Implementation of the serendipity DDR scheme for the Stokes problem in curl-curl formulation. More...

Collaboration diagram for SDDR_stokes:

Classes
struct	HArDCore3D::StokesNorms
	Structure to store norm components (for velocity, its curl, pressure, and its gradient), as well as Hcurl and Hgrad norms of velocity and pressure. More...

struct	HArDCore3D::Stokes
	Assemble a Stokes problem. More...

Typedefs
typedef Eigen::SparseMatrix< double >	HArDCore3D::Stokes::SystemMatrixType

typedef std::function< Eigen::Vector3d(const Eigen::Vector3d &)>	HArDCore3D::Stokes::ForcingTermType

typedef std::function< Eigen::Vector3d(const Eigen::Vector3d &)>	HArDCore3D::Stokes::VelocityType

typedef std::function< Eigen::Vector3d(const Eigen::Vector3d &)>	HArDCore3D::Stokes::VorticityType

typedef std::function< double(const Eigen::Vector3d &)>	HArDCore3D::Stokes::PressureType

typedef std::function< Eigen::Vector3d(const Eigen::Vector3d &)>	HArDCore3D::Stokes::PressureGradientType

typedef IntegralWeight	HArDCore3D::Stokes::ViscosityType

Functions
	HArDCore3D::StokesNorms::StokesNorms (double norm_u, double norm_curl_u, double norm_p, double norm_grad_p)
	Constructor.

	HArDCore3D::StokesNorms::StokesNorms ()

	HArDCore3D::Stokes::Stokes (const DDRCore &ddrcore, bool use_threads, std::ostream &output=std::cout)
	Constructor.

void	HArDCore3D::Stokes::assembleLinearSystem (const ForcingTermType &f, const VelocityType &u, const VorticityType &omega, const ViscosityType &nu)
	Assemble the global system

size_t	HArDCore3D::Stokes::dimensionSpace () const
	Returns the global problem dimension (without Lagrange multiplier, just velocity & pressure)

size_t	HArDCore3D::Stokes::nbSCDOFs_u () const
	Returns the number of statically condensed DOFs (velocity)

size_t	HArDCore3D::Stokes::nbSCDOFs_p () const
	Returns the number of statically condensed DOFs (pressure)

size_t	HArDCore3D::Stokes::nbSCDOFs () const
	Returns the number of statically condensed DOFs (both velocity and pressure)

size_t	HArDCore3D::Stokes::sizeSystem () const
	Returns the size of the statically condensed system (with Lagrange multiplier)

const SXGrad &	HArDCore3D::Stokes::sxGrad () const
	Returns the space SXGrad.

const SXCurl &	HArDCore3D::Stokes::sxCurl () const
	Returns the space SXCurl.

const SXDiv &	HArDCore3D::Stokes::sxDiv () const
	Returns the space XDiv.

const SystemMatrixType &	HArDCore3D::Stokes::systemMatrix () const
	Returns the linear system matrix.

SystemMatrixType &	HArDCore3D::Stokes::systemMatrix ()
	Returns the linear system matrix.

const Eigen::VectorXd &	HArDCore3D::Stokes::systemVector () const
	Returns the linear system right-hand side vector.

Eigen::VectorXd &	HArDCore3D::Stokes::systemVector ()
	Returns the linear system right-hand side vector.

const SystemMatrixType &	HArDCore3D::Stokes::scMatrix () const
	Returns the static condensation recovery operator.

Eigen::VectorXd &	HArDCore3D::Stokes::scVector ()
	Returns the static condensation rhs.

const double &	HArDCore3D::Stokes::stabilizationParameter () const
	Returns the stabilization parameter.

double &	HArDCore3D::Stokes::stabilizationParameter ()
	Returns the stabilization parameter.

std::vector< StokesNorms >	HArDCore3D::Stokes::computeStokesNorms (const std::vector< Eigen::VectorXd > &list_dofs) const
	Compute the discrete L2 norms, for a family of Eigen::VectorXd representing velocities & pressures, of u, curl u, p and grad p.

std::pair< StokesNorms, StokesNorms >	HArDCore3D::Stokes::computeContinuousErrorsNorms (const Eigen::VectorXd &v, const VelocityType &u, const VorticityType &curl_u, const PressureType &p, const PressureGradientType &grad_p) const
	Compute the continuous Hcurl errors in u and Hgrad error in p (1st component), and same with continuous norms (second component)

Variables
static const double	HArDCore3D::PI = boost::math::constants::pi<double>()

static Stokes::VelocityType	HArDCore3D::trigonometric_u

static Stokes::VorticityType	HArDCore3D::trigonometric_curl_u

static Stokes::PressureType	HArDCore3D::trigonometric_p

static Stokes::PressureGradientType	HArDCore3D::trigonometric_grad_p

static Stokes::ForcingTermType	HArDCore3D::trigonometric_f

static Stokes::ViscosityType	HArDCore3D::trigonometric_nu = Stokes::ViscosityType(1.)

static Stokes::VelocityType	HArDCore3D::linear_u

static Stokes::VorticityType	HArDCore3D::linear_curl_u

static Stokes::PressureType	HArDCore3D::linear_p

static Stokes::PressureGradientType	HArDCore3D::linear_grad_p

static Stokes::ForcingTermType	HArDCore3D::linear_f

static Stokes::ViscosityType	HArDCore3D::linear_nu = Stokes::ViscosityType(1.)

static Stokes::VelocityType	HArDCore3D::field_u

static Stokes::VorticityType	HArDCore3D::field_curl_u

static Stokes::PressureType	HArDCore3D::field_p

static Stokes::PressureGradientType	HArDCore3D::field_grad_p

static Stokes::ForcingTermType	HArDCore3D::field_f

static Stokes::ViscosityType	HArDCore3D::field_nu = Stokes::ViscosityType(1.)

static Stokes::VelocityType	HArDCore3D::vertical_u

static Stokes::VorticityType	HArDCore3D::vertical_curl_u

static Stokes::PressureType	HArDCore3D::vertical_p = trigonometric_p

static Stokes::PressureGradientType	HArDCore3D::vertical_grad_p = trigonometric_grad_p

static Stokes::ForcingTermType	HArDCore3D::vertical_curl_u_cross_u

static Stokes::ForcingTermType	HArDCore3D::vertical_f

Detailed Description

Implementation of the serendipity DDR scheme for the Stokes problem in curl-curl formulation.

Typedef Documentation

◆ ForcingTermType

typedef std::function<Eigen::Vector3d(const Eigen::Vector3d &)> HArDCore3D::Stokes::ForcingTermType

◆ PressureGradientType

typedef std::function<Eigen::Vector3d(const Eigen::Vector3d &)> HArDCore3D::Stokes::PressureGradientType

◆ PressureType

typedef std::function<double(const Eigen::Vector3d &)> HArDCore3D::Stokes::PressureType

◆ SystemMatrixType

typedef Eigen::SparseMatrix<double> HArDCore3D::Stokes::SystemMatrixType

◆ VelocityType

typedef std::function<Eigen::Vector3d(const Eigen::Vector3d &)> HArDCore3D::Stokes::VelocityType

◆ ViscosityType

typedef IntegralWeight HArDCore3D::Stokes::ViscosityType

◆ VorticityType

typedef std::function<Eigen::Vector3d(const Eigen::Vector3d &)> HArDCore3D::Stokes::VorticityType

Function Documentation

◆ assembleLinearSystem()

void HArDCore3D::Stokes::assembleLinearSystem	(	const ForcingTermType &	f,
		const VelocityType &	u,
		const VorticityType &	omega,
		const ViscosityType &	nu
	)

Assemble the global system

Parameters

f	Forcing term
u	Boundary condition on velocity
omega	Boundary condition on vorticity
nu	Viscosity

◆ computeContinuousErrorsNorms()

std::pair< StokesNorms, StokesNorms > HArDCore3D::Stokes::computeContinuousErrorsNorms	(	const Eigen::VectorXd &	v,
		const VelocityType &	u,
		const VorticityType &	curl_u,
		const PressureType &	p,
		const PressureGradientType &	grad_p
	)		const

Compute the continuous Hcurl errors in u and Hgrad error in p (1st component), and same with continuous norms (second component)

Parameters

v	The vector, contains both velocity and pressure
u	Continuous velocity
curl_u	Curl of continuous velocity
p	Continuous pressure
grad_p	Grad of continuous pressure

◆ computeStokesNorms()

std::vector< StokesNorms > HArDCore3D::Stokes::computeStokesNorms ( const std::vector< Eigen::VectorXd > & list_dofs ) const

Compute the discrete L2 norms, for a family of Eigen::VectorXd representing velocities & pressures, of u, curl u, p and grad p.

