Defines integration rules for lines, quadrilaterals, triangles, cubes, tetrahedra, pyramids and prisms. More...

Classes
class	TPZInt1d
	Handles the numerical integration for one-dimensional problems. Numerical Integration. More...

class	TPZIntTriang
	Handles the numerical integration for two-dimensional problems using triangular elements. Numerical Integration. More...

class	TPZIntQuad
	Handles the numerical integration for two-dimensional problems using quadrilateral elements. Numerical Integration. More...

class	TPZIntCube3D
	Handles the numerical integration for three-dimensional problems using cube elements. Numerical Integration. More...

class	TPZIntTetra3D
	Handles the numerical integration for three-dimensional problems using tetraedra elements. Numerical Integration. More...

class	TPZIntPyram3D
	Handles the numerical integration for three-dimensional problems using pyramid elements. Numerical Integration. More...

class	TPZIntPrism3D
	Handles the numerical integration for three-dimensional problems using prism elements. Numerical Integration This cubature rule uses a cubature rule for one dimension (zeta) and a cubature rule for triangle (base). More...

class	TPZInt1Point
	Integration rule for one point. Numerical Integration. More...

class	TPZGaussRule
	Implements the Gaussian quadrature. Numerical Integration Abstract class. More...

class	TPZIntPoints
	Abstract class defining integration rules. Numerical Integration. More...

class	TPZIntRuleList
	Creates instances of all integration rules for rapid selection. Numerical Integration. More...

class	TPZIntRuleP3D
	Integration rule for pyramid. Numerical Integration. More...

class	TPZIntRuleT
	Integration rule (points and weights) for triangles. Numerical Integration. More...

class	TPZIntRuleT3D
	Integration rule for tetrahedra. Numerical Integration. More...

class	TPZPrInteg< TFather >
	Prismatic extension of an integration rule. Numerical Integration. More...

Functions
	TPZInt1Point::TPZInt1Point (int order=0)

virtual	TPZInt1Point::~TPZInt1Point ()

int	TPZInt1Point::NPoints () const
	Returns number of points for the cubature rule related. More...

void	TPZInt1Point::Point (int ip, TPZVec< REAL > &pos, REAL &w) const
	Returns i-th point at master element and related weight. More...

void	TPZInt1Point::SetOrder (TPZVec< int > &ord, int type=0)
	Sets the order of the cubature rule. More...

void	TPZInt1Point::GetOrder (TPZVec< int > &ord) const
	Gets the order of the integration rule for each dimension of the master element. More...

int	TPZInt1Point::GetMaxOrder () const
	Returns the minimum order to integrate polinomials exactly for all implemented cubature rules. More...

TPZIntPoints *	TPZInt1Point::PrismExtend (int order)

Variables
static TPZIntRuleList	TPZIntRuleList::gIntRuleList
	Static variable with list of all integration rules. More...

Auxiliar methods to evaluate the Jacobi polinomial
long double	machinePrecision ()

long double	gamma (unsigned int n)
	Evaluate the factorial of a integer. More...

long double	gamma (long double x)
	Evaluates the Gamma function for a real number x, Gamma(x). The computation is based on an algorithm outlined in "An Overview of Software Development for Special Functions, in Numerical Analysis" (Dundee, 1975) by William Cody. More...

Detailed Description

Defines integration rules for lines, quadrilaterals, triangles, cubes, tetrahedra, pyramids and prisms.

Allow the user to define the order of the polynomial, the rule should be able to integrate exactly.

All the computations into this module use and return long double values. Because the precision of the points and weights will be right and are independent of the typedef REAL definition.

Function Documentation

◆ gamma() [1/2]

long double gamma ( unsigned int n )

Evaluate the factorial of a integer.

Parameters

n	The integer to compute the factorial

Note: The argument n cann't be negative.

Evaluates the Gamma function for integers - Factorial function

Definition at line 567 of file tpzgaussrule.cpp.

Referenced by TPZEulerConsLaw::ApproxRoe_Flux(), TPZGaussRule::ComputingGaussJacobiQuadrature(), TPZGaussRule::ComputingGaussLobattoQuadrature(), TPZArtDiff::ContributeExplDiff(), TPZSandlerExtended::DDistFunc1(), TPZElasticityAxiMaterial::Errors(), TPZMixedElasticityMaterial::Errors(), TPZSandlerExtended::F1Cyl(), TPZSandlerExtended::F2Cyl(), TPZEulerEquation::Gamma(), TPZFlowCompMesh::MaxVelocityOfMesh(), QMR(), TPZYCMohrCoulombPV::ReturnMapLeftEdge(), TPZMohrCoulombNeto::ReturnMapLeftEdge(), TPZMohrCoulombPV::ReturnMapLeftEdge(), TPZYCMohrCoulombPV::ReturnMapPlane(), TPZMohrCoulombPV::ReturnMapPlane(), TPZMohrCoulombNeto::ReturnMapPlane(), TPZYCMohrCoulombPV::ReturnMapRightEdge(), TPZMohrCoulombNeto::ReturnMapRightEdge(), TPZMohrCoulombPV::ReturnMapRightEdge(), TPZConservationLaw::SetGamma(), TPZGaussRule::SetParametersJacobi(), TPZYCCamClayPV::SetUp(), TPZSandlerExtended::SurfaceParamF2(), TPZAUSMFlux::TPZAUSMFlux(), TPZConservationLaw::TPZConservationLaw(), TPZDiffusionConsLaw::TPZDiffusionConsLaw(), TPZEulerConsLaw::TPZEulerConsLaw(), and TPZEulerEquation::TPZEulerEquation().

