Public Member Functions
real(kind=dp) function	linenodalpbasis (node, u)


real(kind=dp) function	dlinenodalpbasis (node, u)

real(kind=dp) function	linebubblepbasis (i, u, invertEdge)

real(kind=dp) function	dlinebubblepbasis (i, u, invertEdge)

real(kind=dp) function	quadnodalpbasis (node, u, v)

real(kind=dp) function, dimension(2)	dquadnodalpbasis (node, u, v)

real(kind=dp) function	quadedgepbasis (edge, i, u, v, invertEdge)

real(kind=dp) function	quadpyraedgepbasis (edge, i, u, v, invertEdge)

real(kind=dp) function, dimension(2)	dquadedgepbasis (edge, i, u, v, invertEdge)

real(kind=dp) function, dimension(2)	dquadpyraedgepbasis (edge, i, u, v, invertEdge)

real(kind=dp) function	quadbubblepbasis (i, j, u, v, localNumbers)

real(kind=dp) function, dimension(2)	dquadbubblepbasis (i, j, u, v, localNumbers)

real(kind=dp) function	quadl (which, u, v)

real(kind=dp) function, dimension(2)	dquadl (which, u, v)

real(kind=dp) function	trianglenodalpbasis (node, u, v)

real(kind=dp) function, dimension(2)	dtrianglenodalpbasis (node, u, v)

real(kind=dp) function	triangleedgepbasis (edge, i, u, v, invertEdge)

real(kind=dp) function, dimension(2)	dtriangleedgepbasis (edge, i, u, v, invertEdge)

real(kind=dp) function	trianglebubblepbasis (j, n, u, v, localNumbers)

real(kind=dp) function	triangleebubblepbasis (i, j, u, v, localNumbers)

real(kind=dp) function, dimension(2)	dtrianglebubblepbasis (j, n, u, v, localNumbers)

real(kind=dp) function, dimension(2)	dtriangleebubblepbasis (i, j, u, v, localNumbers)

real(kind=dp) function	bricknodalpbasis (node, u, v, w)

real(kind=dp) function, dimension(3)	dbricknodalpbasis (node, u, v, w)

real(kind=dp) function	brickedgepbasis (edge, i, u, v, w, invertEdge)

real(kind=dp) function, dimension(3)	dbrickedgepbasis (edge, i, u, v, w, invertEdge)

real(kind=dp) function	brickpyraedgepbasis (edge, i, u, v, w, invertEdge)

real(kind=dp) function, dimension(3)	dbrickpyraedgepbasis (edge, i, u, v, w, invertEdge)

real(kind=dp) function	brickfacepbasis (face, i, j, u, v, w, localNumbers)

real(kind=dp) function, dimension(3)	dbrickfacepbasis (face, i, j, u, v, w, localNumbers)

real(kind=dp) function	brickbubblepbasis (i, j, k, u, v, w)

real(kind=dp) function, dimension(3)	dbrickbubblepbasis (i, j, k, u, v, w)

real(kind=dp) function	brickl (which, u, v, w)

real(kind=dp) function, dimension(3)	dbrickl (which, u, v, w)

real(kind=dp) function	tetranodalpbasis (node, u, v, w)

real(kind=dp) function, dimension(3)	dtetranodalpbasis (node, u, v, w)

real(kind=dp) function	tetraedgepbasis (edge, i, u, v, w, tetratype)

real(kind=dp) function, dimension(3)	dtetraedgepbasis (edge, i, u, v, w, tetratype)

real(kind=dp) function	tetrafacepbasis (face, i, j, u, v, w, tetratype)

real(kind=dp) function, dimension(3)	dtetrafacepbasis (face, i, j, u, v, w, tetratype)

real(kind=dp) function	tetrabubblepbasis (i, j, k, u, v, w)

real(kind=dp) function, dimension(3)	dtetrabubblepbasis (i, j, k, u, v, w)

real(kind=dp) function	wedgenodalpbasis (node, u, v, w)

real(kind=dp) function, dimension(3)	dwedgenodalpbasis (node, u, v, w)

real(kind=dp) function	wedgeedgepbasis (edge, i, u, v, w, invertEdge)

