BGG_rmplate

Implementation of the DDR-BGG scheme for the Reissner-Mindlin plate problem. More...

Collaboration diagram for BGG_rmplate:

Classes
struct	HArDCore2D::KLNorms
	Structure to store component norms (displacement total energy) More...
struct	HArDCore2D::KirchhoffLove
	Assemble a RM problem. More...
struct	HArDCore2D::RMParameters
	Structure to store model data. More...
struct	HArDCore2D::RMNorms
	Structure to store component norms (for rotation, displacement, Kirchoff term and total energy) More...
struct	HArDCore2D::ReissnerMindlin
	Assemble a RM problem. More...

Typedefs
typedef Eigen::SparseMatrix< double >	HArDCore2D::KirchhoffLove::SystemMatrixType
typedef std::function< double(const Eigen::Vector2d &)>	HArDCore2D::KirchhoffLove::ForcingTermType
typedef std::function< double(const Eigen::Vector2d &)>	HArDCore2D::KirchhoffLove::SolutionDisplacementType
typedef std::function< Eigen::Vector2d(const Eigen::Vector2d &)>	HArDCore2D::KirchhoffLove::GradientDisplacementType
typedef Eigen::SparseMatrix< double >	HArDCore2D::ReissnerMindlin::SystemMatrixType
typedef std::function< double(const RMParameters &, const Eigen::Vector2d &)>	HArDCore2D::ReissnerMindlin::ForcingTermType
typedef std::function< Eigen::Vector2d(const RMParameters &, const Eigen::Vector2d &)>	HArDCore2D::ReissnerMindlin::SolutionRotationType
typedef std::function< Eigen::Matrix2d(const RMParameters &, const Eigen::Vector2d &)>	HArDCore2D::ReissnerMindlin::GradientRotationType
typedef std::function< double(const RMParameters &, const Eigen::Vector2d &)>	HArDCore2D::ReissnerMindlin::SolutionDisplacementType
typedef std::function< Eigen::Vector2d(const RMParameters &, const Eigen::Vector2d &)>	HArDCore2D::ReissnerMindlin::GradientDisplacementType