◆ gamma() [2/2]

long double gamma ( long double x )

Evaluates the Gamma function for a real number x, Gamma(x). The computation is based on an algorithm outlined in "An Overview of Software Development for Special Functions, in Numerical Analysis" (Dundee, 1975) by William Cody.

Parameters

x	real number to evaluate Gamma(x)

Note: The implementation uses rational functions that approximate the gamma function as long double precision (19 significant digits).

Evaluates the Gamma function for a real number x, Gamma(x)

Definition at line 575 of file tpzgaussrule.cpp.

References exp, log, and test::res.

◆ GetMaxOrder()

int TPZInt1Point::GetMaxOrder ( ) const

inlinevirtual

Returns the minimum order to integrate polinomials exactly for all implemented cubature rules.

Note: To get real maxime order for especific rule call GetRealMaxOrder(), but for Gauss rule 1D the implementation can to compute a cubature rule up to on hundred order.

TPZIntPoints method that returns a coherent maxime order to work It is necessary because now can to be computed rule with integration points up to one thousand.

Reimplemented from TPZIntPoints.

Definition at line 542 of file pzquad.h.

◆ GetOrder()

void TPZInt1Point::GetOrder ( TPZVec< int > & ord ) const

inlinevirtual

Gets the order of the integration rule for each dimension of the master element.

Parameters

ord	Vector (3d) to get the orders of the polinomial integrated exactly.

Implements TPZIntPoints.

Definition at line 539 of file pzquad.h.

◆ machinePrecision()

long double machinePrecision ( )

Returns the machine precision of the computer's arithmetic as long double number

Definition at line 552 of file tpzgaussrule.cpp.

References PZINTEGRAL_MAXITERATIONS_ALLOWED.

Referenced by TPZGaussRule::ComputingGaussJacobiQuadrature(), TPZGaussRule::ComputingGaussLegendreQuadrature(), and TPZGaussRule::SetParametersJacobi().

◆ NPoints()

int TPZInt1Point::NPoints ( ) const

inlinevirtual

Returns number of points for the cubature rule related.

Implements TPZIntPoints.

Definition at line 522 of file pzquad.h.

◆ Point()

void TPZInt1Point::Point	(	int	i,
		TPZVec< REAL > &	pos,
		REAL &	w
	)		const

inlinevirtual

Returns i-th point at master element and related weight.

Parameters

i	Index of the integration point at cubature rule (the sequence is not important)
pos	Vector (3d) to get the coordinates of the point at master element.
w	It gets the weight related with integration point.

Implements TPZIntPoints.

Definition at line 526 of file pzquad.h.

◆ PrismExtend()

TPZIntPoints * TPZInt1Point::PrismExtend ( int order )

inlinevirtual

Implements TPZIntPoints.

Definition at line 546 of file pzquad.h.

◆ SetOrder()

void TPZInt1Point::SetOrder	(	TPZVec< int > &	ord,
		int	type = `0`
	)

inlinevirtual

Sets the order of the cubature rule.

Parameters

ord	Vector of orders for each dimension, to reach a exactly integration for polinomial corresponding
type	Type of the integration rule, mainly important for 1d rules.

Implements TPZIntPoints.

Definition at line 536 of file pzquad.h.

◆ TPZInt1Point()

TPZInt1Point::TPZInt1Point ( int order = 0 )

inline

Definition at line 515 of file pzquad.h.

◆ ~TPZInt1Point()

TPZInt1Point::~TPZInt1Point ( )

inlinevirtual

Definition at line 519 of file pzquad.h.

Variable Documentation

◆ gIntRuleList

TPZIntRuleList TPZIntRuleList::gIntRuleList

static

Static variable with list of all integration rules.

Definition at line 42 of file tpzintrulelist.h.

Referenced by TPZInt1d::SetOrder(), TPZPrInteg< TFather >::SetOrder(), TPZIntTriang::SetOrder(), TPZIntQuad::SetOrder(), TPZIntCube3D::SetOrder(), TPZIntTetra3D::SetOrder(), TPZIntPyram3D::SetOrder(), TPZInt1d::TPZInt1d(), TPZIntCube3D::TPZIntCube3D(), TPZIntPyram3D::TPZIntPyram3D(), TPZIntQuad::TPZIntQuad(), TPZIntTetra3D::TPZIntTetra3D(), TPZIntTriang::TPZIntTriang(), and TPZPrInteg< TFather >::TPZPrInteg().

Classes

Functions

Variables

Auxiliar methods to evaluate the Jacobi polinomial

Detailed Description

Function Documentation

◆ gamma() [1/2]

◆ gamma() [2/2]

◆ GetMaxOrder()

◆ GetOrder()

◆ machinePrecision()

◆ NPoints()

◆ Point()

◆ PrismExtend()

◆ SetOrder()

◆ TPZInt1Point()

◆ ~TPZInt1Point()

Variable Documentation

◆ gIntRuleList