real(kind=dp) function, dimension(3)	dwedgeedgepbasis (edge, i, u, v, w, invertEdge)

real(kind=dp) function	wedgefacepbasis (face, i, j, u, v, w, localNumbers)

real(kind=dp) function, dimension(3)	dwedgefacepbasis (face, i, j, u, v, w, localNumbers)

real(kind=dp) function	wedgebubblepbasis (i, j, k, u, v, w)

real(kind=dp) function, dimension(3)	dwedgebubblepbasis (i, j, k, u, v, w)

real(kind=dp) function	wedgel (which, u, v)

real(kind=dp) function	wedgeh (which, w)

real(kind=dp) function, dimension(3)	dwedgel (which, u, v)

real(kind=dp) function, dimension(3)	dwedgeh (which, w)

real(kind=dp) function	pyramidnodalpbasis (node, u, v, w)

real(kind=dp) function, dimension(3)	dpyramidnodalpbasis (node, u, v, w)

real(kind=dp) function	pyramidedgepbasis (edge, i, u, v, w, invertEdge)

real(kind=dp) function, dimension(3)	dpyramidedgepbasis (edge, i, u, v, w, invertEdge)

real(kind=dp) function	pyramidfacepbasis (face, i, j, u, v, w, localNumbers)

real(kind=dp) function, dimension(3)	dpyramidfacepbasis (face, i, j, u, v, w, localNumbers)

real(kind=dp) function	pyramidbubblepbasis (i, j, k, u, v, w)

real(kind=dp) function, dimension(3)	dpyramidbubblepbasis (i, j, k, u, v, w)

real(kind=dp) function	pyramidt (which, c, t)

real(kind=dp) function, dimension(2)	dpyramidt (which, c, t)

real(kind=dp) function	pyramidl (which, u, v)

real(kind=dp) function, dimension(3)	dpyramidl (which, u, v)

real(kind=dp) function	phi (i, x)

real(kind=dp) function	dphi (i, x)

real(kind=dp) function	varphi (i, x)

real(kind=dp) function	dvarphi (i, x)

recursive function	legendrep (l, x)

recursive function	dlegendrep (l, x)

real(kind=dp) function	toexp (x, n)

Member Function/Subroutine Documentation

real (kind=dp) function pelementbase::brickbubblepbasis	(	integer, intent(in)	i,
		integer, intent(in)	j,
		integer, intent(in)	k,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v,
		real (kind=dp), intent(in)	w
	)

Brick bubble basis at point (u,v,w).

References phi().

Referenced by elementdescription::elementinfo().

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real (kind=dp) function pelementbase::brickedgepbasis	(	integer, intent(in)	edge,
		integer, intent(in)	i,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v,
		real (kind=dp), intent(in)	w,
		logical, optional	invertEdge
	)

Brick edge basis at point (u,v,w).

References messages::fatal(), and phi().

Referenced by elementdescription::elementinfo().

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real (kind=dp) function pelementbase::brickfacepbasis	(	integer, intent(in)	face,
		integer, intent(in)	i,
		integer, intent(in)	j,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v,
		real (kind=dp), intent(in)	w,
		integer, dimension(4), optional	localNumbers
	)

Brick face basis at point (u,v,w)

References brickl(), messages::fatal(), pelementmaps::getbrickfacemap(), and phi().

Referenced by elementdescription::elementinfo().

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real(kind=dp) function pelementbase::brickl	(	integer, intent(in)	which,
		real(kind=dp), intent(in)	u,
		real(kind=dp), intent(in)	v,
		real(kind=dp), intent(in)	w
	)

References messages::fatal().

Referenced by brickfacepbasis(), brickpyraedgepbasis(), dbrickfacepbasis(), and dbrickpyraedgepbasis().

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real(kind=dp) function pelementbase::bricknodalpbasis	(	integer, intent(in)	node,
		real(kind=dp), intent(in)	u,
		real(kind=dp), intent(in)	v,
		real(kind=dp), intent(in)	w
	)

References messages::fatal().

Referenced by brickpyraedgepbasis(), dbrickpyraedgepbasis(), and elementdescription::nodalbasisfunctions().

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real (kind=dp) function pelementbase::brickpyraedgepbasis	(	integer, intent(in)	edge,
		integer, intent(in)	i,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v,
		real (kind=dp), intent(in)	w,
		logical, optional	invertEdge
	)

Brick edge basis at point (u,v,w). Compatible with pyramidal edge basis.

References brickl(), bricknodalpbasis(), messages::fatal(), pelementmaps::getbrickedgemap(), and varphi().

Referenced by elementdescription::elementinfo().

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real (kind=dp) function, dimension(3) pelementbase::dbrickbubblepbasis	(	integer, intent(in)	i,
		integer, intent(in)	j,
		integer, intent(in)	k,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v,
		real (kind=dp), intent(in)	w
	)

Gradient of brick bubble basis at point (u,v,w)

References dphi(), and phi().

Referenced by elementdescription::elementinfo().

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real (kind=dp) function, dimension(3) pelementbase::dbrickedgepbasis	(	integer, intent(in)	edge,
		integer, intent(in)	i,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v,
		real (kind=dp), intent(in)	w,
		logical, optional	invertEdge
	)

Gradient of brick edge basis at point (u,v,w).

References dphi(), messages::fatal(), and phi().

Referenced by elementdescription::elementinfo().

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real (kind=dp) function, dimension(3) pelementbase::dbrickfacepbasis	(	integer, intent(in)	face,
		integer, intent(in)	i,
		integer, intent(in)	j,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v,
		real (kind=dp), intent(in)	w,
		integer, dimension(4), optional	localNumbers
	)

Gradient of brick face basis at point (u,v,w)

References brickl(), dbrickl(), dphi(), messages::fatal(), pelementmaps::getbrickfacemap(), and phi().

Referenced by elementdescription::elementinfo().

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real(kind=dp) function, dimension(3) pelementbase::dbrickl	(	integer, intent(in)	which,
		real(kind=dp), intent(in)	u,
		real(kind=dp), intent(in)	v,
		real(kind=dp), intent(in)	w
	)

References messages::fatal().

Referenced by dbrickfacepbasis(), and dbrickpyraedgepbasis().

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real(kind=dp) function, dimension(3) pelementbase::dbricknodalpbasis	(	integer, intent(in)	node,
		real(kind=dp), intent(in)	u,
		real(kind=dp), intent(in)	v,
		real(kind=dp), intent(in)	w
	)

References messages::fatal().

Referenced by dbrickpyraedgepbasis(), and elementdescription::nodalfirstderivatives().

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real (kind=dp) function, dimension(3) pelementbase::dbrickpyraedgepbasis	(	integer, intent(in)	edge,
		integer, intent(in)	i,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v,
		real (kind=dp), intent(in)	w,
		logical, optional	invertEdge
	)

Gradient of brick edge basis at point (u,v,w).

References brickl(), bricknodalpbasis(), dbrickl(), dbricknodalpbasis(), dvarphi(), messages::fatal(), pelementmaps::getbrickedgemap(), and varphi().

Referenced by elementdescription::elementinfo().

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recursive function pelementbase::dlegendrep	(	integer, intent(in)	l,
		real (kind=dp), intent(in)	x
	)

Function dLegendreP returns value of derivative of l:th Legendre polynomial at point x.

Value of legendre polynomial is precalculated for l=<20 and calculated from recursion for l>20, P,(l+1,x)=x*P,(l,x)+(l+1)*P(l,x), where P,(0,x)=0, P(1,x)=1.

References messages::fatal(), and legendrep().

Referenced by dphi(), dpyramidbubblepbasis(), dpyramidfacepbasis(), dtetrabubblepbasis(), dtetrafacepbasis(), dtriangleebubblepbasis(), dwedgebubblepbasis(), and dwedgefacepbasis().

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real (kind=dp) function pelementbase::dlinebubblepbasis	(	integer, intent(in)	i,
		real (kind=dp), intent(in)	u,
		logical, optional	invertEdge
	)

Derivative of bubble function i of line element.

References dphi().

Referenced by elementdescription::elementinfo().

