Class ae108::solve::GeneralizedNonlinearSolver

template <class Assembler>

ClassList > ae108 > solve > GeneralizedNonlinearSolver

Public Types

Type	Name
typedef std::vector< cpppetsc::GeneralizedConstrainedDOFs >	BoundaryConditionContainer
typedef std::function< void(const cpppetsc::distributed< cpppetsc::Vector > &, double, cpppetsc::distributed< cpppetsc::Vector > *)>	DistributedForceVectorAssembler
typedef std::function< void(const cpppetsc::distributed< cpppetsc::Vector > &, double, cpppetsc::Matrix *)>	DistributedStiffnessMatrixAssembler
typedef std::function< void(const cpppetsc::local< cpppetsc::Vector > &, double, cpppetsc::local< cpppetsc::Vector > *)>	LocalForceVectorAssembler
typedef std::function< void(const cpppetsc::local< cpppetsc::Vector > &, double, cpppetsc::Matrix *)>	LocalStiffnessMatrixAssembler
typedef cpppetsc::Mesh::size_type	size_type
typedef cpppetsc::Mesh::value_type	value_type

Public Functions

Type	Name
	GeneralizedNonlinearSolver (const cpppetsc::Mesh * mesh)
cpppetsc::distributed< cpppetsc::Vector >	computeSolution (const BoundaryConditionContainer & boundaryConditions, cpppetsc::distributed< cpppetsc::Vector > initialGuess, const double time, const Assembler *const assembler) const Calls computeSolution with the default assembler calls (ie. calls assembleForceVector or assembleStiffnessMatrix). Passes on the rest of the arguments.
cpppetsc::distributed< cpppetsc::Vector >	computeSolution (const BoundaryConditionContainer & boundaryConditions, cpppetsc::distributed< cpppetsc::Vector > initialGuess, const double time, LocalForceVectorAssembler assembleForceVector, LocalStiffnessMatrixAssembler assembleStiffnessMatrix) const Calls computeSolution wrapping up the local assembler calls into distributed assembler calls. Passes on the rest of the arguments.
cpppetsc::distributed< cpppetsc::Vector >	computeSolution (const BoundaryConditionContainer & boundaryConditions, cpppetsc::distributed< cpppetsc::Vector > initialGuess, const double time, const DistributedForceVectorAssembler & assembleForceVector, const DistributedStiffnessMatrixAssembler & assembleStiffnessMatrix) const The goal of this function is to find the minimizer x of E(x) -> min, where x satisfies boundary conditions specified by linear equations.

Public Types Documentation

typedef BoundaryConditionContainer

using ae108::solve::GeneralizedNonlinearSolver< Assembler >::BoundaryConditionContainer =  std::vector<cpppetsc::GeneralizedConstrainedDOFs>;

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typedef DistributedForceVectorAssembler

using ae108::solve::GeneralizedNonlinearSolver< Assembler >::DistributedForceVectorAssembler =  std::function<void(const cpppetsc::distributed<cpppetsc::Vector> &, double, cpppetsc::distributed<cpppetsc::Vector> *)>;

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typedef DistributedStiffnessMatrixAssembler

using ae108::solve::GeneralizedNonlinearSolver< Assembler >::DistributedStiffnessMatrixAssembler =  std::function<void(const cpppetsc::distributed<cpppetsc::Vector> &, double, cpppetsc::Matrix *)>;

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typedef LocalForceVectorAssembler

using ae108::solve::GeneralizedNonlinearSolver< Assembler >::LocalForceVectorAssembler =  std::function<void(const cpppetsc::local<cpppetsc::Vector> &, double, cpppetsc::local<cpppetsc::Vector> *)>;

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typedef LocalStiffnessMatrixAssembler

using ae108::solve::GeneralizedNonlinearSolver< Assembler >::LocalStiffnessMatrixAssembler =  std::function<void( const cpppetsc::local<cpppetsc::Vector> &, double, cpppetsc::Matrix *)>;

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typedef size_type

using ae108::solve::GeneralizedNonlinearSolver< Assembler >::size_type =  cpppetsc::Mesh::size_type;

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typedef value_type

using ae108::solve::GeneralizedNonlinearSolver< Assembler >::value_type =  cpppetsc::Mesh::value_type;

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Public Functions Documentation

function GeneralizedNonlinearSolver

explicit ae108::solve::GeneralizedNonlinearSolver::GeneralizedNonlinearSolver (
    const cpppetsc::Mesh * mesh
) 

Parameters:

• mesh A valid nonzero pointer to a cpppetsc::Mesh instance.

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function computeSolution [1/3]

Calls computeSolution with the default assembler calls (ie. calls assembleForceVector or assembleStiffnessMatrix). Passes on the rest of the arguments.

cpppetsc::distributed < cpppetsc::Vector > ae108::solve::GeneralizedNonlinearSolver::computeSolution (
    const BoundaryConditionContainer & boundaryConditions,
    cpppetsc::distributed < cpppetsc::Vector > initialGuess,
    const double time,
    const Assembler *const assembler
) const

Parameters:

• boundaryConditions The generalized boundary conditions.
• initialGuess The global vector to start iterating at.
• time This will be used to configure the assembler. @para assembler Valid nonzero pointer.

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function computeSolution [2/3]

Calls computeSolution wrapping up the local assembler calls into distributed assembler calls. Passes on the rest of the arguments.

cpppetsc::distributed < cpppetsc::Vector > ae108::solve::GeneralizedNonlinearSolver::computeSolution (
    const BoundaryConditionContainer & boundaryConditions,
    cpppetsc::distributed < cpppetsc::Vector > initialGuess,
    const double time,
    LocalForceVectorAssembler assembleForceVector,
    LocalStiffnessMatrixAssembler assembleStiffnessMatrix
) const

Parameters:

• boundaryConditions The generalized boundary conditions.
• initialGuess The global vector to start iterating at.
• time This will be used to configure the assembler.
• assembleForceVector A valid callable. It will be called to assemble the local force vector.
• assembleStiffnessMatrix A valid callable. It will be called to assemble the stiffness matrix.

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function computeSolution [3/3]

The goal of this function is to find the minimizer x of E(x) -> min, where x satisfies boundary conditions specified by linear equations.

cpppetsc::distributed < cpppetsc::Vector > ae108::solve::GeneralizedNonlinearSolver::computeSolution (
    const BoundaryConditionContainer & boundaryConditions,
    cpppetsc::distributed < cpppetsc::Vector > initialGuess,
    const double time,
    const DistributedForceVectorAssembler & assembleForceVector,
    const DistributedStiffnessMatrixAssembler & assembleStiffnessMatrix
) const

More precisely, this function uses an "infeasible start Newton method"-based approach; See S. Boyd, L. Vandenberghe, "Convex Optimization", Cambridge University Press, 2019, pp. 531-534. PETSc's nonlinear solver is used to solve the adapted system.

This method is also widely known as Lagrange Multiplier Method; see Cook, R. D., Malkus, D. S., Plesha, M. E. & Witt, R. J. Concepts and Applications of Finite Element Analysis, 4th Edition. (Wiley, 2001).

Parameters:

• boundaryConditions The generalized boundary conditions.
• initialGuess The global vector to start iterating at.
• time This will be used to configure the assembler.
• assembleForceVector A valid callable. It will be called to assemble the distributed force vector.
• assembleStiffnessMatrix A valid callable. It will be called to assemble the stiffness matrix.

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The documentation for this class was generated from the following file solve/src/include/ae108/solve/GeneralizedNonlinearSolver.h