Parameters

list_dofs List of vectors representing velocities and pressures

◆ dimensionSpace()

size_t HArDCore3D::Stokes::dimensionSpace ( ) const

inline

Returns the global problem dimension (without Lagrange multiplier, just velocity & pressure)

◆ nbSCDOFs()

size_t HArDCore3D::Stokes::nbSCDOFs ( ) const

inline

Returns the number of statically condensed DOFs (both velocity and pressure)

◆ nbSCDOFs_p()

size_t HArDCore3D::Stokes::nbSCDOFs_p ( ) const

inline

Returns the number of statically condensed DOFs (pressure)

◆ nbSCDOFs_u()

size_t HArDCore3D::Stokes::nbSCDOFs_u ( ) const

inline

Returns the number of statically condensed DOFs (velocity)

◆ scMatrix()

const SystemMatrixType & HArDCore3D::Stokes::scMatrix ( ) const

inline

Returns the static condensation recovery operator.

◆ scVector()

Eigen::VectorXd & HArDCore3D::Stokes::scVector ( )

inline

Returns the static condensation rhs.

◆ sizeSystem()

size_t HArDCore3D::Stokes::sizeSystem ( ) const

inline

Returns the size of the statically condensed system (with Lagrange multiplier)

◆ stabilizationParameter() [1/2]

double & HArDCore3D::Stokes::stabilizationParameter ( )

inline

Returns the stabilization parameter.

◆ stabilizationParameter() [2/2]

const double & HArDCore3D::Stokes::stabilizationParameter ( ) const

inline

Returns the stabilization parameter.

◆ Stokes()

HArDCore3D::Stokes::Stokes	(	const DDRCore &	ddrcore,
		bool	use_threads,
		std::ostream &	output = `std::cout`
	)

Constructor.

Parameters

ddrcore	Core for the DDR space sequence
use_threads	True for parallel execution, false for sequential execution
output	Output stream to print status messages

◆ StokesNorms() [1/2]

HArDCore3D::StokesNorms::StokesNorms ( )

inline

◆ StokesNorms() [2/2]

HArDCore3D::StokesNorms::StokesNorms	(	double	norm_u,
		double	norm_curl_u,
		double	norm_p,
		double	norm_grad_p
	)

inline

Constructor.

◆ sxCurl()

const SXCurl & HArDCore3D::Stokes::sxCurl ( ) const

inline

Returns the space SXCurl.

◆ sxDiv()

const SXDiv & HArDCore3D::Stokes::sxDiv ( ) const

inline

Returns the space XDiv.

◆ sxGrad()

const SXGrad & HArDCore3D::Stokes::sxGrad ( ) const

inline

Returns the space SXGrad.

◆ systemMatrix() [1/2]

SystemMatrixType & HArDCore3D::Stokes::systemMatrix ( )

inline

Returns the linear system matrix.

◆ systemMatrix() [2/2]

const SystemMatrixType & HArDCore3D::Stokes::systemMatrix ( ) const

inline

Returns the linear system matrix.

◆ systemVector() [1/2]

Eigen::VectorXd & HArDCore3D::Stokes::systemVector ( )

inline

Returns the linear system right-hand side vector.

◆ systemVector() [2/2]

const Eigen::VectorXd & HArDCore3D::Stokes::systemVector ( ) const

inline

Returns the linear system right-hand side vector.

Variable Documentation

◆ field_curl_u

Stokes::VorticityType HArDCore3D::field_curl_u

static

Initial value:

= [](const Eigen::Vector3d & x) -> Eigen::Vector3d {
                double cux = (PI*PI)*cos(PI*x(0))*cos(PI*x(2))*pow(sin(PI*x(0)),2.0)*pow(sin(PI*x(1)),3.0)*pow(sin(PI*x(2)),2.0)*9.0;
                double cuy = (PI*PI)*cos(PI*x(1))*cos(PI*x(2))*pow(sin(PI*x(0)),3.0)*pow(sin(PI*x(1)),2.0)*pow(sin(PI*x(2)),2.0)*9.0;
                double cuz = (PI*PI)*pow(sin(PI*x(0)),3.0)*pow(sin(PI*x(1)),3.0)*pow(sin(PI*x(2)),3.0)*6.0-(PI*PI)*pow(cos(PI*x(0)),2.0)*sin(PI*x(0))*pow(sin(PI*x(1)),3.0)*pow(sin(PI*x(2)),3.0)*6.0-(PI*PI)*pow(cos(PI*x(1)),2.0)*pow(sin(PI*x(0)),3.0)*sin(PI*x(1))*pow(sin(PI*x(2)),3.0)*6.0;
 
                return Eigen::Vector3d(cux, cuy, cuz);
                }

◆ field_f

Stokes::ForcingTermType HArDCore3D::field_f

static

Initial value:

= [](const Eigen::Vector3d & x) -> Eigen::Vector3d {
              double fx = (PI*PI*PI)*pow(cos(PI*x(1)),3.0)*pow(sin(PI*x(0)),3.0)*pow(sin(PI*x(2)),3.0)*-6.0+(PI*PI*PI)*cos(PI*x(1))*pow(sin(PI*x(0)),3.0)*pow(sin(PI*x(1)),2.0)*pow(sin(PI*x(2)),3.0)*3.9E+1-(PI*PI*PI)*pow(cos(PI*x(0)),2.0)*cos(PI*x(1))*sin(PI*x(0))*pow(sin(PI*x(1)),2.0)*pow(sin(PI*x(2)),3.0)*1.8E+1-(PI*PI*PI)*cos(PI*x(1))*pow(cos(PI*x(2)),2.0)*pow(sin(PI*x(0)),3.0)*pow(sin(PI*x(1)),2.0)*sin(PI*x(2))*1.8E+1;
 
              double fy = (PI*PI*PI)*pow(cos(PI*x(0)),3.0)*pow(sin(PI*x(1)),3.0)*pow(sin(PI*x(2)),3.0)*6.0-(PI*PI*PI)*cos(PI*x(0))*pow(sin(PI*x(0)),2.0)*pow(sin(PI*x(1)),3.0)*pow(sin(PI*x(2)),3.0)*3.9E+1+(PI*PI*PI)*cos(PI*x(0))*pow(cos(PI*x(1)),2.0)*pow(sin(PI*x(0)),2.0)*sin(PI*x(1))*pow(sin(PI*x(2)),3.0)*1.8E+1+(PI*PI*PI)*cos(PI*x(0))*pow(cos(PI*x(2)),2.0)*pow(sin(PI*x(0)),2.0)*pow(sin(PI*x(1)),3.0)*sin(PI*x(2))*1.8E+1;
 
              double fz = 0.;
               return Eigen::Vector3d(fx, fy, fz);
             }

◆ field_grad_p

Stokes::PressureGradientType HArDCore3D::field_grad_p

static

Initial value:

= [](const Eigen::Vector3d & x) -> Eigen::Vector3d {
                    return Eigen::Vector3d(0., 0., 0.);
                  }

◆ field_nu

Stokes::ViscosityType HArDCore3D::field_nu = Stokes::ViscosityType(1.)

static

◆ field_p

Stokes::PressureType HArDCore3D::field_p

static

Initial value:

= [](const Eigen::Vector3d & x) -> double {
               return 0.;
             }

◆ field_u

Stokes::VelocityType HArDCore3D::field_u

static

Initial value:

= [](const Eigen::Vector3d & x) -> Eigen::Vector3d {
               double ux = PI*cos(PI*x(1))*pow(sin(PI*x(0)),3.0)*pow(sin(PI*x(1)),2.0)*pow(sin(PI*x(2)),3.0)*3.0;
               double uy = PI*cos(PI*x(0))*pow(sin(PI*x(0)),2.0)*pow(sin(PI*x(1)),3.0)*pow(sin(PI*x(2)),3.0)*(-3.0);
               return Eigen::Vector3d(ux, uy, 0.);
             }

◆ linear_curl_u

Stokes::VorticityType HArDCore3D::linear_curl_u

static

Initial value:

= [](const Eigen::Vector3d & x) -> Eigen::Vector3d {
                    return Eigen::Vector3d::Zero();
                  }

◆ linear_f

Stokes::ForcingTermType HArDCore3D::linear_f

static

Initial value:

= [](const Eigen::Vector3d & x) -> Eigen::Vector3d {
               return linear_grad_p(x);
             }

◆ linear_grad_p

Stokes::PressureGradientType HArDCore3D::linear_grad_p

static

Initial value:

= [](const Eigen::Vector3d & x) -> Eigen::Vector3d {
                    return pressure_scaling * Eigen::Vector3d(1., -1., 0.);
                  }

◆ linear_nu

Stokes::ViscosityType HArDCore3D::linear_nu = Stokes::ViscosityType(1.)

static

◆ linear_p

Stokes::PressureType HArDCore3D::linear_p

static

Initial value:

= [](const Eigen::Vector3d & x) -> double {
               return pressure_scaling * (x(0) - x(1));
             }

◆ linear_u

Stokes::VelocityType HArDCore3D::linear_u

static

Initial value:

= [](const Eigen::Vector3d & x) -> Eigen::Vector3d {
               return Eigen::Vector3d(x(0), -x(1), 0.);
             }

◆ PI

const double HArDCore3D::PI = boost::math::constants::pi<double>()

static

◆ trigonometric_curl_u

Stokes::VorticityType HArDCore3D::trigonometric_curl_u

static

Initial value:

= [](const Eigen::Vector3d & x) -> Eigen::Vector3d {
                      return 3. * PI * Eigen::Vector3d(
                                                      cos(2. * PI * x(0)) * sin(2. * PI * x(1)) * sin(2. * PI * x(2)),
                                                      -sin(2. * PI * x(0)) * cos(2. * PI * x(1)) * sin(2. * PI * x(2)),
                                                      0.
                                                      );
                         }

◆ trigonometric_f

Stokes::ForcingTermType HArDCore3D::trigonometric_f

static

Initial value:

= [](const Eigen::Vector3d & x) -> Eigen::Vector3d {
                      return 6. * std::pow(PI, 2) * Eigen::Vector3d(
                                                                    sin(2. * PI * x(0)) * cos(2. * PI * x(1)) * cos(2. * PI * x(2)),
                                                                    cos(2. * PI * x(0)) * sin(2. * PI * x(1)) * cos(2. * PI * x(2)),
                                                                    -2. * cos(2. * PI * x(0)) * cos(2. * PI * x(1)) * sin(2. * PI * x(2))
                                                                    )
                        + trigonometric_grad_p(x);
                    }

◆ trigonometric_grad_p

Stokes::PressureGradientType HArDCore3D::trigonometric_grad_p

static

Initial value:

= [](const Eigen::Vector3d & x) -> Eigen::Vector3d {
                      return pressure_scaling * 2. * PI * Eigen::Vector3d(
                                                      cos(2. * PI * x(0)) * sin(2. * PI * x(1)) * sin(2. * PI * x(2)),
                                                      sin(2. * PI * x(0)) * cos(2. * PI * x(1)) * sin(2. * PI * x(2)),
                                                      sin(2. * PI * x(0)) * sin(2. * PI * x(1)) * cos(2. * PI * x(2))
                                                      );
                         }

◆ trigonometric_nu

Stokes::ViscosityType HArDCore3D::trigonometric_nu = Stokes::ViscosityType(1.)

static

◆ trigonometric_p

Stokes::PressureType HArDCore3D::trigonometric_p

static

Initial value:

= [](const Eigen::Vector3d & x) -> double {
                      return pressure_scaling * sin(2. * PI * x(0)) * sin(2. * PI * x(1)) * sin(2. * PI * x(2));
                    }

◆ trigonometric_u

Stokes::VelocityType HArDCore3D::trigonometric_u

static

Initial value:

= [](const Eigen::Vector3d & x) -> Eigen::Vector3d {
                      return Eigen::Vector3d(
                                             0.5 * sin(2. * PI * x(0)) * cos(2. * PI * x(1)) * cos(2. * PI * x(2)),
                                             0.5 * cos(2. * PI * x(0)) * sin(2. * PI * x(1)) * cos(2. * PI * x(2)),
                                             -cos(2. * PI * x(0)) * cos(2. * PI * x(1)) * sin(2. * PI * x(2))
                                             );
                    }

◆ vertical_curl_u

Stokes::VorticityType HArDCore3D::vertical_curl_u

static

Initial value:

= [](const Eigen::Vector3d & x) -> Eigen::Vector3d {
                      return Eigen::Vector3d(0, 0, -PI*sin(PI*x.x()) + PI*sin(PI*x.y()) );
                         }

◆ vertical_curl_u_cross_u

Stokes::ForcingTermType HArDCore3D::vertical_curl_u_cross_u

static

Initial value:

= [](const Eigen::Vector3d & x) -> Eigen::Vector3d {
                      return Eigen::Vector3d (
                                             -(-PI*sin(PI*x.x()) + PI*sin(PI*x.y()))*cos(PI*x.x()),
                                             (-PI*sin(PI*x.x()) + PI*sin(PI*x.y()))*cos(PI*x.y()), 
                                             0.
                                             );
                    }

◆ vertical_f

Stokes::ForcingTermType HArDCore3D::vertical_f

static

Initial value:

= [](const Eigen::Vector3d & x) -> Eigen::Vector3d {
                      return Eigen::Vector3d(pow(PI, 2)*cos(PI*x.y()), pow(PI, 2)*cos(PI*x.x()), 0.)
                        + vertical_grad_p(x);
                    }

◆ vertical_grad_p

Stokes::PressureGradientType HArDCore3D::vertical_grad_p = trigonometric_grad_p

static

◆ vertical_p

Stokes::PressureType HArDCore3D::vertical_p = trigonometric_p

static

◆ vertical_u

Stokes::VelocityType HArDCore3D::vertical_u

static

Initial value:

= [](const Eigen::Vector3d & x) -> Eigen::Vector3d {
                      return Eigen::Vector3d( cos(PI*x.y()), cos(PI*x.x()), 1.);
                    }

Classes

Typedefs

Functions

Variables

Detailed Description

Typedef Documentation

◆ ForcingTermType

◆ PressureGradientType

◆ PressureType

◆ SystemMatrixType

◆ VelocityType

◆ ViscosityType

◆ VorticityType

Function Documentation

◆ assembleLinearSystem()

◆ computeContinuousErrorsNorms()

◆ computeStokesNorms()

◆ dimensionSpace()

◆ nbSCDOFs()

◆ nbSCDOFs_p()

◆ nbSCDOFs_u()

◆ scMatrix()

◆ scVector()

◆ sizeSystem()

◆ stabilizationParameter() [1/2]

◆ stabilizationParameter() [2/2]

◆ Stokes()

◆ StokesNorms() [1/2]

◆ StokesNorms() [2/2]

◆ sxCurl()

◆ sxDiv()

◆ sxGrad()

◆ systemMatrix() [1/2]

◆ systemMatrix() [2/2]

◆ systemVector() [1/2]

◆ systemVector() [2/2]

Variable Documentation

◆ field_curl_u

◆ field_f

◆ field_grad_p

◆ field_nu

◆ field_p

◆ field_u

◆ linear_curl_u

◆ linear_f

◆ linear_grad_p

◆ linear_nu

◆ linear_p

◆ linear_u

◆ PI

◆ trigonometric_curl_u

◆ trigonometric_f

◆ trigonometric_grad_p

◆ trigonometric_nu

◆ trigonometric_p

◆ trigonometric_u

◆ vertical_curl_u

◆ vertical_curl_u_cross_u

◆ vertical_f

◆ vertical_grad_p

◆ vertical_p

◆ vertical_u