Functions
	HArDCore2D::KLNorms::KLNorms (double norm_displacement)
	Constructor.
	HArDCore2D::KirchhoffLove::KirchhoffLove (const DDRCore &ddrcore, const DDRCore &ddrcore_plus, const SerendipityProblem &sp, const SerendipityProblem &sp_plus, const BoundaryConditions &BC_u, bool use_threads, std::ostream &output=std::cout)
	Constructor.
void	HArDCore2D::KirchhoffLove::assembleLinearSystem (const ForcingTermType &f, const SolutionDisplacementType &u, const GradientDisplacementType &grad_u, size_t iT_dirac)
	Assemble the global system
size_t	HArDCore2D::KirchhoffLove::dimensionSpace () const
	Returns the dimension of the rotation + displacement space (with BC)
size_t	HArDCore2D::KirchhoffLove::nb_bdryDOFs () const
	Returns the nb of DOFs for BC.
size_t	HArDCore2D::KirchhoffLove::sizeSystem () const
	Returns the size of the system without BC.
const std::vector< std::pair< size_t, size_t > > &	HArDCore2D::KirchhoffLove::locUKN () const
	Returns the location of the unknowns among the DOFs.
std::vector< size_t >	HArDCore2D::KirchhoffLove::globalDOFIndices (const Cell &T) const
	Create the vector of DOF indices for cell T, which combines the DOFs for the spaces VSXgrad and Xhess.
const VSXGrad &	HArDCore2D::KirchhoffLove::vsxGrad () const
	Returns the space VSXGrad.
const XHess &	HArDCore2D::KirchhoffLove::xHess () const
	Returns the space XHess.
const SystemMatrixType &	HArDCore2D::KirchhoffLove::systemMatrix () const
	Returns the linear system matrix.
SystemMatrixType &	HArDCore2D::KirchhoffLove::systemMatrix ()
	Returns the linear system matrix.
const Eigen::VectorXd &	HArDCore2D::KirchhoffLove::systemVector () const
	Returns the linear system right-hand side vector.
Eigen::VectorXd &	HArDCore2D::KirchhoffLove::systemVector ()
	Returns the linear system right-hand side vector.
const SystemMatrixType &	HArDCore2D::KirchhoffLove::bdryMatrix () const
	Returns the Matrix for BC.
const Eigen::VectorXd &	HArDCore2D::KirchhoffLove::bdryValues () const
	Returns the boundary values.
const double &	HArDCore2D::KirchhoffLove::stabilizationParameter () const
	Returns the stabilization parameter.
double &	HArDCore2D::KirchhoffLove::stabilizationParameter ()
	Returns the stabilization parameter.
KLNorms	HArDCore2D::KirchhoffLove::computeNorms (const Eigen::VectorXd &v) const
	Compute the discrete norms: displacement,and energy.
template<typename outValue , typename Fct >
std::function< outValue(const Eigen::Vector2d &)>	HArDCore2D::KirchhoffLove::contractPara (const Fct &F) const
	Takes a function dependent on KLParameter and a position x, and returns a function depending only on x (using the parameters of this class)
	HArDCore2D::RMParameters::RMParameters (const double thickness, const double young_modulus, const double poisson_ratio)
	Constructor.
	HArDCore2D::RMNorms::RMNorms (double norm_rotation, double norm_displacement, double norm_kirchoff)
	Constructor.
	HArDCore2D::ReissnerMindlin::ReissnerMindlin (const DDRCore &ddrcore, const DDRCore &ddrcore_plus, const SerendipityProblem &sp, const SerendipityProblem &sp_plus, const RMParameters &para, const BoundaryConditions &BC_theta, const BoundaryConditions &BC_u, bool use_threads, std::ostream &output=std::cout)
	Constructor.
void	HArDCore2D::ReissnerMindlin::assembleLinearSystem (const ForcingTermType &f, const SolutionRotationType &theta, const GradientRotationType &grad_theta, const SolutionDisplacementType &u, const GradientDisplacementType &grad_u)
	Assemble the global system
size_t	HArDCore2D::ReissnerMindlin::dimensionSpace () const
	Returns the dimension of the rotation + displacement space (with BC)
size_t	HArDCore2D::ReissnerMindlin::nb_bdryDOFs () const
	Returns the nb of DOFs for BC.
size_t	HArDCore2D::ReissnerMindlin::sizeSystem () const
	Returns the size of the system without BC.
const std::vector< std::pair< size_t, size_t > > &	HArDCore2D::ReissnerMindlin::locUKN () const
	Returns the location of the unknowns among the DOFs.
const Eigen::VectorXi &	HArDCore2D::ReissnerMindlin::DOFtoUKN () const
	Returns the map from global DOFs to system unknowns.
const BoundaryConditions &	HArDCore2D::ReissnerMindlin::BC_u () const
	Returns the boundary conditions for u.
std::vector< size_t >	HArDCore2D::ReissnerMindlin::globalDOFIndices (const Cell &T) const
	Create the vector of DOF indices for cell T, which combines the DOFs for the spaces VSXgrad and Xhess.
const RMParameters &	HArDCore2D::ReissnerMindlin::para () const
	Returns the parameters.
const VSXGrad &	HArDCore2D::ReissnerMindlin::vsxGrad () const
	Returns the space VSXGrad.
const VSXCurl &	HArDCore2D::ReissnerMindlin::vsxCurl () const
	Returns the space VSXCurl.
const XHessFull &	HArDCore2D::ReissnerMindlin::xHess () const
	Returns the space XHess.
const SystemMatrixType &	HArDCore2D::ReissnerMindlin::systemMatrix () const
	Returns the linear system matrix.
SystemMatrixType &	HArDCore2D::ReissnerMindlin::systemMatrix ()
	Returns the linear system matrix.
const Eigen::VectorXd &	HArDCore2D::ReissnerMindlin::systemVector () const
	Returns the linear system right-hand side vector.
Eigen::VectorXd &	HArDCore2D::ReissnerMindlin::systemVector ()
	Returns the linear system right-hand side vector.
const SystemMatrixType &	HArDCore2D::ReissnerMindlin::bdryMatrix () const
	Returns the Matrix for BC.
const Eigen::VectorXd &	HArDCore2D::ReissnerMindlin::bdryValues () const
	Returns the boundary values.
const double &	HArDCore2D::ReissnerMindlin::stabilizationParameter () const
	Returns the stabilization parameter.
double &	HArDCore2D::ReissnerMindlin::stabilizationParameter ()
	Returns the stabilization parameter.
RMNorms	HArDCore2D::ReissnerMindlin::computeNorms (const Eigen::VectorXd &v) const
	Compute the discrete norms: rotation, displacement, Kirchoff term, and complete energy.
template<typename outValue , typename Fct >
std::function< outValue(const Eigen::Vector2d &)>	HArDCore2D::ReissnerMindlin::contractPara (const Fct &F) const
	Takes a function dependent on RMParameter and a position x, and returns a function depending only on x (using the parameters of this class)

