#include <level_set_elem_base.h>

Inheritance diagram for MAST::LevelSetElementBase:

Collaboration diagram for MAST::LevelSetElementBase:

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Public Member Functions
	LevelSetElementBase (MAST::SystemInitialization &sys, MAST::AssemblyBase &assembly, const MAST::GeomElem &elem)
	Constructor. More...

virtual	~LevelSetElementBase ()

void	set_velocity_function (const MAST::FieldFunction< Real > &vel)

void	set_propagation_mode (bool f)
	This can operate in one of two modes: propagation of level set given Vn, or reinitialization of level set so that \|grad(phi)\|=1. More...

void	set_reference_solution_for_initialization (const RealVectorX &sol)
	For reinitialization to $\|\nabla(\phi)\| = 1$ , the solution before initialization is used to calculate the source and velocity switching. More...

virtual bool	internal_residual (bool request_jacobian, RealVectorX &f, RealMatrixX &jac)
	internal force contribution to system residual More...

virtual bool	velocity_residual (bool request_jacobian, RealVectorX &f, RealMatrixX &jac_xdot, RealMatrixX &jac)
	inertial force contribution to system residual More...

bool	side_external_residual (bool request_jacobian, RealVectorX &f, RealMatrixX &jac, std::multimap< libMesh::boundary_id_type, MAST::BoundaryConditionBase * > &bc)
	side external force contribution to system residual More...

bool	volume_external_residual (bool request_jacobian, RealVectorX &f, RealMatrixX &jac, std::multimap< libMesh::subdomain_id_type, MAST::BoundaryConditionBase * > &bc)
	volume external force contribution to system residual More...

virtual bool	internal_residual_sensitivity (bool request_jacobian, RealVectorX &f, RealMatrixX &jac)
	sensitivity of the internal force contribution to system residual More...

virtual bool	velocity_residual_sensitivity (bool request_jacobian, RealVectorX &f, RealMatrixX &jac)
	sensitivity of the damping force contribution to system residual More...

bool	side_external_residual_sensitivity (bool request_jacobian, RealVectorX &f, RealMatrixX &jac, std::multimap< libMesh::boundary_id_type, MAST::BoundaryConditionBase * > &bc)
	sensitivity of the side external force contribution to system residual More...

bool	volume_external_residual_sensitivity (bool request_jacobian, RealVectorX &f, RealMatrixX &jac, std::multimap< libMesh::subdomain_id_type, MAST::BoundaryConditionBase * > &bc)
	sensitivity of the volume external force contribution to system residual More...

Real	volume ()

Real	perimeter ()
	Approximates the integral of the Dirac delta function to approximate the perimeter. More...

Real	perimeter_sensitivity ()
	computes the partial derivative of the integral of the Dirac delta function using the solution and sensitivity solution set for this element. More...

Real	volume_boundary_velocity_on_side (unsigned int s)

Public Member Functions inherited from MAST::ElementBase
	ElementBase (MAST::SystemInitialization &sys, MAST::AssemblyBase &assembly, const MAST::GeomElem &elem)
	The default constructor. More...

virtual	~ElementBase ()
	Default virtual destructor. More...

MAST::SystemInitialization &	system_initialization ()

MAST::AssemblyBase &	assembly ()

MAST::NonlinearSystem &	system ()

const MAST::GeomElem &	elem () const

const RealVectorX &	sol (bool if_sens=false) const

virtual void	set_solution (const RealVectorX &vec, bool if_sens=false)
	stores `vec` as solution for element level calculations, or its sensitivity if `if_sens` is true. More...

virtual void	set_perturbed_solution (const RealVectorX &vec, bool if_sens=false)
	This provides the perturbed solution (or its sensitivity if `if_sens` is true.) for linearized analysis. More...

virtual void	set_complex_solution (const ComplexVectorX &vec, bool if_sens=false)
	This provides the complex solution (or its sensitivity if `if_sens` is true.) for frequecy-domain analysis. More...

virtual void	set_velocity (const RealVectorX &vec, bool if_sens=false)
	stores `vec` as velocity for element level calculations, or its sensitivity if `if_sens` is true. More...

