Inheritance diagram for tutorial03:

Public Member Functions
	tutorial03 (int argc, char *argv[])
	Constructor.

void	offlineSolve ()
	Perform an Offline solve.

Public Member Functions inherited from steadyNS
	steadyNS ()
	Null constructor.

	steadyNS (int argc, char *argv[])
	Construct with argc and argv.

	~steadyNS ()

void	truthSolve (List< scalar > mu_now)
	Perform a truthsolve.

void	solvesupremizer (word type="snapshots")
	solve the supremizer either with the use of the pressure snaphots or the pressure modes

void	liftSolve ()
	Perform a lift solve.

void	projectPPE (fileName folder, label NUmodes, label NPmodes, label NSUPmodes=0)
	Project using the Poisson Equation for pressure.

void	projectSUP (fileName folder, label NUmodes, label NPmodes, label NSUPmodes)
	Project using a supremizer approach.

void	discretizeThenProject (fileName folder, label NUmodes, label NPmodes, label NSUPmodes=0)
	Project using the Discretize-then-project approach.

Eigen::MatrixXd	diffusive_term (label NUmodes, label NPmodes, label NSUPmodes)
	Diffusive Term.

Eigen::MatrixXd	diffusive_term_sym (label NUmodes, label NPmodes, label NSUPmodes)
	Symetric diffusive Term.

Eigen::MatrixXd	pressure_gradient_term (label NUmodes, label NPmodes, label NSUPmodes)
	Gradient of pressure.

List< Eigen::MatrixXd >	convective_term (label NUmodes, label NPmodes, label NSUPmodes)
	Convective Term.

Eigen::MatrixXd	mass_term (label NUmodes, label NPmodes, label NSUPmodes)
	Mass Term.

Eigen::MatrixXd	divergence_term (label NUmodes, label NPmodes, label NSUPmodes)
	Divergence Term (supremizer approach)

List< Eigen::MatrixXd >	div_momentum (label NUmodes, label NPmodes)
	Divergence of convective term (PPE approach)

Eigen::Tensor< double, 3 >	divMomentum (label NUmodes, label NPmodes)
	Divergence of convective term (PPE approach)

Eigen::MatrixXd	laplacian_pressure (label NPmodes)
	Laplacian of pressure term (PPE approach)

Eigen::MatrixXd	pressure_BC1 (label NPmodes, label NUmodes)
	Term N° 1 given by the additional boundary condition using a PPE approach.

List< Eigen::MatrixXd >	pressure_BC2 (label NPmodes, label NUmodes)
	Term N° 2 given by the additional boundary condition using a PPE approach.

Eigen::Tensor< double, 3 >	pressureBC2 (label NPmodes, label NUmodes)
	Term N° 2 given by the additional boundary condition using a PPE approach.

Eigen::MatrixXd	pressure_BC3 (label NPmodes, label NUmodes)
	Term N° 3 given by the additional boundary condition using a PPE approach.

Eigen::MatrixXd	pressure_BC4 (label NPmodes, label NUmodes)
	Term N° 4 given by the additional boundary condition using a PPE approach for time-dependent BCs.

List< Eigen::MatrixXd >	bcVelocityVec (label NUmodes, label NSUPmodes)
	Boundary integral modes on boundary used by the penaly method.

List< Eigen::MatrixXd >	bcVelocityMat (label NUmodes, label NSUPmodes)
	Boundary integral modes on boundary used by the penaly method.

Eigen::MatrixXd	diffusive_term_flux_method (label NUmodes, label NPmodes, label NSUPmodes)
	Diffusive Flux Method.

List< Eigen::MatrixXd >	boundary_vector_diffusion (label NUmodes, label NPmodes, label NSUPmodes)
	Boundary vector diffusion term.

List< Eigen::MatrixXd >	boundary_vector_convection (label NUmodes, label NPmodes, label NSUPmodes)
	Boundary vector convection term.

Eigen::Tensor< double, 3 >	convective_term_flux_tens (label NUmodes, label NPmodes, label NSUPmodes)
	Convective Term.

List< Eigen::MatrixXd >	pressure_gradient_term_linsys_div (label NPmodes)
	Laplacian of pressure Linear System - Divergence term.

List< Eigen::MatrixXd >	pressure_gradient_term_linsys_diff (label NPmodes)
	Laplacian of pressure Linear System - Diffusion term.