Variables
double	HArDCore2D::KLNorms::displacement
	Norm of displacement.
double	HArDCore2D::KLNorms::energy
	Total energy.
static const double	HArDCore2D::PI = boost::math::constants::pi<double>()
static KirchhoffLove::SolutionDisplacementType	HArDCore2D::constant_u
static KirchhoffLove::GradientDisplacementType	HArDCore2D::constant_grad_u
static KirchhoffLove::ForcingTermType	HArDCore2D::constant_f
static KirchhoffLove::SolutionDisplacementType	HArDCore2D::polynomial_u
static KirchhoffLove::GradientDisplacementType	HArDCore2D::polynomial_grad_u
static KirchhoffLove::ForcingTermType	HArDCore2D::polynomial_f
static KirchhoffLove::SolutionDisplacementType	HArDCore2D::trigo_u
static KirchhoffLove::GradientDisplacementType	HArDCore2D::trigo_grad_u
static KirchhoffLove::ForcingTermType	HArDCore2D::trigo_f
static KirchhoffLove::SolutionDisplacementType	HArDCore2D::dirac_u
static KirchhoffLove::GradientDisplacementType	HArDCore2D::dirac_grad_u
static KirchhoffLove::ForcingTermType	HArDCore2D::dirac_f
double	HArDCore2D::RMParameters::t
double	HArDCore2D::RMParameters::E
double	HArDCore2D::RMParameters::nu
double	HArDCore2D::RMParameters::beta0
double	HArDCore2D::RMParameters::beta1
double	HArDCore2D::RMParameters::kappa
double	HArDCore2D::RMNorms::rotation
	Norm of rotation.
double	HArDCore2D::RMNorms::displacement
	Norm of displacement.
double	HArDCore2D::RMNorms::kirchoff
	Norm of kirchoff term.
double	HArDCore2D::RMNorms::energy
	Total energy.
static const double	HArDCore2D::PI = boost::math::constants::pi<double>()
static ReissnerMindlin::SolutionRotationType	HArDCore2D::constant_theta
static ReissnerMindlin::GradientRotationType	HArDCore2D::constant_grad_theta
static ReissnerMindlin::SolutionDisplacementType	HArDCore2D::constant_u
static ReissnerMindlin::GradientDisplacementType	HArDCore2D::constant_grad_u
static ReissnerMindlin::ForcingTermType	HArDCore2D::constant_f
static ReissnerMindlin::SolutionRotationType	HArDCore2D::polynomial_theta
static ReissnerMindlin::GradientRotationType	HArDCore2D::polynomial_grad_theta
static ReissnerMindlin::SolutionDisplacementType	HArDCore2D::polynomial_u
static ReissnerMindlin::ForcingTermType	HArDCore2D::polynomial_f
static ReissnerMindlin::GradientDisplacementType	HArDCore2D::polynomial_grad_u
static std::function< double(const VectorRd &)>	HArDCore2D::an_g = [](const VectorRd &x)->double { return sin(PI*x(0))*sin(PI*x(1)); }
static std::function< VectorRd(const VectorRd &)>	HArDCore2D::an_GRAD_g
static std::function< MatrixRd(const VectorRd &)>	HArDCore2D::an_HESS_g
static std::function< double(const VectorRd &)>	HArDCore2D::an_LAPL_g = [](const VectorRd &x)->double { return -2*pow(PI,2)*sin(PI*x(0))*sin(PI*x(1)); }
static std::function< double(const VectorRd &)>	HArDCore2D::an_V = [](const VectorRd &x)->double { return x(0) * exp(-x(0))*cos(x(1)); }
static std::function< VectorRd(const VectorRd &)>	HArDCore2D::an_GRAD_V
static std::function< MatrixRd(const VectorRd &)>	HArDCore2D::an_HESS_V
static std::function< double(const VectorRd &)>	HArDCore2D::an_LAPL_V = [](const VectorRd &x)->double { return -2.* exp(-x(0))*cos(x(1)); }
static ReissnerMindlin::SolutionDisplacementType	HArDCore2D::an_v
static ReissnerMindlin::SolutionRotationType	HArDCore2D::an_GRAD_v
static ReissnerMindlin::GradientRotationType	HArDCore2D::an_HESS_v
static ReissnerMindlin::SolutionDisplacementType	HArDCore2D::an_LAPL_v
static ReissnerMindlin::SolutionRotationType	HArDCore2D::analytical_theta = an_GRAD_v
static ReissnerMindlin::GradientRotationType	HArDCore2D::analytical_grad_theta = an_HESS_v
static ReissnerMindlin::SolutionDisplacementType	HArDCore2D::analytical_u
static ReissnerMindlin::ForcingTermType	HArDCore2D::analytical_f
static std::function< VectorRd(const VectorRd &)>	HArDCore2D::an_GRAD_LAPL_g
static std::function< VectorRd(const VectorRd &)>	HArDCore2D::an_GRAD_LAPL_V
static ReissnerMindlin::SolutionRotationType	HArDCore2D::an_GRAD_LAPL_v
static ReissnerMindlin::GradientDisplacementType	HArDCore2D::analytical_grad_u
static ReissnerMindlin::SolutionRotationType	HArDCore2D::ukn_theta
static ReissnerMindlin::GradientRotationType	HArDCore2D::ukn_grad_theta
static ReissnerMindlin::SolutionDisplacementType	HArDCore2D::ukn_u
static ReissnerMindlin::GradientDisplacementType	HArDCore2D::ukn_grad_u
static ReissnerMindlin::ForcingTermType	HArDCore2D::ukn_f
static ReissnerMindlin::SolutionRotationType	HArDCore2D::kir_theta
static ReissnerMindlin::GradientRotationType	HArDCore2D::kir_grad_theta
static ReissnerMindlin::SolutionDisplacementType	HArDCore2D::kir_u
static ReissnerMindlin::GradientDisplacementType	HArDCore2D::kir_grad_u
static ReissnerMindlin::ForcingTermType	HArDCore2D::kir_f

Detailed Description

Implementation of the DDR-BGG scheme for the Reissner-Mindlin plate problem.

Typedef Documentation

ForcingTermType [1/2]

typedef std::function<double(const Eigen::Vector2d &)> HArDCore2D::KirchhoffLove::ForcingTermType

ForcingTermType [2/2]

typedef std::function<double(const RMParameters &, const Eigen::Vector2d &)> HArDCore2D::ReissnerMindlin::ForcingTermType

GradientDisplacementType [1/2]

typedef std::function<Eigen::Vector2d(const Eigen::Vector2d&)> HArDCore2D::KirchhoffLove::GradientDisplacementType

GradientDisplacementType [2/2]

typedef std::function<Eigen::Vector2d(const RMParameters&, const Eigen::Vector2d&)> HArDCore2D::ReissnerMindlin::GradientDisplacementType

GradientRotationType

typedef std::function<Eigen::Matrix2d(const RMParameters &, const Eigen::Vector2d &)> HArDCore2D::ReissnerMindlin::GradientRotationType

SolutionDisplacementType [1/2]

typedef std::function<double(const Eigen::Vector2d &)> HArDCore2D::KirchhoffLove::SolutionDisplacementType