virtual void	set_perturbed_velocity (const RealVectorX &vec, bool if_sens=false)
	stores `vec` as perturbed velocity for element level calculations, or its sensitivity if `if_sens` is true. More...

virtual void	set_acceleration (const RealVectorX &vec, bool if_sens=false)
	stores `vec` as acceleration for element level calculations, or its sensitivity if `if_sens` is true. More...

virtual void	set_perturbed_acceleration (const RealVectorX &vec, bool if_sens=false)
	stores `vec` as perturbed acceleration for element level calculations, or its sensitivity if `if_sens` is true. More...

void	attach_active_solution_function (MAST::FunctionBase &f)
	Attaches the function that represents the system solution. More...

void	detach_active_solution_function ()
	Detaches the function object that may have been attached to the element. More...

Protected Member Functions
void	_velocity_and_source (const unsigned int qp, const libMesh::Point &p, const Real t, const MAST::FEMOperatorMatrix &Bmat, const std::vector< MAST::FEMOperatorMatrix > &dBmat, RealVectorX &vel, Real &source)
	calculates the velocity at the quadrature point More...

void	_tau (const MAST::FEBase &fe, unsigned int qp, const MAST::FEMOperatorMatrix &Bmat, const std::vector< MAST::FEMOperatorMatrix > &dBmat, const RealVectorX &vel, RealMatrixX &tau)
	initializes the tau operator More...

void	_dc_operator (const MAST::FEBase &fe, const unsigned int qp, const std::vector< MAST::FEMOperatorMatrix > &dB_mat, const RealVectorX &vel, Real &dc)

void	_calculate_dxidX (const MAST::FEBase &fe, const unsigned int qp, RealMatrixX &dxi_dX)

void	_initialize_fem_operators (const unsigned int qp, const MAST::FEBase &fe, MAST::FEMOperatorMatrix &Bmat, std::vector< MAST::FEMOperatorMatrix > &dBmat)
	When `mass` = false, initializes the FEM operator matrix to the shape functions as $B = \left[ \begin{array}{c} {\bf N} \\ {\bf N} \\ {\bf N} \end{array} \right]$ $dB[0] = \frac{\partial {\bf N}}{\partial x}$ . More...

Protected Attributes
const MAST::FieldFunction< Real > *	_phi_vel
	element property More...

bool	_if_propagation
	this can operate in one of two modes: propagation of level set given Vn, or reinitialization of level set so that \|grad(phi)\|=1 More...

RealVectorX	_ref_sol
	reference solution for reinitialization of the level set More...

Protected Attributes inherited from MAST::ElementBase
MAST::SystemInitialization &	_system
	SystemInitialization object associated with this element. More...

MAST::AssemblyBase &	_assembly
	Assembly object. More...

const MAST::GeomElem &	_elem
	geometric element for which the computations are performed More...

MAST::FunctionBase *	_active_sol_function
	pointer to the active solution mesh field function. More...

const Real &	_time
	time for which system is being assembled More...

RealVectorX	_sol
	local solution More...

RealVectorX	_sol_sens
	local solution sensitivity More...

ComplexVectorX	_complex_sol
	local solution used for frequency domain analysis More...

ComplexVectorX	_complex_sol_sens
	local solution used for frequency domain analysis More...

RealVectorX	_delta_sol
	local solution used for linearized analysis More...

RealVectorX	_delta_sol_sens
	local solution used for linearized analysis More...

RealVectorX	_vel
	local velocity More...

RealVectorX	_vel_sens
	local velocity More...

RealVectorX	_delta_vel
	local velocity More...

RealVectorX	_delta_vel_sens
	local velocity More...

RealVectorX	_accel
	local acceleration More...

RealVectorX	_accel_sens
	local acceleration More...

RealVectorX	_delta_accel
	local acceleration More...

RealVectorX	_delta_accel_sens
	local acceleration More...

Detailed Description

Definition at line 36 of file level_set_elem_base.h.

Constructor & Destructor Documentation

MAST::LevelSetElementBase::LevelSetElementBase	(	MAST::SystemInitialization &	sys,
		MAST::AssemblyBase &	assembly,
		const MAST::GeomElem &	elem
	)

Constructor.

Definition at line 37 of file level_set_elem_base.cpp.

MAST::LevelSetElementBase::~LevelSetElementBase ( )

virtual

Definition at line 48 of file level_set_elem_base.cpp.

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Member Function Documentation

void MAST::LevelSetElementBase::_calculate_dxidX	(	const MAST::FEBase &	fe,
		const unsigned int	qp,
		RealMatrixX &	dxi_dX
	)

protected

Definition at line 615 of file level_set_elem_base.cpp.

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void MAST::LevelSetElementBase::_dc_operator	(	const MAST::FEBase &	fe,
		const unsigned int	qp,
		const std::vector< MAST::FEMOperatorMatrix > &	dB_mat,
		const RealVectorX &	vel,
		Real &	dc
	)

protected

Definition at line 567 of file level_set_elem_base.cpp.

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void MAST::LevelSetElementBase::_initialize_fem_operators	(	const unsigned int	qp,
		const MAST::FEBase &	fe,
		MAST::FEMOperatorMatrix &	Bmat,
		std::vector< MAST::FEMOperatorMatrix > &	dBmat
	)

protected

When mass = false, initializes the FEM operator matrix to the shape functions as

$B = \left[ \begin{array}{c} {\bf N} \\ {\bf N} \\ {\bf N} \end{array} \right]$

$dB[0] = \frac{\partial {\bf N}}{\partial x}$

.

$dB[1] = \frac{\partial {\bf N}}{\partial y}$

$dB[2] = \frac{\partial {\bf N}}{\partial z}$

Definition at line 689 of file level_set_elem_base.cpp.

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void MAST::LevelSetElementBase::_tau	(	const MAST::FEBase &	fe,
		unsigned int	qp,
		const MAST::FEMOperatorMatrix &	Bmat,
		const std::vector< MAST::FEMOperatorMatrix > &	dBmat,
		const RealVectorX &	vel,
		RealMatrixX &	tau
	)

protected

initializes the tau operator

Definition at line 525 of file level_set_elem_base.cpp.

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void MAST::LevelSetElementBase::_velocity_and_source	(	const unsigned int	qp,
		const libMesh::Point &	p,
		const Real	t,
		const MAST::FEMOperatorMatrix &	Bmat,
		const std::vector< MAST::FEMOperatorMatrix > &	dBmat,
		RealVectorX &	vel,
		Real &	source
	)

protected

calculates the velocity at the quadrature point

Definition at line 471 of file level_set_elem_base.cpp.

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bool MAST::LevelSetElementBase::internal_residual	(	bool	request_jacobian,
		RealVectorX &	f,
		RealMatrixX &	jac
	)

virtual

internal force contribution to system residual

Definition at line 65 of file level_set_elem_base.cpp.

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bool MAST::LevelSetElementBase::internal_residual_sensitivity	(	bool	request_jacobian,
		RealVectorX &	f,
		RealMatrixX &	jac
	)

virtual

sensitivity of the internal force contribution to system residual

Definition at line 291 of file level_set_elem_base.cpp.

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Real MAST::LevelSetElementBase::perimeter ( )

Approximates the integral of the Dirac delta function to approximate the perimeter.

The approximation of Dirac delta function is obtained from the derivative of an approximation to the Heaviside function

$H_d(\phi) \approx \frac{1}{2} \left( 1 + \frac{2}{\pi} \arctan(\phi/d) \right).$

Then, the derivative defines the Dirac delta function

$\delta_d(\phi) = \frac{dH_d(\phi)}{d\phi} = \frac{1}{\pi d} \frac{1}{1+(\phi/d)^2} .$

Sensitivity analysis requires the derivative of this function with respect to a variable, which is expressed as

$\frac{d\delta_d(\phi)}{d\alpha} = \frac{-2 \phi}{\pi d^3} \frac{1}{\left(1+(\phi/d)^2\right)^2} \frac{d\phi}{d\alpha}.$

Returns: the computed integral of $\delta_d(\phi)$

Definition at line 345 of file level_set_elem_base.cpp.

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Real MAST::LevelSetElementBase::perimeter_sensitivity ( )

computes the partial derivative of the integral of the Dirac delta function using the solution and sensitivity solution set for this element.

Definition at line 378 of file level_set_elem_base.cpp.