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real (kind=dp) function pelementbase::dlinenodalpbasis	(	integer, intent(in)	node,
		real (kind=dp), intent(in)	u
	)

Derivative of line elements nodal basis at point (u).

References messages::fatal().

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real (kind=dp) function pelementbase::dphi	(	integer, intent(in)	i,
		real (kind=dp), intent(in)	x
	)

Derivative of phi function value at point x. Phi,(i,x)=SQRT(1/(2*(2*i-1)))(P,(i,x)-P,(i-2,x)), i=2,3,... where P,(i,x) are derivatives of legendre polynomials.

References dlegendrep(), and messages::fatal().

Referenced by dbrickbubblepbasis(), dbrickedgepbasis(), dbrickfacepbasis(), dlinebubblepbasis(), dquadbubblepbasis(), dquadedgepbasis(), dvarphi(), dwedgebubblepbasis(), dwedgeedgepbasis(), and dwedgefacepbasis().

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real(kind=dp) function, dimension(3) pelementbase::dpyramidbubblepbasis	(	integer, intent(in)	i,
		integer, intent(in)	j,
		integer, intent(in)	k,
		real(kind=dp), intent(in)	u,
		real(kind=dp), intent(in)	v,
		real(kind=dp), intent(in)	w
	)

Gradient of pyramid bubble basis at point (u,v,w)

References dlegendrep(), dpyramidnodalpbasis(), legendrep(), and pyramidnodalpbasis().

Referenced by elementdescription::elementinfo().

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real(kind=dp) function, dimension(3) pelementbase::dpyramidedgepbasis	(	integer, intent(in)	edge,
		integer, intent(in)	i,
		real(kind=dp), intent(in)	u,
		real(kind=dp), intent(in)	v,
		real(kind=dp), intent(in)	w,
		logical, intent(in), optional	invertEdge
	)

Gradient of pyramid edge basis at point (u,v,w)

References dpyramidnodalpbasis(), dvarphi(), messages::fatal(), pyramidnodalpbasis(), and varphi().

Referenced by elementdescription::elementinfo().

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real(kind=dp) function, dimension(3) pelementbase::dpyramidfacepbasis	(	integer, intent(in)	face,
		integer, intent(in)	i,
		integer, intent(in)	j,
		real(kind=dp), intent(in)	u,
		real(kind=dp), intent(in)	v,
		real(kind=dp), intent(in)	w,
		integer, dimension(4), intent(in), optional	localNumbers
	)

Gradient of pyramid face basis at point (u,v,w)

References dlegendrep(), dpyramidl(), dpyramidnodalpbasis(), dvarphi(), messages::fatal(), pelementmaps::getpyramidfacemap(), legendrep(), pyramidl(), pyramidnodalpbasis(), and varphi().

Referenced by elementdescription::elementinfo().

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real(kind=dp) function, dimension(3) pelementbase::dpyramidl	(	integer, intent(in)	which,
		real(kind=dp), intent(in)	u,
		real(kind=dp), intent(in)	v
	)

References messages::fatal().

Referenced by dpyramidfacepbasis().

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real(kind=dp) function, dimension(3) pelementbase::dpyramidnodalpbasis	(	integer, intent(in)	node,
		real(kind=dp), intent(in)	u,
		real(kind=dp), intent(in)	v,
		real(kind=dp), intent(in)	w
	)

Gradient of pyramids nodal basis at point (u,v,w)

References dpyramidt(), messages::fatal(), and pyramidt().

Referenced by dpyramidbubblepbasis(), dpyramidedgepbasis(), dpyramidfacepbasis(), and elementdescription::nodalfirstderivatives().

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real(kind=dp) function, dimension(2) pelementbase::dpyramidt	(	integer, intent(in)	which,
		real(kind=dp), intent(in)	c,
		real(kind=dp), intent(in)	t
	)

References messages::fatal().

Referenced by dpyramidnodalpbasis().

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real(kind=dp) function, dimension(2) pelementbase::dquadbubblepbasis	(	integer, intent(in)	i,
		integer, intent(in)	j,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v,
		integer, dimension(4), optional	localNumbers
	)

Gradient of quadrilateral bubble basis at point (u,v).

