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] (http://www.scholarpedia.org/article/Differential-algebraic_equations#Numerical_methods.2FDirect_discretization) [8].

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.

Interplay of the different parts of the ODE

solver library at the example of a first-order implicit quasilinear ODE."@image latex ode-solver-concept.pdf "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. <table class="markdownTable"> <tr class="markdownTableHead"> <th class="markdownTableHeadRight"> Class 1

Class 2






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


class  NumLib::EquationSystem
class  NumLib::MatrixTranslator< ODETag >
class  NumLib::MatrixTranslator< ODESystemTag::FirstOrderImplicitQuasilinear >
class  NumLib::MatrixTranslatorGeneral< ODETag >
class  NumLib::MatrixTranslatorGeneral< 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::PETScNonlinearSolver
class  NumLib::TimeDiscretization
class  NumLib::BackwardEuler
 Backward Euler scheme. More...
class  NumLib::TimeDiscretizedODESystemBase< NLTag >
class  NumLib::TimeDiscretizedODESystem< ODETag, NLTag >
class  NumLib::TimeDiscretizedODESystem< ODESystemTag::FirstOrderImplicitQuasilinear, NonlinearSolverTag::Newton >
class  NumLib::TimeDiscretizedODESystem< ODESystemTag::FirstOrderImplicitQuasilinear, NonlinearSolverTag::Picard >


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


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 class NumLib::IterationResult : char

Status flags telling the NonlinearSolver if an iteration succeeded.


Definition at line 21 of file EquationSystem.h.

◆ NonlinearSolverTag

enum class NumLib::NonlinearSolverTag : bool

Tag used to specify which nonlinear solver will be used.


Picard fixpoint iteration scheme


Newton-Raphson iteration scheme

Definition at line 19 of file Types.h.

◆ ODESystemTag

enum class NumLib::ODESystemTag : char

Tag used to specify the type of ODE.


First order implicit quasi-linear ODE

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


Definition at line 26 of file Types.h.

35 NeumannBC // Sure, that's misuse of this enum, so sue me!

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 129 of file MatrixTranslator.h.

132 return std::unique_ptr<MatrixTranslator<ODETag>>(
133 new MatrixTranslatorGeneral<ODETag>(timeDisc));

◆ 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.

linear_solverthe linear solver that will be used by the nonlinear solver
configconfiguration settings
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:
Input File Parameter:
Input File Parameter:
Input File Parameter:

Definition at line 494 of file NonlinearSolver.cpp.

498 auto const type = config.getConfigParameter<std::string>("type");
500 auto const max_iter = config.getConfigParameter<int>("max_iter");
502 if (type == "Picard")
503 {
504 auto const tag = NonlinearSolverTag::Picard;
505 using ConcreteNLS = NonlinearSolver<tag>;
506 return std::make_pair(
507 std::make_unique<ConcreteNLS>(linear_solver, max_iter), tag);
508 }
509 if (type == "Newton")
510 {
512 auto const damping = config.getConfigParameter<double>("damping", 1.0);
513 if (damping <= 0)
514 {
516 "The damping factor for the Newon method must be positive, got "
517 "{:g}.",
518 damping);
519 }
520 auto const tag = NonlinearSolverTag::Newton;
521 using ConcreteNLS = NonlinearSolver<tag>;
522 return std::make_pair(
523 std::make_unique<ConcreteNLS>(linear_solver, max_iter, damping),
524 tag);
525 }
526#ifdef USE_PETSC
527 if (boost::iequals(type, "PETScSNES"))
528 {
529 auto prefix =
531 config.getConfigParameter<std::string>("prefix", "");
532 auto const tag = NonlinearSolverTag::Newton;
533 using ConcreteNLS = PETScNonlinearSolver;
534 return std::make_pair(std::make_unique<ConcreteNLS>(
535 linear_solver, max_iter, std::move(prefix)),
536 tag);
537 }
540 OGS_FATAL("Unsupported nonlinear solver type '{:s}'.", type.c_str());
#define OGS_FATAL(...)
Definition: Error.h:26

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

Referenced by ProjectData::parseNonlinearSolvers().