List< Eigen::MatrixXd >	pressure_gradient_term_linsys_conv (label NPmodes)
	Laplacian of pressure Linear System - Convection term.

Eigen::MatrixXd	diffusive_term_consistent (label NUmodes, label NPmodes, label NSUPmodes)
	Diffusion Term (consistent flux method)

List< Eigen::MatrixXd >	boundary_vector_diffusion_consistent (label NUmodes, label NSUPmodes)
	Boundary vector diffusion term (consistent flux method)

List< Eigen::MatrixXd >	boundary_vector_convection_consistent (label NUmodes, label NSUPmodes)
	Boundary vector convection term - Consistent Flux Method.

Eigen::MatrixXd	mass_matrix_newtime_consistent (label NUmodes, label NPmodes, label NSUPmodes)
	Mass Matrix new time step (consistent flux method)

Eigen::MatrixXd	mass_matrix_oldtime_consistent (label NUmodes, label NPmodes, label NSUPmodes)
	Mass Matrix old time step (consistent flux method)

Eigen::MatrixXd	pressure_gradient_term_consistent (label NUmodes, label NPmodes, label NSUPmodes)
	Pressure Gradient Term (consistent flux method)

Eigen::Tensor< double, 3 >	convective_term_consistent_tens (label NUmodes, label NPmodes, label NSUPmodes)
	Convective Term (consistent flux method)

void	change_viscosity (double mu)
	Function to change the viscosity.

void	forcesMatrices (label NUmodes, label NPmodes, label NSUPmodes)
	Compute lift and drag matrices.

void	forcesMatrices (label nModes)
	Compute lift and drag matrices offline matrices for the case of same number of velocity and pressure modes.

void	reconstructLiftAndDrag (const Eigen::MatrixXd &velCoeffs, const Eigen::MatrixXd &pressureCoeffs, fileName folder)
	Method to reconstruct the forces using velocity and pressure coefficients.

Eigen::Tensor< double, 3 >	convective_term_tens (label NUmodes, label NPmodes, label NSUPmodes)
	Export convective term as a tensor.

void	restart ()
	set U and P back to the values into the 0 folder

Public Member Functions inherited from reductionProblem
	reductionProblem ()
	Construct Null.

	~reductionProblem ()

void	setParameters ()
	Set Parameters Problems.

void	genRandPar ()
	Generate Random Numbers.

void	genRandPar (label tsize)
	Generate Random Numbers given the dimension of the training set.

void	genEquiPar ()
	Generate Equidistributed Numbers.

void	truthSolve ()
	Perform a TruthSolve.

void	assignBC (volVectorField &s, label BC_ind, Vector< double > &value)
	Assign Boundary Condition to a volVectorField.

void	assignBC (volScalarField &s, label BC_ind, double &value)
	Assign Boundary Condition to a volScalarField.

void	reconstructFromMatrix (PtrList< volVectorField > &rec_field2, PtrList< volVectorField > &modes, label Nmodes, Eigen::MatrixXd coeff_matrix)
	Exact reconstruction using a certain number of modes for vector list of fields and the projection coefficients (volVectorField)

void	reconstructFromMatrix (PtrList< volScalarField > &rec_field2, PtrList< volScalarField > &modes, label Nmodes, Eigen::MatrixXd coeff_matrix)
	Exact reconstruction using a certain number of modes for vector list of fields and the projection coefficients (volScalarField)

template<typename T , typename G >
void	assignIF (T &s, G &value)
	Assign internal field condition.

template<typename T >
void	computeLift (T &Lfield, T &liftfield, T &omfield)
	Homogenize the snapshot matrix, it works with PtrList of volVectorField and volScalarField.

template<typename T >
void	computeLiftT (T &Lfield, T &liftfield, T &omfield)
	Virtual function to compute the lifting function.

void	liftSolve ()
	Virtual function to compute the lifting function for scalar field.

void	liftSolveT ()

void	project ()
	General projection operation.

void	writeMu (List< scalar > mu_now)
	Write out a list of scalar corresponding to the parameters used in the truthSolve.

std::vector< SPLINTER::RBFSpline >	getCoeffManifoldRBF (PtrList< volVectorField > snapshots, PtrList< volVectorField > &modes, word rbfBasis="GAUSSIAN")
	Constructs the parameters-coefficients manifold for vector fields, based on RBF-spline model.

std::vector< SPLINTER::RBFSpline >	getCoeffManifoldRBF (PtrList< volScalarField > snapshots, PtrList< volScalarField > &modes, word rbfBasis="GAUSSIAN")
	Constructs the parameters-coefficients manifold for scalar fields, based on RBF-spline model.

std::vector< SPLINTER::BSpline >	getCoeffManifoldSPL (PtrList< volVectorField > snapshots, PtrList< volVectorField > &modes, label splDeg=3)
	Constructs the parameters-coefficients manifold for vector fields, based on the B-spline model.

std::vector< SPLINTER::BSpline >	getCoeffManifoldSPL (PtrList< volScalarField > snapshots, PtrList< volScalarField > &modes, label splDeg=3)
	Constructs the parameters-coefficients manifold for scalar fields, based on the B-spline model.

Public Attributes
volVectorField &	U
	Velocity field.

volScalarField &	p
	Pressure field.

argList &	args
	Arg List.

Public Attributes inherited from steadyNS
ITHACAparameters *	para

PtrList< volScalarField >	Pfield
	List of pointers used to form the pressure snapshots matrix.

PtrList< volVectorField >	Ufield
	List of pointers used to form the velocity snapshots matrix.

PtrList< volVectorField >	supfield
	List of pointers used to form the supremizer snapshots matrix.

PtrList< surfaceScalarField >	Phifield
	List of pointers used to form the flux snapshots matrix.

volScalarModes	Pmodes
	List of pointers used to form the pressure modes.

volVectorModes	Umodes
	List of pointers used to form the velocity modes.

volVectorModes	supmodes
	List of pointers used to form the supremizer modes.

surfaceScalarModes	Phimodes
	List of pointers used to form the flux modes.

PtrList< volVectorField >	liftfield
	List of pointers used to form the list of lifting functions.

PtrList< volVectorField >	Uomfield
	List of pointers used to form the homogeneous velocity snapshots.

volVectorModes	L_U_SUPmodes
	List of pointers containing the total number of lift, supremizer and velocity modes.

surfaceScalarModes	L_PHImodes
	List of pointers containing the total number of flux modes.

scalar	tolerance
	Tolerance for the residual of the stationary problems, there is the same tolerance for velocity and pressure.

scalar	maxIter
	Number of maximum iterations to be done for the computation of the truth solution.

label	NUmodesOut
	Number of velocity modes to be calculated.

label	NPmodesOut
	Number of pressure modes to be calculated.

label	NSUPmodesOut
	Number of supremizer modes to be calculated.

label	NNutModesOut
	Number of nut modes to be calculated.

label	NUmodes
	Number of velocity modes used for the projection.

label	NPmodes
	Number of pressure modes used for the projection.

label	NSUPmodes
	Number of supremizer modes used for the projection.

label	NNutModes
	Number of nut modes used for the projection.

Eigen::MatrixXd	tauMatrix
	Viscous forces.

Eigen::MatrixXd	nMatrix
	Pressure forces.

List< Eigen::MatrixXd >	bcVelVec
	Boundary term for penalty method - vector.

List< Eigen::MatrixXd >	bcVelMat
	Boundary term for penalty method - matrix.

Eigen::MatrixXd	BP_matrix
	Diffusion term for flux method PPE.

List< Eigen::MatrixXd >	RD_matrix
	Boundary term for diffusion term.

List< Eigen::MatrixXd >	RC_matrix
	Boundary vector for convection term.

List< Eigen::MatrixXd >	SD_matrix
	Boundary term for diffusion term - Consistent Flux Method.

List< Eigen::MatrixXd >	SC_matrix
	Boundary term for convection term - Consistent Flux Method.

Eigen::Tensor< double, 3 >	Cf_tensor
	Convection term for flux method.

Eigen::Tensor< double, 3 >	Ci_tensor
	Convection term - Consistent Flux Method.

List< Eigen::MatrixXd >	LinSysDiv
	Projection Peqn onto Pressure modes - Divergence term.

List< Eigen::MatrixXd >	LinSysDiff
	Projection Peqn onto Pressure modes - Diffusion term.

List< Eigen::MatrixXd >	LinSysConv
	Projection Peqn onto Pressure modes - Convection term.

bool	supex
	Boolean variable to check the existence of the supremizer modes.

autoPtr< volScalarField >	_p
	Pressure field.

autoPtr< volVectorField >	_U
	Velocity field.

autoPtr< volScalarField >	_p0
	Initial Pressure field (for restart purposes)

autoPtr< volVectorField >	_U0
	Initial Velocity field (for restart purposes)

autoPtr< volVectorField >	Uinl
	Initial dummy field with all Dirichlet boundary conditions.

autoPtr< dimensionedScalar >	dt_dummy
	Dummy time step including unit.

autoPtr< dimensionedScalar >	nu_dummy
	Dummy viscocity including unit.

autoPtr< fvMesh >	_mesh
	Mesh.

autoPtr< simpleControl >	_simple
	simpleControl

autoPtr< fv::options >	_fvOptions
	fvOptions

autoPtr< Time >	_runTime
	Time.

autoPtr< surfaceScalarField >	_phi
	Flux.

autoPtr< surfaceScalarField >	_phi0
	Initial Flux (for restart purposes)

autoPtr< incompressible::turbulenceModel >	turbulence
	Turbulence model.

autoPtr< singlePhaseTransportModel >	_laminarTransport
	Laminar transport (used by turbulence model)

autoPtr< IOMRFZoneList >	_MRF
	MRF variable.

label	pRefCell
	Reference pressure cell.

scalar	pRefValue
	Reference pressure value.

scalar	cumulativeContErr = 0
	continuity error

word	bcMethod
	Boundary Method.

word	fluxMethod
	Flux Method.

Eigen::MatrixXd	B_matrix
	Diffusion term.

Eigen::MatrixXd	M_matrix
	Mass Matrix.

Eigen::MatrixXd	K_matrix
	Gradient of pressure matrix.

List< Eigen::MatrixXd >	C_matrix
	Non linear term.

Eigen::Tensor< double, 3 >	C_tensor
	Diffusion term.

Eigen::MatrixXd	P_matrix
	Div of velocity.

Eigen::MatrixXd	D_matrix
	Laplacian term PPE.

List< Eigen::MatrixXd >	G_matrix
	Divergence of momentum PPE.

Eigen::Tensor< double, 3 >	gTensor
	Divergence of momentum PPE.

Eigen::MatrixXd	BC1_matrix
	PPE BC1.

List< Eigen::MatrixXd >	BC2_matrix
	PPE BC2.

Eigen::Tensor< double, 3 >	bc2Tensor
	PPE BC2.

Eigen::MatrixXd	BC3_matrix
	PPE BC3.

Eigen::MatrixXd	BC4_matrix
	PPE BC4.

Eigen::MatrixXd	W_matrix
	Mass Matrix New Time Step - Consistent Flux Method.

Eigen::MatrixXd	I_matrix
	Mass Matrix Old Time Step - Consistent Flux Method.

Eigen::MatrixXd	DF_matrix
	Diffusion Term - Consistent Flux Method.

Eigen::MatrixXd	KF_matrix
	Pressure Gradient Term - Consistent Flux Method.

Public Attributes inherited from reductionProblem
label	Pnumber
	Number of parameters.

label	Tnumber
	Dimension of the training set (used only when gerating parameters without input)

Eigen::MatrixXd	mu
	Row matrix of parameters.

Eigen::MatrixXd	mu_range
	Range of the parameter spaces.

Eigen::MatrixXd	mu_samples
	Matrix of parameters to be used for PODI, where each row corresponds to a sample point. In this matrix the time dimension is regarded as a parameter for unsteady problems.

double	mu_cur
	Current value of the parameter.

bool	podex
	Boolean variable, it is 1 if the POD has already been computed, else 0.

bool	offline
	Boolean variable, it is 1 if the Offline phase has already been computed, else 0.

IOdictionary *	ITHACAdict
	dictionary to store input output infos

autoPtr< argList >	_args
	argList

ITHACAparallel *	paral
	parallel handling

label	folderN = 1
	Counter to save intermediate steps in the correct folder, for unsteady and some stationary cases.

label	counter = 1
	Counter used for the output of the full order solutions.

Eigen::MatrixXi	inletIndex
	Matrix that contains informations about the inlet boundaries.

Eigen::MatrixXi	inletPatch
	Matrix that contains informations about the inlet boundaries without specifing the direction Rows = Number of parametrized boundary conditions Cols = 1 Example: example.inletIndex.resize(2, 1); example.inletIndex(0, 0) = 0; example.inletIndex(1, 0) = 1; Means that there are two parametrized boundary conditions of which the first row is of patch 0 and the second row of patch 1.

Eigen::MatrixXi	inletIndexT