SolutionDisplacementType [2/2]

typedef std::function<double(const RMParameters &, const Eigen::Vector2d &)> HArDCore2D::ReissnerMindlin::SolutionDisplacementType

SolutionRotationType

typedef std::function<Eigen::Vector2d(const RMParameters &, const Eigen::Vector2d &)> HArDCore2D::ReissnerMindlin::SolutionRotationType

SystemMatrixType [1/2]

typedef Eigen::SparseMatrix<double> HArDCore2D::KirchhoffLove::SystemMatrixType

SystemMatrixType [2/2]

typedef Eigen::SparseMatrix<double> HArDCore2D::ReissnerMindlin::SystemMatrixType

Function Documentation

assembleLinearSystem() [1/2]

void KirchhoffLove::assembleLinearSystem	(	const ForcingTermType &	f,
		const SolutionDisplacementType &	u,
		const GradientDisplacementType &	grad_u,
		size_t	iT_dirac
	)

Assemble the global system

Parameters

f	Forcing term
u	Boundary value
grad_u	Boundary value
iT_dirac	Index of the cell containing the Dirac delta

assembleLinearSystem() [2/2]

void ReissnerMindlin::assembleLinearSystem	(	const ForcingTermType &	f,
		const SolutionRotationType &	theta,
		const GradientRotationType &	grad_theta,
		const SolutionDisplacementType &	u,
		const GradientDisplacementType &	grad_u
	)

Assemble the global system

Parameters

f	Forcing term
theta	Boundary value
grad_theta	Boundary value
u	Boundary value
grad_u	Boundary value

BC_u()

const BoundaryConditions & HArDCore2D::ReissnerMindlin::BC_u ( ) const

inline

Returns the boundary conditions for u.

bdryMatrix() [1/2]

const SystemMatrixType & HArDCore2D::KirchhoffLove::bdryMatrix ( ) const

inline

Returns the Matrix for BC.

bdryMatrix() [2/2]

const SystemMatrixType & HArDCore2D::ReissnerMindlin::bdryMatrix ( ) const

inline

Returns the Matrix for BC.

bdryValues() [1/2]

const Eigen::VectorXd & HArDCore2D::KirchhoffLove::bdryValues ( ) const

inline

Returns the boundary values.

bdryValues() [2/2]

const Eigen::VectorXd & HArDCore2D::ReissnerMindlin::bdryValues ( ) const

inline

Returns the boundary values.

computeNorms() [1/2]

KLNorms KirchhoffLove::computeNorms

(

const Eigen::VectorXd &

v

)

const

Compute the discrete norms: displacement,and energy.

Parameters

v	The vector

computeNorms() [2/2]

RMNorms ReissnerMindlin::computeNorms

(

const Eigen::VectorXd &

v

)

const

Compute the discrete norms: rotation, displacement, Kirchoff term, and complete energy.

Parameters

v	The vector

contractPara() [1/2]

template<typename outValue , typename Fct >

std::function< outValue(const Eigen::Vector2d &)> HArDCore2D::KirchhoffLove::contractPara ( const Fct &  F ) const

inline

Takes a function dependent on KLParameter and a position x, and returns a function depending only on x (using the parameters of this class)

contractPara() [2/2]

template<typename outValue , typename Fct >

std::function< outValue(const Eigen::Vector2d &)> HArDCore2D::ReissnerMindlin::contractPara ( const Fct &  F ) const

inline

Takes a function dependent on RMParameter and a position x, and returns a function depending only on x (using the parameters of this class)

dimensionSpace() [1/2]

size_t HArDCore2D::KirchhoffLove::dimensionSpace ( ) const

inline

Returns the dimension of the rotation + displacement space (with BC)

dimensionSpace() [2/2]

size_t HArDCore2D::ReissnerMindlin::dimensionSpace ( ) const

inline

Returns the dimension of the rotation + displacement space (with BC)

DOFtoUKN()

const Eigen::VectorXi & HArDCore2D::ReissnerMindlin::DOFtoUKN ( ) const

inline

Returns the map from global DOFs to system unknowns.

globalDOFIndices() [1/2]

std::vector< size_t > HArDCore2D::KirchhoffLove::globalDOFIndices ( const Cell &  T ) const

inline

Create the vector of DOF indices for cell T, which combines the DOFs for the spaces VSXgrad and Xhess.

globalDOFIndices() [2/2]

std::vector< size_t > HArDCore2D::ReissnerMindlin::globalDOFIndices ( const Cell &  T ) const

inline

Create the vector of DOF indices for cell T, which combines the DOFs for the spaces VSXgrad and Xhess.

KirchhoffLove()

KirchhoffLove::KirchhoffLove	(	const DDRCore &	ddrcore,
		const DDRCore &	ddrcore_plus,
		const SerendipityProblem &	sp,
		const SerendipityProblem &	sp_plus,
		const BoundaryConditions &	BC_u,
		bool	use_threads,
		std::ostream &	output = std::cout
	)

Constructor.

