslatorGeneral< ODESystemTag::FirstOrderImplicitQuasilinear >
 
class  NumLib::MatrixTranslatorForwardEuler< ODETag >
 
class  NumLib::MatrixTranslatorForwardEuler< ODESystemTag::FirstOrderImplicitQuasilinear >
 
class  NumLib::MatrixTranslatorCrankNicolson< ODETag >
 
class  NumLib::MatrixTranslatorCrankNicolson< ODESystemTag::FirstOrderImplicitQuasilinear >
 
class  NumLib::NonlinearSolver< NLTag >
 
class  NumLib::NonlinearSolver< NonlinearSolverTag::Newton >
 
class  NumLib::NonlinearSolver< NonlinearSolverTag::Picard >
 
class  NumLib::NonlinearSystem< NLTag >
 
class  NumLib::NonlinearSystem< NonlinearSolverTag::Newton >
 
class  NumLib::NonlinearSystem< NonlinearSolverTag::Picard >
 
class  NumLib::ODESystem< ODETag, NLTag >
 
class  NumLib::ODESystem< ODESystemTag::FirstOrderImplicitQuasilinear, NonlinearSolverTag::Picard >
 
class  NumLib::ODESystem< ODESystemTag::FirstOrderImplicitQuasilinear, NonlinearSolverTag::Newton >
 
class  NumLib::InternalMatrixStorage
 
class  NumLib::TimeDiscretization
 
class  NumLib::BackwardEuler
 Backward Euler scheme. More...
 
class  NumLib::ForwardEuler
 Forward Euler scheme. More...
 
class  NumLib::CrankNicolson
 Generalized Crank-Nicolson scheme. More...
 
class  NumLib::BackwardDifferentiationFormula
 Backward differentiation formula. More...
 
class  NumLib::TimeDiscretizedODESystemBase< NLTag >
 
class  NumLib::TimeDiscretizedODESystem< ODETag, NLTag >
 
class  NumLib::TimeDiscretizedODESystem< ODESystemTag::FirstOrderImplicitQuasilinear, NonlinearSolverTag::Newton >
 
class  NumLib::TimeDiscretizedODESystem< ODESystemTag::FirstOrderImplicitQuasilinear, NonlinearSolverTag::Picard >
 

Enumerations

enum  NumLib::IterationResult : char { NumLib::IterationResult::SUCCESS, NumLib::IterationResult::FAILURE, NumLib::IterationResult::REPEAT_ITERATION }
 Status flags telling the NonlinearSolver if an iteration succeeded. More...
 
enum  NumLib::NonlinearSolverTag : bool { NumLib::NonlinearSolverTag::Picard, NumLib::NonlinearSolverTag::Newton }
 Tag used to specify which nonlinear solver will be used. More...
 
enum  NumLib::ODESystemTag : char { NumLib::ODESystemTag::FirstOrderImplicitQuasilinear, NumLib::ODESystemTag::NeumannBC }
 Tag used to specify the type of ODE. More...
 

Functions

template<ODESystemTag ODETag>
std::unique_ptr< MatrixTranslator< ODETag > > NumLib::createMatrixTranslator (TimeDiscretization const &timeDisc)
 
std::pair< std::unique_ptr< NonlinearSolverBase >, NonlinearSolverTagNumLib::createNonlinearSolver (GlobalLinearSolver &linear_solver, BaseLib::ConfigTree const &config)
 

Enumeration Type Documentation

◆ IterationResult

enum NumLib::IterationResult : char
strong

Status flags telling the NonlinearSolver if an iteration succeeded.

Enumerator
SUCCESS 
FAILURE 
REPEAT_ITERATION 

Definition at line 20 of file EquationSystem.h.

◆ NonlinearSolverTag

enum NumLib::NonlinearSolverTag : bool
strong

Tag used to specify which nonlinear solver will be used.

Enumerator
Picard 

Picard fixpoint iteration scheme

Newton 

Newton-Raphson iteration scheme

Definition at line 19 of file Types.h.

◆ ODESystemTag

enum NumLib::ODESystemTag : char
strong

Tag used to specify the type of ODE.

Enumerator
FirstOrderImplicitQuasilinear 

First order implicit quasi-linear ODE

This is an ODE of the form $ M(x,t)\cdot \dot x + K(x,t) \cdot x - b(x,t) =: r(\dot x, x, t) \stackrel{!}{=} 0 $

NeumannBC 

Definition at line 25 of file Types.h.

25  : char
26 {
34  NeumannBC // Sure, that's misuse of this enum, so sue me!
35 };

Function Documentation

◆ createMatrixTranslator()

template<ODESystemTag ODETag>
std::unique_ptr<MatrixTranslator<ODETag> > NumLib::createMatrixTranslator ( TimeDiscretization const &  timeDisc)

Creates a GlobalMatrix translator suitable to work together with the given time discretization scheme.

Definition at line 290 of file MatrixTranslator.h.

292 {
293  if (auto* fwd_euler = dynamic_cast<ForwardEuler const*>(&timeDisc))
294  {
295  return std::unique_ptr<MatrixTranslator<ODETag>>(
296  new MatrixTranslatorForwardEuler<ODETag>(*fwd_euler));
297  }
298  if (auto* crank = dynamic_cast<CrankNicolson const*>(&timeDisc))
299  {
300  return std::unique_ptr<MatrixTranslator<ODETag>>(
301  new MatrixTranslatorCrankNicolson<ODETag>(*crank));
302  }
303 
304  return std::unique_ptr<MatrixTranslator<ODETag>>(
305  new MatrixTranslatorGeneral<ODETag>(timeDisc));
306 }

◆ createNonlinearSolver()

std::pair< std::unique_ptr< NonlinearSolverBase >, NonlinearSolverTag > NumLib::createNonlinearSolver ( GlobalLinearSolver &  linear_solver,
BaseLib::ConfigTree const &  config 
)

Creates a new nonlinear solver from the given configuration.

Parameters
linear_solverthe linear solver that will be used by the nonlinear solver
configconfiguration settings
Returns
a pair (nl_slv, tag) where nl_slv is the generated nonlinear solver instance and the tag indicates if it uses the Picard or Newton-Raphson method
Input File Parameter:
prj__nonlinear_solvers__nonlinear_solver__type
Input File Parameter:
prj__nonlinear_solvers__nonlinear_solver__max_iter
Input File Parameter:
prj__nonlinear_solvers__nonlinear_solver__damping

Definition at line 343 of file NonlinearSolver.cpp.

References BaseLib::ConfigTree::getConfigParameter(), NumLib::Newton, OGS_FATAL, and NumLib::Picard.

Referenced by ProjectData::parseNonlinearSolvers().

345 {
347  auto const type = config.getConfigParameter<std::string>("type");
349  auto const max_iter = config.getConfigParameter<int>("max_iter");
350 
351  if (type == "Picard") {
352  auto const tag = NonlinearSolverTag::Picard;
353  using ConcreteNLS = NonlinearSolver<tag>;
354  return std::make_pair(
355  std::make_unique<ConcreteNLS>(linear_solver, max_iter), tag);
356  }
357  if (type == "Newton")
358  {
360  auto const damping = config.getConfigParameter<double>("damping", 1.0);
361  if (damping <= 0)
362  {
363  OGS_FATAL(
364  "The damping factor for the Newon method must be positive, got "
365  "%g.",
366  damping);
367  }
368  auto const tag = NonlinearSolverTag::Newton;
369  using ConcreteNLS = NonlinearSolver<tag>;
370  return std::make_pair(
371  std::make_unique<ConcreteNLS>(linear_solver, max_iter, damping),
372  tag);
373  }
374  OGS_FATAL("Unsupported nonlinear solver type");
375 }
#define OGS_FATAL(fmt,...)
Definition: Error.h:63