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void MAST::LevelSetElementBase::set_propagation_mode ( bool f )

inline

This can operate in one of two modes: propagation of level set given Vn, or reinitialization of level set so that |grad(phi)|=1.

This method sets the flag for propagation to true or false.

Definition at line 63 of file level_set_elem_base.h.

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void MAST::LevelSetElementBase::set_reference_solution_for_initialization ( const RealVectorX & sol )

For reinitialization to $|\nabla(\phi)| = 1$ , the solution before initialization is used to calculate the source and velocity switching.

This method sets that solution

Definition at line 56 of file level_set_elem_base.cpp.

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void MAST::LevelSetElementBase::set_velocity_function ( const MAST::FieldFunction< Real > & vel )

inline

Definition at line 52 of file level_set_elem_base.h.

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bool MAST::LevelSetElementBase::side_external_residual	(	bool	request_jacobian,
		RealVectorX &	f,
		RealMatrixX &	jac,
		std::multimap< libMesh::boundary_id_type, MAST::BoundaryConditionBase * > &	bc
	)

side external force contribution to system residual

Definition at line 235 of file level_set_elem_base.cpp.

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bool MAST::LevelSetElementBase::side_external_residual_sensitivity	(	bool	request_jacobian,
		RealVectorX &	f,
		RealMatrixX &	jac,
		std::multimap< libMesh::boundary_id_type, MAST::BoundaryConditionBase * > &	bc
	)

sensitivity of the side external force contribution to system residual

Definition at line 263 of file level_set_elem_base.cpp.

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bool MAST::LevelSetElementBase::velocity_residual	(	bool	request_jacobian,
		RealVectorX &	f,
		RealMatrixX &	jac_xdot,
		RealMatrixX &	jac
	)

virtual

inertial force contribution to system residual

Definition at line 159 of file level_set_elem_base.cpp.

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bool MAST::LevelSetElementBase::velocity_residual_sensitivity	(	bool	request_jacobian,
		RealVectorX &	f,
		RealMatrixX &	jac
	)

virtual

sensitivity of the damping force contribution to system residual

Definition at line 303 of file level_set_elem_base.cpp.

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Real MAST::LevelSetElementBase::volume ( )

Returns: the element volume over the domain of the element that has positive level set function

Definition at line 314 of file level_set_elem_base.cpp.

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Real MAST::LevelSetElementBase::volume_boundary_velocity_on_side ( unsigned int s )

Returns: the contribution of the side to $\int_\Gamma V_n d\Gamma$ , where is the boundary normal velocity evaluated from the solution and sensitivity.

Definition at line 415 of file level_set_elem_base.cpp.

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bool MAST::LevelSetElementBase::volume_external_residual	(	bool	request_jacobian,
		RealVectorX &	f,
		RealMatrixX &	jac,
		std::multimap< libMesh::subdomain_id_type, MAST::BoundaryConditionBase * > &	bc
	)

volume external force contribution to system residual

Definition at line 250 of file level_set_elem_base.cpp.

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bool MAST::LevelSetElementBase::volume_external_residual_sensitivity	(	bool	request_jacobian,
		RealVectorX &	f,
		RealMatrixX &	jac,
		std::multimap< libMesh::subdomain_id_type, MAST::BoundaryConditionBase * > &	bc
	)

sensitivity of the volume external force contribution to system residual

Definition at line 277 of file level_set_elem_base.cpp.

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Member Data Documentation

bool MAST::LevelSetElementBase::_if_propagation

protected

this can operate in one of two modes: propagation of level set given Vn, or reinitialization of level set so that |grad(phi)|=1

Definition at line 250 of file level_set_elem_base.h.

const MAST::FieldFunction<Real>* MAST::LevelSetElementBase::_phi_vel

protected

element property

Definition at line 244 of file level_set_elem_base.h.

RealVectorX MAST::LevelSetElementBase::_ref_sol

protected

reference solution for reinitialization of the level set

Definition at line 255 of file level_set_elem_base.h.

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

/home/travis/build/MASTmultiphysics/mast-multiphysics/src/level_set/level_set_elem_base.h
/home/travis/build/MASTmultiphysics/mast-multiphysics/src/level_set/level_set_elem_base.cpp

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation