constraint equation is defined along the path $ s $ as

$g(X, p, ds) = (x-x0) dx/ds + (p-p0) dp/ds - ds = 0,$

where, $ X $ is the solution, $ p $ is the load parameter, and $ ds $ is the chord length. More...

#include <arclength_continuation_solver.h>

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Public Member Functions
	ArclengthContinuationSolver ()

virtual	~ArclengthContinuationSolver ()

virtual void	initialize (Real dp)
	sets the arc length using a nonlinear solution using a step `dp`. More...

Public Member Functions inherited from MAST::ContinuationSolverBase
	ContinuationSolverBase ()

virtual	~ContinuationSolverBase ()

void	set_assembly_and_load_parameter (MAST::AssemblyElemOperations &elem_ops, MAST::AssemblyBase &assembly, MAST::Parameter &p)
	sets the assembly object for this solver More...

void	clear_assembly_and_load_parameters ()
	clears the assembly object from this solver More...

virtual void	solve ()
	solves for the next load step More...

Protected Member Functions
virtual void	_solve_NR_iterate (libMesh::NumericVector< Real > &X, MAST::Parameter &p)

virtual void	_dXdp (const libMesh::NumericVector< Real > &X, const MAST::Parameter &p, libMesh::NumericVector< Real > &dfdp, libMesh::NumericVector< Real > &dXdp)

virtual Real	_g (const libMesh::NumericVector< Real > &X, const MAST::Parameter &p)
	$g(X, p, ds) = X_{scale} * (X-X0) (dX/ds)_{scaled} + p_{scale} * (p-p0) (dp/ds)_{scaled} - ds_{scaled} = 0$ More...

void	_g (const libMesh::NumericVector< Real > &X, const MAST::Parameter &p, libMesh::NumericVector< Real > &dfdp, libMesh::NumericVector< Real > &dXdp, Real &g, Real &dgdp, libMesh::NumericVector< Real > *dgdX)
	$\begin{eqnarray} g(X, p, ds) & = & X_{scale} (X-X0) (dX/ds)_{scaled} + p_{scale} * (p-p0) (dp/ds)_{scaled} - ds_{scaled} = 0 \\ dg/dp & = & p_{scale} * (dp/ds)_{scaled} \\ dg/dX & = & X_{scale} * (dX/ds)_{scaled} \end{eqnarray*}$ More...

virtual void	_save_iteration_data ()
	method saves any data for possible resuse if the solution step is restarted. More...

virtual void	_reset_iterations ()
	method resets any data if a soltion step is restarted. More...

Protected Member Functions inherited from MAST::ContinuationSolverBase
void	_solve (const libMesh::NumericVector< Real > &X, const MAST::Parameter &p, libMesh::NumericVector< Real > &f, bool update_f, libMesh::NumericVector< Real > &dfdp, bool update_dfdp, const libMesh::NumericVector< Real > &dgdX, const Real dgdp, const Real g, libMesh::NumericVector< Real > &dX, Real &dp)
	solves for the linear system of equation as a monolithic system $\left[ \begin{array}{cc} df/dx & df/dp \\ dg/dx & dg/dp \end{array}\right] \left\{ \begin{array}{c} dx \\ dp \end{array} \right\} = - \left\{ \begin{array}{c} f \\ g \end{array} \right\}$ `dX` and `dp` are returned from the solution More...

void	_solve_schur_factorization (const libMesh::NumericVector< Real > &X, const MAST::Parameter &p, libMesh::SparseMatrix< Real > &jac, bool update_jac, libMesh::NumericVector< Real > &f, bool update_f, libMesh::NumericVector< Real > &dfdp, bool update_dfdp, libMesh::NumericVector< Real > &dXdp, bool update_dXdp, const libMesh::NumericVector< Real > &dgdX, const Real dgdp, const Real g, libMesh::NumericVector< Real > &dX, Real &dp)
	solves for the linear system of equation using Schur factorization. More...

Real	_res_norm (const libMesh::NumericVector< Real > &X, const MAST::Parameter &p)

Protected Attributes
Real	_dpds_sign

Protected Attributes inherited from MAST::ContinuationSolverBase
bool	_initialized

MAST::AssemblyElemOperations *	_elem_ops

MAST::AssemblyBase *	_assembly

MAST::Parameter *	_p

Real	_p0

Real	_X_scale

Real	_p_scale

std::unique_ptr< libMesh::NumericVector< Real > >	_X0

Additional Inherited Members
Public Attributes inherited from MAST::ContinuationSolverBase
unsigned int	max_it
	Maximum number of Newton-Raphson iterations for the solver. More...

Real	abs_tol
	Absolute tolerance for the solver. More...

Real	rel_tol
	Relative tolerance for the solver. More...

Real	arc_length
	arc length that the solver is required to satisfy for the update. More...

Real	min_step
	minimum step size allowed with adaptivity More...

Real	max_step
	maximum step size allowed with adaptivity More...

Real	step_size_change_exponent
	exponent used in step size update. More...

unsigned int	step_desired_iters
	desired N-R iterations per load-step. More...

bool	schur_factorization
	flag to use Schur-factorizaiton (default) or monolithic solver More...

Detailed Description

constraint equation is defined along the path $ s $ as

$g(X, p, ds) = (x-x0) dx/ds + (p-p0) dp/ds - ds = 0,$

where, $ X $ is the solution, $ p $ is the load parameter, and $ ds $ is the chord length.

Definition at line 35 of file arclength_continuation_solver.h.

Constructor & Destructor Documentation

MAST::ArclengthContinuationSolver::ArclengthContinuationSolver ( )

Definition at line 31 of file arclength_continuation_solver.cpp.

MAST::ArclengthContinuationSolver::~ArclengthContinuationSolver ( )

virtual

Definition at line 38 of file arclength_continuation_solver.cpp.

Member Function Documentation

void MAST::ArclengthContinuationSolver::_dXdp	(	const libMesh::NumericVector< Real > &	X,
		const MAST::Parameter &	p,
		libMesh::NumericVector< Real > &	dfdp,
		libMesh::NumericVector< Real > &	dXdp
	)

protectedvirtual

Definition at line 125 of file arclength_continuation_solver.cpp.

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Real MAST::ArclengthContinuationSolver::_g	(	const libMesh::NumericVector< Real > &	X,
		const MAST::Parameter &	p
	)

protectedvirtual

$g(X, p, ds) = X_{scale} * (X-X0) (dX/ds)_{scaled} + p_{scale} * (p-p0) (dp/ds)_{scaled} - ds_{scaled} = 0$

Implements MAST::ContinuationSolverBase.

Definition at line 176 of file arclength_continuation_solver.cpp.

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void MAST::ArclengthContinuationSolver::_g	(	const libMesh::NumericVector< Real > &	X,
		const MAST::Parameter &	p,
		libMesh::NumericVector< Real > &	dfdp,
		libMesh::NumericVector< Real > &	dXdp,
		Real &	g,
		Real &	dgdp,
		libMesh::NumericVector< Real > *	dgdX
	)

protected

$\begin{eqnarray*} g(X, p, ds) & = & X_{scale} * (X-X0) (dX/ds)_{scaled} + p_{scale} * (p-p0) (dp/ds)_{scaled} - ds_{scaled} = 0 \\ dg/dp & = & p_{scale} * (dp/ds)_{scaled} \\ dg/dX & = & X_{scale} * (dX/ds)_{scaled} \end{eqnarray*}$

Definition at line 194 of file arclength_continuation_solver.cpp.

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virtual void MAST::ArclengthContinuationSolver::_reset_iterations ( )

inlineprotectedvirtual

method resets any data if a soltion step is restarted.

Nothing to be done here.

Implements MAST::ContinuationSolverBase.

Definition at line 101 of file arclength_continuation_solver.h.

virtual void MAST::ArclengthContinuationSolver::_save_iteration_data ( )

inlineprotectedvirtual

method saves any data for possible resuse if the solution step is restarted.

Nothing to be done for this solver.

Implements MAST::ContinuationSolverBase.

Definition at line 95 of file arclength_continuation_solver.h.

void MAST::ArclengthContinuationSolver::_solve_NR_iterate	(	libMesh::NumericVector< Real > &	X,
		MAST::Parameter &	p
	)

protectedvirtual

Implements MAST::ContinuationSolverBase.

Definition at line 79 of file arclength_continuation_solver.cpp.

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void MAST::ArclengthContinuationSolver::initialize ( Real dp )

virtual

sets the arc length using a nonlinear solution using a step dp.

Implements MAST::ContinuationSolverBase.

Definition at line 44 of file arclength_continuation_solver.cpp.

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Member Data Documentation

Real MAST::ArclengthContinuationSolver::_dpds_sign

protected

Definition at line 104 of file arclength_continuation_solver.h.

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

/home/travis/build/MASTmultiphysics/mast-multiphysics/src/solver/arclength_continuation_solver.h
/home/travis/build/MASTmultiphysics/mast-multiphysics/src/solver/arclength_continuation_solver.cpp

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation