BiharmonicTestFunctions2 Namespace Reference

Functions
void	boundary_N (const double &s, Vector< double > &r)
void	boundary_E (const double &s, Vector< double > &r)
void	boundary_S (const double &s, Vector< double > &r)
void	boundary_W (const double &s, Vector< double > &r)
void	normal_N (const double &s, Vector< double > &n)
void	normal_E (const double &s, Vector< double > &n)
void	normal_S (const double &s, Vector< double > &n)
void	normal_W (const double &s, Vector< double > &n)
void	u_N (const double &s, double &u)
void	u_E (const double &s, double &u)
void	u_S (const double &s, double &u)
void	u_W (const double &s, double &u)
double	dudx_0 (const Vector< double > x)
double	dudx_1 (const Vector< double > x)
void	dudn_N (const double &s, double &dudn)
void	dudn_E (const double &s, double &dudn)
void	dudn_S (const double &s, double &dudn)
void	dudn_W (const double &s, double &dudn)
void	surface_load (const Vector< double > &x, double &f)
void	solution (const Vector< double > &x, Vector< double > &u)

Variables
double	Pi = MathematicalConstants::Pi
double	theta = Pi/4
double	r_min = sqrt(1*Pi)
double	r_max = sqrt(3*Pi)

Function Documentation

boundary_E()

void BiharmonicTestFunctions2::boundary_E	(	const double &	s,
		Vector< double > &	r
	)

 {    
  r[0] = r_max * cos((s+1)*theta/2);
  r[1] = r_max * sin((s+1)*theta/2);
 } 

References cos(), UniformPSDSelfTest::r, r_max, s, sin(), and theta.

Referenced by BiharmonicTestProblem2::BiharmonicTestProblem2(), and dudn_E().

boundary_N()

void BiharmonicTestFunctions2::boundary_N	(	const double &	s,
		Vector< double > &	r
	)

 {  
  r[0] = (r_min + (0.5*(s+1)*(r_max-r_min)))*cos(theta);  
  r[1] = (r_min + (0.5*(s+1)*(r_max-r_min)))*sin(theta);
 }

References cos(), UniformPSDSelfTest::r, r_max, r_min, s, sin(), and theta.

Referenced by BiharmonicTestProblem2::BiharmonicTestProblem2(), and dudn_N().

boundary_S()

void BiharmonicTestFunctions2::boundary_S	(	const double &	s,
		Vector< double > &	r
	)

 {
  r[0] = r_min + (0.5*(s+1)*(r_max-r_min));  
  r[1] = 0.0;
 }

References UniformPSDSelfTest::r, r_max, r_min, and s.

Referenced by BiharmonicTestProblem2::BiharmonicTestProblem2().

boundary_W()

void BiharmonicTestFunctions2::boundary_W	(	const double &	s,
		Vector< double > &	r
	)

 {
  r[0] = r_min * cos((s+1)*theta/2);
  r[1] = r_min * sin((s+1)*theta/2);
 }

References cos(), UniformPSDSelfTest::r, r_min, s, sin(), and theta.

Referenced by BiharmonicTestProblem2::BiharmonicTestProblem2(), and dudn_W().

dudn_E()

void BiharmonicTestFunctions2::dudn_E	(	const double &	s,
		double &	dudn
	)

 {  
  Vector<double> x(2);
  boundary_E(s,x);
  Vector<double> n(2);
  normal_E(s,n);
  dudn = dudx_0(x)*n[0] + dudx_1(x)*n[1];
 }

References boundary_E(), dudx_0(), dudx_1(), n, normal_E(), s, and plotDoE::x.

Referenced by BiharmonicTestProblem2::BiharmonicTestProblem2().

dudn_N()

void BiharmonicTestFunctions2::dudn_N	(	const double &	s,
		double &	dudn
	)

 {  
  Vector<double> x(2);
  boundary_N(s,x);
  Vector<double> n(2);
  normal_N(s,n);
  dudn = dudx_0(x)*n[0] + dudx_1(x)*n[1];
 }

References boundary_N(), dudx_0(), dudx_1(), n, normal_N(), s, and plotDoE::x.

Referenced by BiharmonicTestProblem2::BiharmonicTestProblem2().

dudn_S()

void BiharmonicTestFunctions2::dudn_S	(	const double &	s,
		double &	dudn
	)

 {
  double x = r_min+0.5*(s+1)*(r_max-r_min);
  dudn = -sin(x*x)/x;
 }

References r_max, r_min, s, sin(), and plotDoE::x.

Referenced by BiharmonicTestProblem2::BiharmonicTestProblem2().

dudn_W()

void BiharmonicTestFunctions2::dudn_W	(	const double &	s,
		double &	dudn
	)

 {  
  Vector<double> x(2);
  boundary_W(s,x);
  Vector<double> n(2);
  normal_W(s,n);
  dudn = dudx_0(x)*n[0] + dudx_1(x)*n[1];
 } 

References boundary_W(), dudx_0(), dudx_1(), n, normal_W(), s, and plotDoE::x.

Referenced by BiharmonicTestProblem2::BiharmonicTestProblem2().

dudx_0()

double BiharmonicTestFunctions2::dudx_0

(

const Vector< double >

x

)

 {
  return(2*cos(x[0]*x[0]+x[1]*x[1])*x[1]
         -sin(x[0]*x[0]+x[1]*x[1])*x[1]/(x[0]*x[0]));
 }

References cos(), sin(), and plotDoE::x.

Referenced by dudn_E(), dudn_N(), and dudn_W().

dudx_1()

double BiharmonicTestFunctions2::dudx_1

(

const Vector< double >

x

)

 {
  return(2*cos(x[0]*x[0]+x[1]*x[1])*x[1]*x[1]/x[0]
         +sin(x[0]*x[0]+x[1]*x[1])/x[0]);
 }

References cos(), sin(), and plotDoE::x.

Referenced by dudn_E(), dudn_N(), and dudn_W().

normal_E()

void BiharmonicTestFunctions2::normal_E	(	const double &	s,
		Vector< double > &	n
	)

 {
  double t = (s+1)*theta/2; 
  n[0] = cos(t);
  n[1] = sin(t);
 }

References cos(), n, s, sin(), plotPSD::t, and theta.

Referenced by dudn_E().

normal_N()

void BiharmonicTestFunctions2::normal_N	(	const double &	s,
		Vector< double > &	n
	)

 {
  n[0] = -sin(theta);
  n[1] = cos(theta);
 }

References cos(), n, sin(), and theta.

Referenced by dudn_N().

normal_S()

void BiharmonicTestFunctions2::normal_S	(	const double &	s,
		Vector< double > &	n
	)

 {
  n[0] = 0.0;
  n[1] = -1.0;
 }

References n.

normal_W()

void BiharmonicTestFunctions2::normal_W	(	const double &	s,
		Vector< double > &	n
	)

 {
  double t = (s+1)*theta/2; 
  n[0] = -cos(t);
  n[1] = -sin(t);
 }

References cos(), n, s, sin(), plotPSD::t, and theta.

Referenced by dudn_W().

solution()

void BiharmonicTestFunctions2::solution	(	const Vector< double > &	x,
		Vector< double > &	u
	)

 {
  u[0] = sin(x[0]*x[0] + x[1]*x[1])*x[1]/x[0];
 }

References sin(), and plotDoE::x.

Referenced by main().

surface_load()

void BiharmonicTestFunctions2::surface_load	(	const Vector< double > &	x,
		double &	f
	)

 {
  double sinr2 = sin(x[0]*x[0]+x[1]*x[1]);
  double cosr2 = cos(x[0]*x[0]+x[1]*x[1]);
  f = (16*sinr2*x[0]*x[0]*x[0]*x[1]
       -64*cosr2*x[0]*x[1]
       -48*sinr2*x[1]/x[0]
       +24*sinr2*x[1]/(x[0]*x[0]*x[0]*x[0]*x[0])
       +16*sinr2*x[1]*x[1]*x[1]*x[1]*x[1]/x[0]
       -64*cosr2*x[1]*x[1]*x[1]/x[0]
       +32*sinr2*x[1]*x[1]*x[1]*x[0]
       -16*sinr2*x[1]*x[1]*x[1]/(x[0]*x[0]*x[0]));
 }

References cos(), f(), sin(), and plotDoE::x.

Referenced by BiharmonicTestProblem1::BiharmonicTestProblem1(), and BiharmonicTestProblem2::BiharmonicTestProblem2().

u_E()

void BiharmonicTestFunctions2::u_E	(	const double &	s,
		double &	u
	)

 {
  double t = (s+1)*theta/2;
  u = sin(r_max*r_max)*tan(t);
 } 

References r_max, s, sin(), plotPSD::t, Eigen::bfloat16_impl::tan(), and theta.

Referenced by BiharmonicTestProblem2::BiharmonicTestProblem2().

u_N()

void BiharmonicTestFunctions2::u_N	(	const double &	s,
		double &	u
	)

 {  
  double r = r_min+0.5*(s+1)*(r_max-r_min);
  u = sin(r*r)*tan(theta);
 }

References UniformPSDSelfTest::r, r_max, r_min, s, sin(), Eigen::bfloat16_impl::tan(), and theta.

Referenced by BiharmonicTestProblem2::BiharmonicTestProblem2().

u_S()

void BiharmonicTestFunctions2::u_S	(	const double &	s,
		double &	u
	)

 {
  u = 0;
 }

Referenced by BiharmonicTestProblem2::BiharmonicTestProblem2().

u_W()

void BiharmonicTestFunctions2::u_W	(	const double &	s,
		double &	u
	)

 {  
  double t = (s+1)*theta/2;
  u = sin(r_min*r_min)*tan(t);
 }

References r_min, s, sin(), plotPSD::t, Eigen::bfloat16_impl::tan(), and theta.

Referenced by BiharmonicTestProblem2::BiharmonicTestProblem2().

Variable Documentation

Pi

double BiharmonicTestFunctions2::Pi = MathematicalConstants::Pi

Referenced by AxisymOscillatingDisk::accel(), MeltContactProblem< ELEMENT >::actions_before_implicit_timestep(), SolarRadiationProblem< ELEMENT >::actions_before_implicit_timestep(), ContactProblem< ELEMENT >::actions_before_implicit_timestep(), FSIDrivenCavityProblem< ELEMENT >::actions_before_implicit_timestep(), PseudoElasticCollapsibleChannelProblem< FLUID_ELEMENT, SOLID_ELEMENT >::actions_before_implicit_timestep(), UnstructuredFSIProblem< FLUID_ELEMENT, SOLID_ELEMENT >::actions_before_implicit_timestep(), UnstructuredFluidProblem< ELEMENT >::actions_before_implicit_timestep(), RayleighProblem< ELEMENT, TIMESTEPPER >::actions_before_implicit_timestep(), Global_Parameters::analytic_solution1(), Global_Parameters::analytic_solution2(), ProblemParameters::atmospheric_radiation(), AxisymmetricVibratingShellProblem< ELEMENT >::AxisymmetricVibratingShellProblem(), AxisymOscillatingDisk::AxisymOscillatingDisk(), Global_parameters::b(), Global_Parameters::blend(), BubbleInChannelProblem< ELEMENT >::BubbleInChannelProblem(), RefineableUnsteadyHeatProblem< ELEMENT >::build_mesh(), check_locate_zeta(), PoissonProblem< ELEMENT >::complex_domain_with_holes(), FlowAroundHalfCylinderProblem< ELEMENT >::compute_drag_nusselt(), ContactProblem< ELEMENT >::ContactProblem(), SinusoidalWall::d2position(), InterfaceProblem< ELEMENT, TIMESTEPPER >::deform_free_surface(), TwoLayerInterfaceProblem< ELEMENT >::deform_interface(), Global_Variables::degtorad(), ContactProblem< ELEMENT >::doc_solution(), GeomObjectAsGeneralisedElementProblem::doc_solution(), RefineableUnsteadyHeatProblem< ELEMENT >::doc_solution(), CapProblem< ELEMENT >::doc_solution(), PseudoSolidCapProblem< ELEMENT >::doc_solution(), OscRingNStProblem< ELEMENT >::doc_solution(), OscEllipseProblem< ELEMENT, TIMESTEPPER >::doc_solution(), OscRingNStProblem< ELEMENT >::doc_solution_historic(), SinusoidalWall::dposition(), DropInChannelProblem< ELEMENT >::DropInChannelProblem(), ElasticAnnulusProblem< ELASTICITY_ELEMENT >::ElasticAnnulusProblem(), ElasticRingProblem< ELEMENT >::ElasticRingProblem(), EultingSphereProblem< ELEMENT >::EultingSphereProblem(), Global_Parameters::exact_axisym_radiated_power(), SarahBL::exact_soln(), Global_Parameters::exact_solution(), PerturbationSolution::first_order_veloc_and_pressure(), Global_Physical_Variables::fluid_inflow_boundary_traction(), Global_Physical_Variables::flux(), Global_Parameters::flux(), ProblemParameters::flux(), oomph::Problem_Parameter::free_surface_profile(), FreeSurfaceRotationProblem< ELEMENT >::FreeSurfaceRotationProblem(), SarahBL::full_exact_soln(), Global_Physical_Variables::get_exact_u(), ExactSoln::get_exact_u(), GlobalParameters::get_exact_u(), TanhSolnForUnsteadyHeat::get_exact_u(), Global_parameters::get_exact_u(), GlobalFct::get_residuals(), TanhSolnForUnsteadyHeat::get_source(), Global_Parameters::grad_blend(), Global_parameters::grad_f1(), Global_parameters::grad_f2(), Global_Parameters::grad_pressure_singularity1(), Global_Parameters::grad_velocity_singularity1(), Global_Parameters::grad_velocity_singularity2(), PoissonProblem< ELEMENT >::half_circle_domain(), PoissonProblem< ELEMENT >::half_circle_domain_with_internal_boundaries(), Global_Physical_Variables::height(), HomogenisationProblem< ELEMENT >::HomogenisationProblem(), PerturbationSolution::leading_order_veloc_and_pressure(), LinearWaveProblem< ELEMENT, TIMESTEPPER >::LinearWaveProblem(), Flag_definition::lower_tip(), main(), MeltContactProblem< ELEMENT >::MeltContactProblem(), MyHelicalCylinder::MyHelicalCylinder(), OscEllipseProblem< ELEMENT, TIMESTEPPER >::OscEllipseProblem(), oomph::Problem_Parameter::oscillation(), OscRingNStProblem< ELEMENT >::OscRingNStProblem(), HeatedCircularPenetratorElement::output(), CircularPenetratorElement::output(), ElasticBeamProblem::parameter_study(), CapProblem< ELEMENT >::parameter_study(), PseudoSolidCapProblem< ELEMENT >::parameter_study(), Global_Parameters::periodic_traction(), Leaflet::position(), Flag_definition::TopOfFlag::position(), Flag_definition::BottomOfFlag::position(), OscillatingWall::position(), GeneralCircle::position(), MyHelicalCylinder::position(), MyEllipse::position(), AxisymOscillatingDisk::position(), WarpedLine::position(), WarpedPlane::position(), WavyWall::position(), SinusoidalWall::position(), GlobalParameters::prescribed_flux_on_fixed_y_boundary(), TanhSolnForUnsteadyHeat::prescribed_flux_on_fixed_y_boundary(), GlobalPhysicalParameters::prescribed_pressure_gradient(), ExactSoln::prescribed_traction(), GlobalPhysicalParameters::prescribed_volume_flux(), Global_Parameters::pressure_load(), Global_Parameters::pressure_singularity1(), Global_Parameters::pressure_singularity2(), PseudoElasticCollapsibleChannelProblem< FLUID_ELEMENT, SOLID_ELEMENT >::PseudoElasticCollapsibleChannelProblem(), RefineableElutingSphereProblem< ELEMENT >::RefineableElutingSphereProblem(), RefineableSphereConvectionProblem< ELEMENT >::RefineableSphereConvectionProblem(), RefineableSphericalCouetteProblem< ELEMENT >::RefineableSphericalCouetteProblem(), RefineableSphericalSpinUpProblem< ELEMENT >::RefineableSphericalSpinUpProblem(), RefineableUnsteadyHeatProblem< ELEMENT >::RefineableUnsteadyHeatProblem(), RingWithTRibProblem< ELASTICITY_ELEMENT >::RingWithTRibProblem(), run_navier_stokes_outflow(), PerturbationSolution::second_order_veloc_and_pressure(), GlobalParameters::setup_dependent_parameters_and_sanity_check(), RefineableDrivenCavityProblem< ELEMENT >::setup_line_plot_points(), RectangularDrivenCavityProblem< ELEMENT >::setup_line_plot_points(), GlobalParameters::sin_cos_velocity_field(), GlobalParameters::sin_cos_vorticity(), SolarRadiationProblem< ELEMENT >::SolarRadiationProblem(), SolidFreeSurfaceRotationProblem< ELEMENT >::SolidFreeSurfaceRotationProblem(), Global_parameters::source_function(), SphericalSpinUpProblem< ELEMENT >::SphericalSpinUpProblem(), SphericalSteadyRotationProblem< ELEMENT >::SphericalSteadyRotationProblem(), SteadyCurvedTubeProblem< ELEMENT >::SteadyCurvedTubeProblem(), SteadyHelicalProblem< ELEMENT >::SteadyHelicalProblem(), SteadyTubeProblem< ELEMENT >::SteadyTubeProblem(), GlobalParameters::step_position(), TanhSolnForUnsteadyHeat::step_position(), HeatedCircularPenetratorElement::temperature(), TorusProblem< ELEMENT >::TorusProblem(), ElasticInterfaceProblem< ELEMENT, TIMESTEPPER >::unsteady_run(), UnstructuredFluidProblem< ELEMENT >::UnstructuredFluidProblem(), UnstructuredFvKProblem< ELEMENT >::UnstructuredFvKProblem(), UnstructuredImmersedEllipseProblem< ELEMENT >::UnstructuredImmersedEllipseProblem(), UnstructuredPoissonProblem< ELEMENT >::UnstructuredPoissonProblem(), UnstructuredTorusProblem< ELEMENT >::UnstructuredTorusProblem(), Flag_definition::upper_tip(), AxisymOscillatingDisk::veloc(), Global_Parameters::velocity_singularity1(), Global_Parameters::velocity_singularity2(), VibratingShellProblem< ELEMENT >::VibratingShellProblem(), WallMesh< ELEMENT >::WallMesh(), and Wind_fct_pt().

r_max

double BiharmonicTestFunctions2::r_max = sqrt(3*Pi)

Referenced by AnnularQuadMesh< ELEMENT >::AnnularQuadMesh(), oomph::AnnularSpineMesh< ELEMENT >::AnnularSpineMesh(), boundary_E(), boundary_N(), boundary_S(), dudn_S(), FourierDecomposedHelmholtzProblem< ELEMENT >::FourierDecomposedHelmholtzProblem(), PolarNSProblem< ELEMENT >::get_symmetry(), InterfaceProblem< ELEMENT, TIMESTEPPER >::InterfaceProblem(), main(), PMLFourierDecomposedHelmholtzProblem< ELEMENT >::PMLFourierDecomposedHelmholtzProblem(), PseudoElasticCollapsibleChannelProblem< FLUID_ELEMENT, SOLID_ELEMENT >::PseudoElasticCollapsibleChannelProblem(), RefineableDrivenCavityProblem< ELEMENT >::setup_line_plot_points(), RectangularDrivenCavityProblem< ELEMENT >::setup_line_plot_points(), u_E(), u_N(), and WallMesh< ELEMENT >::WallMesh().

r_min

double BiharmonicTestFunctions2::r_min = sqrt(1*Pi)

Referenced by AnnularQuadMesh< ELEMENT >::AnnularQuadMesh(), oomph::AnnularSpineMesh< ELEMENT >::AnnularSpineMesh(), boundary_N(), boundary_S(), boundary_W(), dudn_S(), FourierDecomposedHelmholtzProblem< ELEMENT >::FourierDecomposedHelmholtzProblem(), PolarNSProblem< ELEMENT >::get_symmetry(), InterfaceProblem< ELEMENT, TIMESTEPPER >::InterfaceProblem(), main(), PMLFourierDecomposedHelmholtzProblem< ELEMENT >::PMLFourierDecomposedHelmholtzProblem(), PseudoElasticCollapsibleChannelProblem< FLUID_ELEMENT, SOLID_ELEMENT >::PseudoElasticCollapsibleChannelProblem(), u_N(), u_W(), and WallMesh< ELEMENT >::WallMesh().

theta

double BiharmonicTestFunctions2::theta = Pi/4

Referenced by oomph::SphericalNavierStokesEquations::actual(), oomph::SphericalNavierStokesEquations::actual_dr(), oomph::SphericalNavierStokesEquations::actual_dth(), Global_Parameters::analytic_solution1(), Global_Parameters::analytic_solution2(), oomph::AnnularSpineMesh< ELEMENT >::AnnularSpineMesh(), oomph::SolarRadiationBase::atmospheric_radiation(), boundary_E(), boundary_N(), boundary_W(), check_locate_zeta(), check_slerp(), oomph::SphericalNavierStokesEquations::compute_error_e(), oomph::FourierDecomposedHelmholtzDtNBoundaryElement< ELEMENT >::compute_gamma_contribution(), BaseCluster::computeInternalStructure(), SinterLinInteraction::computeNormalForce(), computeRoots(), Eigen::internal::direct_selfadjoint_eigenvalues< SolverType, 3, false >::computeRoots(), oomph::DiskWithTorusAroundEdgeTetMeshFacetedSurface::DiskWithTorusAroundEdgeTetMeshFacetedSurface(), ProblemParameters::exact_minus_dudr(), Global::exact_solution(), oomph::SphericalNavierStokesEquations::extract_velocity(), oomph::LineFluidInterfaceBoundingElement::fill_in_generic_residual_contribution_interface_boundary(), oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::fill_in_off_diagonal_jacobian_blocks_analytic(), FreeSurfaceRotationProblem< ELEMENT >::FreeSurfaceRotationProblem(), PlanarWave::get_exact_u(), ProblemParameters::get_exact_u(), GlobalParameters::get_exact_u(), oomph::SphericalNavierStokesEquations::get_pressure_and_velocity_mass_matrix_diagonal(), StokesFlowExactWind::get_wind(), RNG::getNormalVariate(), getQuadratureValues95(), oomph::FourierDecomposedHelmholtzBCElementBase< ELEMENT >::global_power_contribution(), oomph::PMLFourierDecomposedHelmholtzPowerMonitorElement< ELEMENT >::global_power_contribution(), LoadFinalOrient(), LoadInitOrient(), oomph::AnnularDomain::macro_element_boundary(), main(), WallFunction::normal(), normal_E(), normal_N(), normal_W(), oomph::SphericalAdvectionDiffusionEquations::output(), oomph::AxisymmetricPVDEquations::output(), oomph::AxisymDiagHermitePVDElement::output(), oomph::AxisymmetricPVDEquationsWithPressure::output(), oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::output(), oomph::PolarNavierStokesEquations::output(), oomph::SphericalNavierStokesEquations::output(), BaseCluster::particleInsertionSuccessful(), GlobalParameters::prescribed_incoming_flux(), Global_Parameters::pressure_singularity1(), Global_Parameters::pressure_singularity2(), ClumpParticle::rotatePrincipalDirections(), FlowAroundCylinderProblem< ELEMENT >::set_boundary_conditions(), RefineableRotatingCylinderProblem< ELEMENT >::set_boundary_conditions(), RefineableSphereConvectionProblem< ELEMENT >::set_boundary_conditions(), oomph::FourierDecomposedHelmholtzDtNMesh< ELEMENT >::setup_gamma(), MinimalExampleDrum::setupInitialConditions(), RotatingDrum::setupInitialConditions(), Eigen::QuaternionBase< Derived >::slerp(), slerp_gael(), slerp_legacy(), slerp_legacy_nlerp(), slerp_rw(), FallingBlockProblem< ELEMENT >::snap_onto_sphere(), RisingBubbleProblem< ELEMENT >::snap_onto_sphere(), sphericalHarmonics::sphericalHarmonics(), SphericalSpinUpProblem< ELEMENT >::SphericalSpinUpProblem(), SphericalSteadyRotationProblem< ELEMENT >::SphericalSteadyRotationProblem(), oomph::AnnularSpineMesh< ELEMENT >::spine_node_update(), TwoDDGMesh< ELEMENT >::TwoDDGMesh(), u_E(), u_N(), u_W(), UniformRandomPDs(), Camera::updateProjectionMatrix(), Global_Parameters::velocity_couette(), Global_Parameters::velocity_singularity1(), and Global_Parameters::velocity_singularity2().