References dphi(), dquadl(), phi(), and quadl().

Referenced by elementdescription::elementinfo().

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real (kind=dp) function, dimension(2) pelementbase::dquadedgepbasis	(	integer, intent(in)	edge,
		integer, intent(in)	i,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v,
		logical, optional	invertEdge
	)

Gradient of quadrilateral edge basis at point (u,v).

References dphi(), messages::fatal(), and phi().

Referenced by elementdescription::elementinfo().

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real(kind=dp) function, dimension(2) pelementbase::dquadl	(	integer, intent(in)	which,
		real(kind=dp), intent(in)	u,
		real(kind=dp), intent(in)	v
	)

Defines gradients of linear functions for quadrilateral nodes. For use see QuadL.

References messages::fatal().

Referenced by dquadbubblepbasis(), and dquadpyraedgepbasis().

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real (kind=dp) function, dimension(2) pelementbase::dquadnodalpbasis	(	integer, intent(in)	node,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v
	)

Gradient of quadrilateral nodal basis at point (u,v).

References messages::fatal().

Referenced by dquadpyraedgepbasis(), and elementdescription::nodalfirstderivatives().

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real (kind=dp) function, dimension(2) pelementbase::dquadpyraedgepbasis	(	integer, intent(in)	edge,
		integer, intent(in)	i,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v,
		logical, optional	invertEdge
	)

Gradient of quadrilateral edge basis at point (u,v) which is compatible with pyramidal 3d element square face edges.

References dquadl(), dquadnodalpbasis(), dvarphi(), messages::fatal(), pelementmaps::getquadedgemap(), quadl(), quadnodalpbasis(), and varphi().

Referenced by elementdescription::elementinfo().

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real (kind=dp) function, dimension(3) pelementbase::dtetrabubblepbasis	(	integer, intent(in)	i,
		integer, intent(in)	j,
		integer, intent(in)	k,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v,
		real (kind=dp), intent(in)	w
	)

Gradient of tetra bubble basis at point (u,v,w)

References dlegendrep(), legendrep(), and tetranodalpbasis().

Referenced by elementdescription::elementinfo().

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real (kind=dp) function, dimension(3) pelementbase::dtetraedgepbasis	(	integer, intent(in)	edge,
		integer, intent(in)	i,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v,
		real (kind=dp), intent(in)	w,
		integer, intent(in), optional	tetratype
	)

Gradient of tetrahedrons edge basis at point (u,v,w)

References dtetranodalpbasis(), dvarphi(), messages::fatal(), tetranodalpbasis(), and varphi().

Referenced by elementdescription::elementinfo().

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real (kind=dp) function, dimension(3) pelementbase::dtetrafacepbasis	(	integer, intent(in)	face,
		integer, intent(in)	i,
		integer, intent(in)	j,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v,
		real (kind=dp), intent(in)	w,
		integer, intent(in), optional	tetratype
	)

Gradient of tetra face basis at point (u,v,w)

References dlegendrep(), dtetranodalpbasis(), messages::fatal(), legendrep(), and tetranodalpbasis().

Referenced by elementdescription::elementinfo().

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real (kind=dp) function, dimension(3) pelementbase::dtetranodalpbasis	(	integer, intent(in)	node,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v,
		real (kind=dp), intent(in)	w
	)

Gradient of tetrahedrons nodal basis at point (u,v,w)

References messages::fatal().

Referenced by dtetraedgepbasis(), dtetrafacepbasis(), elementdescription::nodalfirstderivatives(), and elementdescription::rtandbdmelementinfo().

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real (kind=dp) function, dimension(2) pelementbase::dtrianglebubblepbasis	(	integer, intent(in)	j,
		integer, intent(in)	n,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v,
		integer, dimension(3), optional	localNumbers
	)

Gradient of triangles bubble basis at point (u,v).

References dtrianglenodalpbasis(), toexp(), and trianglenodalpbasis().

Referenced by elementdescription::elementinfo().

