The constraint equation is defined along the path $ s $ as

$g(X, p, ds) = (Y - \tilde{Y} )^T t_1 = 0 ,$

where, $Y = \{ X^T p \}^T$ , $ X $ is the solution, $ p $ is the load parameter, $\tilde{Y}$ is the predictor based on the search direction $ t_1 $ . More...

#include <pseudo_arclength_continuation_solver.h>

Inheritance diagram for MAST::PseudoArclengthContinuationSolver:

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Public Member Functions
	PseudoArclengthContinuationSolver ()

virtual	~PseudoArclengthContinuationSolver ()

virtual void	initialize (Real dp)
	initializes the search direction using the specified load 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)

void	_update_search_direction (const libMesh::NumericVector< Real > &X, const MAST::Parameter &p, libMesh::SparseMatrix< Real > &jac, libMesh::NumericVector< Real > &t1_X, Real &t1_p)
	updates for the current iterate `X` and `p`, and stores these values to `_t0_X` and `_t0_p` for next computation. More...

virtual Real	_g (const libMesh::NumericVector< Real > &X, const MAST::Parameter &p)
	$g(X, p, ds) = X_{scale} * (X-X0) (dX/ds)_{scaled} + p_{scale} * (p-p0) (dp/ds)_{scaled} - ds = 0,$ where, $t_1^{X} = (dX/ds)_{scaled}$ and $t_1^{p} = (dp/ds)_{scaled}$ . More...

void	_g (const libMesh::NumericVector< Real > &X, const MAST::Parameter &p, libMesh::NumericVector< Real > &t1_X, Real &t1_p, Real &g)
	$\begin{eqnarray} g(X, p, ds) & = & (Y-Y_0)^T t_1 - ds = 0 \\ Y & = & \{ X_{scale} X^T, p_{scale} p\}^T \\ dg/dp & = & p_{scale} t_1^p \\ dg/dX & = & X_{scale} t_1^X, \end{eqnarray}$ where , $t_1^{X} = (dX/ds)_{scaled}$ and $t_1^{p} = (dp/ds)_{scaled}$ . 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 solution 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
std::unique_ptr< libMesh::NumericVector< Real > >	_t0_X

std::unique_ptr< libMesh::NumericVector< Real > >	_t0_X_orig

Real	_t0_p

Real	_t0_p_orig

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

The constraint equation is defined along the path $ s $ as

$g(X, p, ds) = (Y - \tilde{Y} )^T t_1 = 0 ,$

where, $Y = \{ X^T p \}^T$ , $ X $ is the solution, $ p $ is the load parameter, $\tilde{Y}$ is the predictor based on the search direction $ t_1 $ .

Given that the predictor is defined as $\tilde{Y} = Y_0 - ds t_1$ , with $ ds $ as the step size, the constraint is rewritten as

$(Y - Y_0 - ds * t_1)^T t_1 = 0 ,$

or, assuming $\| t_1 \| = 1$ ,

$Y^T t_1 - Y_0^T t_1 - ds = 0 .$

The search direction is evaluated based on:

$\left[ \begin{array}{cc} df/dx & df/dp \\ t_0^X & t_0^p \end{array} \right] \left\{ \begin{array}{c} t_1^X \\ t_1^p \end{array} \right\} = \left\{ \begin{array}{c} 0 \\ 1 \end{array} \right\}$

and, $ t_1 $ is then scaled to unit norm.

Definition at line 49 of file pseudo_arclength_continuation_solver.h.

Constructor & Destructor Documentation

MAST::PseudoArclengthContinuationSolver::PseudoArclengthContinuationSolver ( )

Definition at line 31 of file pseudo_arclength_continuation_solver.cpp.

MAST::PseudoArclengthContinuationSolver::~PseudoArclengthContinuationSolver ( )

virtual

Definition at line 39 of file pseudo_arclength_continuation_solver.cpp.

Member Function Documentation

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

protectedvirtual

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

where, $t_1^{X} = (dX/ds)_{scaled}$ and $t_1^{p} = (dp/ds)_{scaled}$ .

Implements MAST::ContinuationSolverBase.

Definition at line 205 of file pseudo_arclength_continuation_solver.cpp.

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void MAST::PseudoArclengthContinuationSolver::_g	(	const libMesh::NumericVector< Real > &	X,
		const MAST::Parameter &	p,
		libMesh::NumericVector< Real > &	t1_X,
		Real &	t1_p,
		Real &	g
	)

protected

$\begin{eqnarray*} g(X, p, ds) & = & (Y-Y_0)^T t_1 - ds = 0 \\ Y & = & \{ X_{scale} X^T, p_{scale} p\}^T \\ dg/dp & = & p_{scale} t_1^p \\ dg/dX & = & X_{scale} t_1^X, \end{eqnarray*}$

where $ $ , $t_1^{X} = (dX/ds)_{scaled}$ and $t_1^{p} = (dp/ds)_{scaled}$ .

Definition at line 228 of file pseudo_arclength_continuation_solver.cpp.

void MAST::PseudoArclengthContinuationSolver::_reset_iterations ( )

protectedvirtual

method resets any data if a solution step is restarted

Implements MAST::ContinuationSolverBase.

Definition at line 259 of file pseudo_arclength_continuation_solver.cpp.

void MAST::PseudoArclengthContinuationSolver::_save_iteration_data ( )

protectedvirtual

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

Implements MAST::ContinuationSolverBase.

Definition at line 248 of file pseudo_arclength_continuation_solver.cpp.

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

protectedvirtual

Implements MAST::ContinuationSolverBase.

Definition at line 86 of file pseudo_arclength_continuation_solver.cpp.

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void MAST::PseudoArclengthContinuationSolver::_update_search_direction	(	const libMesh::NumericVector< Real > &	X,
		const MAST::Parameter &	p,
		libMesh::SparseMatrix< Real > &	jac,
		libMesh::NumericVector< Real > &	t1_X,
		Real &	t1_p
	)

protected

updates $ t_1 $ for the current iterate X and p, and stores these values to _t0_X and _t0_p for next computation.

Definition at line 144 of file pseudo_arclength_continuation_solver.cpp.

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

virtual

initializes the search direction using the specified load step dp.

Implements MAST::ContinuationSolverBase.

Definition at line 45 of file pseudo_arclength_continuation_solver.cpp.

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Member Data Documentation

Real MAST::PseudoArclengthContinuationSolver::_t0_p

protected

Definition at line 128 of file pseudo_arclength_continuation_solver.h.

Real MAST::PseudoArclengthContinuationSolver::_t0_p_orig

protected

Definition at line 128 of file pseudo_arclength_continuation_solver.h.

std::unique_ptr<libMesh::NumericVector<Real> > MAST::PseudoArclengthContinuationSolver::_t0_X

protected

Definition at line 127 of file pseudo_arclength_continuation_solver.h.

std::unique_ptr<libMesh::NumericVector<Real> > MAST::PseudoArclengthContinuationSolver::_t0_X_orig

protected

Definition at line 127 of file pseudo_arclength_continuation_solver.h.

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

/home/travis/build/MASTmultiphysics/mast-multiphysics/src/solver/pseudo_arclength_continuation_solver.h
/home/travis/build/MASTmultiphysics/mast-multiphysics/src/solver/pseudo_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