Parameters

ddrcore	Core for the DDR space sequence
ddrcore_plus	Core for the DDR space sequence of degree +1
sp_plus	Serendipity problem of degree +1
BC_u	Boundary conditions for displacement
use_threads	True for parallel execution, false for sequential execution
output	Output stream to print status messages

KLNorms()

HArDCore2D::KLNorms::KLNorms ( double  norm_displacement )

inline

Constructor.

locUKN() [1/2]

const std::vector< std::pair< size_t, size_t > > & HArDCore2D::KirchhoffLove::locUKN ( ) const

inline

Returns the location of the unknowns among the DOFs.

locUKN() [2/2]

const std::vector< std::pair< size_t, size_t > > & HArDCore2D::ReissnerMindlin::locUKN ( ) const

inline

Returns the location of the unknowns among the DOFs.

nb_bdryDOFs() [1/2]

size_t HArDCore2D::KirchhoffLove::nb_bdryDOFs ( ) const

inline

Returns the nb of DOFs for BC.

nb_bdryDOFs() [2/2]

size_t HArDCore2D::ReissnerMindlin::nb_bdryDOFs ( ) const

inline

Returns the nb of DOFs for BC.

para()

const RMParameters & HArDCore2D::ReissnerMindlin::para ( ) const

inline

Returns the parameters.

ReissnerMindlin()

ReissnerMindlin::ReissnerMindlin	(	const DDRCore &	ddrcore,
		const DDRCore &	ddrcore_plus,
		const SerendipityProblem &	sp,
		const SerendipityProblem &	sp_plus,
		const RMParameters &	para,
		const BoundaryConditions &	BC_theta,
		const BoundaryConditions &	BC_u,
		bool	use_threads,
		std::ostream &	output = std::cout
	)

Constructor.

Parameters

ddrcore	Core for the DDR space sequence
ddrcore_plus	Core for the DDR space sequence of degree +1
sp_plus	Serendipity problem of degree +1
para	Physical parameters
BC_theta	Boundary conditions for rotation
BC_u	Boundary conditions for displacement
use_threads	True for parallel execution, false for sequential execution
output	Output stream to print status messages

RMNorms()

HArDCore2D::RMNorms::RMNorms ( double  norm_rotation, double  norm_displacement, double  norm_kirchoff  )

inline

Constructor.

RMParameters()

HArDCore2D::RMParameters::RMParameters ( const double  thickness, const double  young_modulus, const double  poisson_ratio  )

inline

Constructor.

sizeSystem() [1/2]

size_t HArDCore2D::KirchhoffLove::sizeSystem ( ) const

inline

Returns the size of the system without BC.

sizeSystem() [2/2]

size_t HArDCore2D::ReissnerMindlin::sizeSystem ( ) const

inline

Returns the size of the system without BC.

stabilizationParameter() [1/4]

double & HArDCore2D::KirchhoffLove::stabilizationParameter ( )

inline

Returns the stabilization parameter.

stabilizationParameter() [2/4]

double & HArDCore2D::ReissnerMindlin::stabilizationParameter ( )

inline

Returns the stabilization parameter.

stabilizationParameter() [3/4]

const double & HArDCore2D::KirchhoffLove::stabilizationParameter ( ) const

inline

Returns the stabilization parameter.

stabilizationParameter() [4/4]

const double & HArDCore2D::ReissnerMindlin::stabilizationParameter ( ) const

inline

Returns the stabilization parameter.

systemMatrix() [1/4]

SystemMatrixType & HArDCore2D::KirchhoffLove::systemMatrix ( )

inline

Returns the linear system matrix.

systemMatrix() [2/4]

SystemMatrixType & HArDCore2D::ReissnerMindlin::systemMatrix ( )

inline

Returns the linear system matrix.

systemMatrix() [3/4]

const SystemMatrixType & HArDCore2D::KirchhoffLove::systemMatrix ( ) const

inline

Returns the linear system matrix.

systemMatrix() [4/4]

const SystemMatrixType & HArDCore2D::ReissnerMindlin::systemMatrix ( ) const

inline

Returns the linear system matrix.

systemVector() [1/4]

Eigen::VectorXd & HArDCore2D::KirchhoffLove::systemVector ( )

inline

Returns the linear system right-hand side vector.

systemVector() [2/4]

Eigen::VectorXd & HArDCore2D::ReissnerMindlin::systemVector ( )

inline

Returns the linear system right-hand side vector.

systemVector() [3/4]

const Eigen::VectorXd & HArDCore2D::KirchhoffLove::systemVector ( ) const

inline

Returns the linear system right-hand side vector.

systemVector() [4/4]

const Eigen::VectorXd & HArDCore2D::ReissnerMindlin::systemVector ( ) const

inline

Returns the linear system right-hand side vector.

vsxCurl()

const VSXCurl & HArDCore2D::ReissnerMindlin::vsxCurl ( ) const

inline

Returns the space VSXCurl.

vsxGrad() [1/2]

const VSXGrad & HArDCore2D::KirchhoffLove::vsxGrad ( ) const

inline

Returns the space VSXGrad.

vsxGrad() [2/2]

const VSXGrad & HArDCore2D::ReissnerMindlin::vsxGrad ( ) const

inline

Returns the space VSXGrad.

xHess() [1/2]

const XHess & HArDCore2D::KirchhoffLove::xHess ( ) const

inline

Returns the space XHess.

xHess() [2/2]

const XHessFull & HArDCore2D::ReissnerMindlin::xHess ( ) const

inline

Returns the space XHess.

Variable Documentation

an_g

std::function<double(const VectorRd &)> HArDCore2D::an_g = [](const VectorRd &x)->double { return sin(PI*x(0))*sin(PI*x(1)); }

static

an_GRAD_g

std::function<VectorRd(const VectorRd &)> HArDCore2D::an_GRAD_g

static

Initial value:

= [](const VectorRd & x) -> VectorRd {
                 return VectorRd( PI*cos(PI*x(0))*sin(PI*x(1)), PI*sin(PI*x(0))*cos(PI*x(1)) ); 
               }

an_GRAD_LAPL_g

std::function<VectorRd(const VectorRd &)> HArDCore2D::an_GRAD_LAPL_g

static

Initial value:

= [](const VectorRd & x) -> VectorRd {
  return VectorRd(
    -2.0 * pow(PI,3) * cos(PI*x(0)) * sin(PI*x(1)),
    -2.0 * pow(PI,3) * sin(PI*x(0)) * cos(PI*x(1))
  );
}

an_GRAD_LAPL_V

std::function<VectorRd(const VectorRd &)> HArDCore2D::an_GRAD_LAPL_V

static

Initial value:

= [](const VectorRd & x) -> VectorRd {
  return VectorRd(
    2.0 * exp(-x(0)) * cos(x(1)),
    2.0 * exp(-x(0)) * sin(x(1))
  );
}

an_GRAD_LAPL_v

ReissnerMindlin::SolutionRotationType HArDCore2D::an_GRAD_LAPL_v

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> VectorRd {
  return an_GRAD_LAPL_V(x/para.t) + an_GRAD_LAPL_g(x);
}

an_GRAD_V

std::function<VectorRd(const VectorRd &)> HArDCore2D::an_GRAD_V

static

Initial value:

= [](const VectorRd & x) -> VectorRd {
                 return VectorRd((1.-x(0))*exp(-x(0))*cos(x(1)), -x(0)*exp(-x(0))*sin(x(1))); 
               }

an_GRAD_v

ReissnerMindlin::SolutionRotationType HArDCore2D::an_GRAD_v

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> VectorRd {
                 return pow(para.t, 2) * an_GRAD_V(x/para.t) + an_GRAD_g(x);
               }

an_HESS_g

std::function<MatrixRd(const VectorRd &)> HArDCore2D::an_HESS_g

static

Initial value:

= [](const VectorRd & x) -> MatrixRd {
                MatrixRd H = MatrixRd::Zero();
                H.row(0) << -PI*PI*sin(PI*x(0))*sin(PI*x(1)), PI*PI*cos(PI*x(0))*cos(PI*x(1));
                H.row(1) << PI*PI*cos(PI*x(0))*cos(PI*x(1)), -PI*PI*sin(PI*x(0))*sin(PI*x(1));
                return H;
              }

an_HESS_V

std::function<MatrixRd(const VectorRd &)> HArDCore2D::an_HESS_V

static

Initial value:

= [](const VectorRd & x) -> MatrixRd {
                MatrixRd H = MatrixRd::Zero();
                H.row(0) << (x(0)-2.)*exp(-x(0))*cos(x(1)), -(1.-x(0))*exp(-x(0))*sin(x(1));
                H.row(1) << -(1.-x(0))*exp(-x(0))*sin(x(1)), -x(0)*exp(-x(0))*cos(x(1));
                return H;
              }

an_HESS_v

ReissnerMindlin::GradientRotationType HArDCore2D::an_HESS_v

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> MatrixRd {
                  return para.t * an_HESS_V(x/para.t) + an_HESS_g(x);
              }

an_LAPL_g

std::function<double(const VectorRd &)> HArDCore2D::an_LAPL_g = [](const VectorRd &x)->double { return -2*pow(PI,2)*sin(PI*x(0))*sin(PI*x(1)); }

static

an_LAPL_V

std::function<double(const VectorRd &)> HArDCore2D::an_LAPL_V = [](const VectorRd &x)->double { return -2.* exp(-x(0))*cos(x(1)); }

static

an_LAPL_v

ReissnerMindlin::SolutionDisplacementType HArDCore2D::an_LAPL_v

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> double {
                     return para.t * (an_LAPL_V)(x/para.t) + an_LAPL_g(x);
                   }

an_V

std::function<double(const VectorRd &)> HArDCore2D::an_V = [](const VectorRd &x)->double { return x(0) * exp(-x(0))*cos(x(1)); }

static

an_v

ReissnerMindlin::SolutionDisplacementType HArDCore2D::an_v

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> double {
                     return pow(para.t,3) * an_V(x/para.t) + an_g(x);
                   }

analytical_f

ReissnerMindlin::ForcingTermType HArDCore2D::analytical_f

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> double {
                 return (para.beta0+para.beta1) * 4 * pow(PI,4)*sin(PI*x(0))*sin(PI*x(1));
               }

analytical_grad_theta

ReissnerMindlin::GradientRotationType HArDCore2D::analytical_grad_theta = an_HESS_v

static

analytical_grad_u

ReissnerMindlin::GradientDisplacementType HArDCore2D::analytical_grad_u

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> VectorRd {
  return an_GRAD_v(para, x)
       - pow(para.t, 2) * ((para.beta0 + para.beta1) / para.kappa)
         * an_GRAD_LAPL_v(para, x);
}

analytical_theta

ReissnerMindlin::SolutionRotationType HArDCore2D::analytical_theta = an_GRAD_v

static

analytical_u

ReissnerMindlin::SolutionDisplacementType HArDCore2D::analytical_u

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> double {
                     return an_v(para, x) - pow(para.t,2) * ( (para.beta0+para.beta1)/para.kappa ) * an_LAPL_v(para, x);
                   }

beta0

double HArDCore2D::RMParameters::beta0

beta1

double HArDCore2D::RMParameters::beta1

constant_f [1/2]

KirchhoffLove::ForcingTermType HArDCore2D::constant_f

static

Initial value:

= [](const VectorRd & x) -> double {
                 return 0.;
               }

constant_f [2/2]

ReissnerMindlin::ForcingTermType HArDCore2D::constant_f

static

Initial value:

= [](const RMParameters &, const VectorRd &) -> double {
    return 0.0;
}

constant_grad_theta

ReissnerMindlin::GradientRotationType HArDCore2D::constant_grad_theta

static

Initial value:

= [](const RMParameters &, const VectorRd &) -> Eigen::Matrix2d {
    return Eigen::Matrix2d::Zero();
}

constant_grad_u [1/2]

KirchhoffLove::GradientDisplacementType HArDCore2D::constant_grad_u

static

Initial value:

= [](const VectorRd & ) -> VectorRd{
                    return VectorRd::Zero();
                }

constant_grad_u [2/2]

ReissnerMindlin::GradientDisplacementType HArDCore2D::constant_grad_u

static

Initial value:

= [](const RMParameters &, const VectorRd &) -> VectorRd {
    VectorRd g;
    g.setZero();
    g(0) = 1.0;
    return g;
}

constant_theta

ReissnerMindlin::SolutionRotationType HArDCore2D::constant_theta

static

Initial value:

= [](const RMParameters &, const VectorRd &) -> VectorRd {
    return VectorRd(1, 0.);
}

constant_u [1/2]

KirchhoffLove::SolutionDisplacementType HArDCore2D::constant_u

static

Initial value:

= [](const VectorRd & x) -> double {
                     return 1.;
                   }

constant_u [2/2]

ReissnerMindlin::SolutionDisplacementType HArDCore2D::constant_u

static

Initial value:

= [](const RMParameters &, const VectorRd & x) -> double {
    return x(0);
}

dirac_f

KirchhoffLove::ForcingTermType HArDCore2D::dirac_f

static

Initial value:

= [](const VectorRd & x) -> double {
  const double rayon = 1e-2;
  const VectorRd center(0.3, 0.7);
 
  if ((x - center).squaredNorm() < rayon*rayon) {
      return 1.0 / (M_PI*rayon*rayon);  
  } else {
      return 0.0;
  }
}

dirac_grad_u

KirchhoffLove::GradientDisplacementType HArDCore2D::dirac_grad_u

static

Initial value:

= [](const VectorRd & x) -> VectorRd {
  VectorRd grad;
  grad(0) = 0.0;
  grad(1) = 0.0;
  return grad;
}

dirac_u

KirchhoffLove::SolutionDisplacementType HArDCore2D::dirac_u

static

Initial value:

= [](const VectorRd & x) -> double {
  return 1.0;
}

displacement [1/2]

double HArDCore2D::KLNorms::displacement

Norm of displacement.

displacement [2/2]

double HArDCore2D::RMNorms::displacement

Norm of displacement.

E

double HArDCore2D::RMParameters::E

energy [1/2]

double HArDCore2D::KLNorms::energy

Total energy.

energy [2/2]

double HArDCore2D::RMNorms::energy

Total energy.

kappa

double HArDCore2D::RMParameters::kappa

kir_f

ReissnerMindlin::ForcingTermType HArDCore2D::kir_f

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> double {
                return sin(PI*x(0))*sin(PI*x(1));
               }

kir_grad_theta

ReissnerMindlin::GradientRotationType HArDCore2D::kir_grad_theta

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> Eigen::Matrix2d {
                 double coef = 12.*(1-pow(para.nu,2))/ (para.E * 4.*pow(PI, 4));
                 Eigen::Matrix2d H = Eigen::Matrix2d::Zero();
                 H.row(0) << -PI*PI*sin(PI*x(0))*sin(PI*x(1)), PI*PI*cos(PI*x(0))*cos(PI*x(1));
                 H.row(1) <<  PI*PI*cos(PI*x(0))*cos(PI*x(1)), -PI*PI*sin(PI*x(0))*sin(PI*x(1));
                 return coef * H;
               }

kir_grad_u

ReissnerMindlin::GradientDisplacementType HArDCore2D::kir_grad_u

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> VectorRd {
                double coef = 12. * (1 - pow(para.nu, 2)) / (para.E * 4. * pow(PI, 4));
                VectorRd grad = VectorRd::Zero();
                grad(0) = coef * PI * cos(PI * x(0)) * sin(PI * x(1));
                grad(1) = coef * PI * sin(PI * x(0)) * cos(PI * x(1));
                return grad;
              }

kir_theta

ReissnerMindlin::SolutionRotationType HArDCore2D::kir_theta

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> VectorRd {
                double coef = 12.*(1-pow(para.nu,2))/ (para.E * 4.*pow(PI, 4));
                return coef * PI * VectorRd(cos(PI*x(0))*sin(PI*x(1)), sin(PI*x(0))*cos(PI*x(1)));
               }

kir_u

ReissnerMindlin::SolutionDisplacementType HArDCore2D::kir_u

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> double {
                  double coef = 12.*(1-pow(para.nu,2))/ (para.E * 4.*pow(PI, 4));
                  return coef  * sin(PI*x(0))*sin(PI*x(1));
               }

kirchoff

double HArDCore2D::RMNorms::kirchoff

Norm of kirchoff term.

nu

double HArDCore2D::RMParameters::nu

PI [1/2]

const double HArDCore2D::PI = boost::math::constants::pi<double>()

static

PI [2/2]

const double HArDCore2D::PI = boost::math::constants::pi<double>()

static

polynomial_f [1/2]

KirchhoffLove::ForcingTermType HArDCore2D::polynomial_f

static

Initial value:

= [](const VectorRd & x) -> double {
                 return 120. * (x(0) + x(1));
               }

polynomial_f [2/2]

ReissnerMindlin::ForcingTermType HArDCore2D::polynomial_f

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> double {
                double val = 0;
                
                val += 12*x(1)*(x(1)-1)*(5*x(0)*x(0)-5*x(0)+1) * 
                        ( 2*x(1)*x(1)*(x(1)-1)*(x(1)-1) + x(0)*(x(0)-1)*(5*x(1)*x(1)-5*x(1)+1) );
                val += 12*x(0)*(x(0)-1)*(5*x(1)*x(1)-5*x(1)+1) * 
                        ( 2*x(0)*x(0)*(x(0)-1)*(x(0)-1) + x(1)*(x(1)-1)*(5*x(0)*x(0)-5*x(0)+1) );
                
                return val * para.E / (12* (1.-para.nu*para.nu) );
               }

polynomial_grad_theta

ReissnerMindlin::GradientRotationType HArDCore2D::polynomial_grad_theta

static

polynomial_grad_u [1/2]

KirchhoffLove::GradientDisplacementType HArDCore2D::polynomial_grad_u

static

Initial value:

= [](const VectorRd & x) -> VectorRd {
      VectorRd grad;
      grad(0) = 5.0 * pow(x(0), 4);
      grad(1) = 5.0 * pow(x(1), 4);
  return grad;
  }

polynomial_grad_u [2/2]

ReissnerMindlin::GradientDisplacementType HArDCore2D::polynomial_grad_u

static

polynomial_theta

ReissnerMindlin::SolutionRotationType HArDCore2D::polynomial_theta

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> VectorRd {
                 return VectorRd(
                          pow(x(1),3)*pow(x(1)-1,3)*pow(x(0),2)*pow(x(0)-1,2)*(2*x(0)-1),
                          pow(x(0),3)*pow(x(0)-1,3)*pow(x(1),2)*pow(x(1)-1,2)*(2*x(1)-1)
                          );
               }

polynomial_u [1/2]

KirchhoffLove::SolutionDisplacementType HArDCore2D::polynomial_u

static

Initial value:

= [](const VectorRd & x) -> double {
    return pow(x(0), 5) + pow(x(1), 5);
  }

polynomial_u [2/2]

ReissnerMindlin::SolutionDisplacementType HArDCore2D::polynomial_u

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> double {
                 double val = 0;
                 
                 val += (1./3.)*pow(x(0),3)*pow(x(0)-1,3)*pow(x(1),3)*pow(x(1)-1,3);
                 
                 val -= ( 2*pow(para.t,2) / (5*(1.-para.nu)) ) *
                          ( pow(x(1),3)*pow(x(1)-1,3)*x(0)*(x(0)-1)*(5*x(0)*x(0)-5*x(0)+1)
                            + pow(x(0),3)*pow(x(0)-1,3)*x(1)*(x(1)-1)*(5*x(1)*x(1)-5*x(1)+1) );
                 
                 return val;
                 }

rotation

double HArDCore2D::RMNorms::rotation

Norm of rotation.

t

double HArDCore2D::RMParameters::t

trigo_f

KirchhoffLove::ForcingTermType HArDCore2D::trigo_f

static

Initial value:

= [](const VectorRd & x) -> double {
  double u = std::sin(M_PI * x(0)) * std::sin(M_PI * x(1));
  return 4.0 * std::pow(M_PI, 4) * u;
}

trigo_grad_u

KirchhoffLove::GradientDisplacementType HArDCore2D::trigo_grad_u

static

Initial value:

= [](const VectorRd & x) -> VectorRd {
  VectorRd grad;
  grad(0) = M_PI * std::cos(M_PI * x(0)) * std::sin(M_PI * x(1));
  grad(1) = M_PI * std::sin(M_PI * x(0)) * std::cos(M_PI * x(1));
  return grad;
}

trigo_u

KirchhoffLove::SolutionDisplacementType HArDCore2D::trigo_u

static

Initial value:

= [](const VectorRd & x) -> double {
  return std::sin(M_PI * x(0)) * std::sin(M_PI * x(1));
}

ukn_f

ReissnerMindlin::ForcingTermType HArDCore2D::ukn_f

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> double {
                double val = 1.;
                if (x(0)<.5){
                  val = -1.;
                }
                return val;
               }

ukn_grad_theta

ReissnerMindlin::GradientRotationType HArDCore2D::ukn_grad_theta

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> Eigen::Matrix2d {
                 return Eigen::Matrix2d::Zero();
               }

ukn_grad_u

ReissnerMindlin::GradientDisplacementType HArDCore2D::ukn_grad_u

static

Initial value:

= [](const RMParameters & , const VectorRd & ) -> VectorRd {
  VectorRd grad = VectorRd::Zero();
  grad(0) = 1.0;
                    return grad;
                  }

ukn_theta

ReissnerMindlin::SolutionRotationType HArDCore2D::ukn_theta

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> VectorRd {
                 return VectorRd(0., 0.);
               }

ukn_u

ReissnerMindlin::SolutionDisplacementType HArDCore2D::ukn_u

static

Initial value:

= [](const RMParameters & para, const VectorRd & x) -> double {
                     return x(0);
                   }