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real (kind=dp) function, dimension(2) pelementbase::dtriangleebubblepbasis	(	integer, intent(in)	i,
		integer, intent(in)	j,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v,
		integer, dimension(3), optional	localNumbers
	)

References dlegendrep(), dtrianglenodalpbasis(), legendrep(), and trianglenodalpbasis().

Referenced by elementdescription::elementinfo().

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real (kind=dp) function, dimension(2) pelementbase::dtriangleedgepbasis	(	integer, intent(in)	edge,
		integer, intent(in)	i,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v,
		logical, optional	invertEdge
	)

Gradient of triangle edge basis at point (u,v).

References dvarphi(), messages::fatal(), trianglenodalpbasis(), and varphi().

Referenced by elementdescription::elementinfo().

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real (kind=dp) function, dimension(2) pelementbase::dtrianglenodalpbasis	(	integer, intent(in)	node,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v
	)

Gradient of triangle nodal basis at point (u,v).

References messages::fatal().

Referenced by dtrianglebubblepbasis(), dtriangleebubblepbasis(), elementdescription::nodalfirstderivatives(), and elementdescription::rtandbdmelementinfo().

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real (kind=dp) function pelementbase::dvarphi	(	integer, intent(in)	i,
		real (kind=dp), intent(in)	x
	)

Derivative of varPhi function at point x.

References dphi(), messages::fatal(), and phi().

Referenced by dbrickpyraedgepbasis(), dpyramidedgepbasis(), dpyramidfacepbasis(), dquadpyraedgepbasis(), dtetraedgepbasis(), dtriangleedgepbasis(), dwedgeedgepbasis(), and dwedgefacepbasis().

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real(kind=dp) function, dimension(3) pelementbase::dwedgebubblepbasis	(	integer, intent(in)	i,
		integer, intent(in)	j,
		integer, intent(in)	k,
		real(kind=dp), intent(in)	u,
		real(kind=dp), intent(in)	v,
		real(kind=dp), intent(in)	w
	)

Gradient of wedge bubble basis at point (u,v,w)

References dlegendrep(), dphi(), dwedgel(), legendrep(), phi(), and wedgel().

Referenced by elementdescription::elementinfo().

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real(kind=dp) function, dimension(3) pelementbase::dwedgeedgepbasis	(	integer, intent(in)	edge,
		integer, intent(in)	i,
		real(kind=dp), intent(in)	u,
		real(kind=dp), intent(in)	v,
		real(kind=dp), intent(in)	w,
		logical, optional	invertEdge
	)

Gradient of wedge edge basis at point (u,v,w)

References dphi(), dvarphi(), dwedgel(), messages::fatal(), phi(), varphi(), and wedgel().

Referenced by elementdescription::elementinfo().

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real(kind=dp) function, dimension(3) pelementbase::dwedgefacepbasis	(	integer, intent(in)	face,
		integer, intent(in)	i,
		integer, intent(in)	j,
		real(kind=dp), intent(in)	u,
		real(kind=dp), intent(in)	v,
		real(kind=dp), intent(in)	w,
		integer, dimension(4), optional	localNumbers
	)

Gradient of wedge face basis at point (u,v,w)

References dlegendrep(), dphi(), dvarphi(), dwedgeh(), dwedgel(), messages::fatal(), pelementmaps::getwedgefacemap(), legendrep(), phi(), varphi(), wedgeh(), and wedgel().

Referenced by elementdescription::elementinfo().

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real(kind=dp) function, dimension(3) pelementbase::dwedgeh	(	integer, intent(in)	which,
		real(kind=dp), intent(in)	w
	)

References messages::fatal().

Referenced by dwedgefacepbasis().

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real(kind=dp) function, dimension(3) pelementbase::dwedgel	(	integer, intent(in)	which,
		real(kind=dp), intent(in)	u,
		real(kind=dp), intent(in)	v
	)

References messages::fatal().

Referenced by dwedgebubblepbasis(), dwedgeedgepbasis(), dwedgefacepbasis(), and dwedgenodalpbasis().

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real(kind=dp) function, dimension(3) pelementbase::dwedgenodalpbasis	(	integer, intent(in)	node,
		real(kind=dp), intent(in)	u,
		real(kind=dp), intent(in)	v,
		real(kind=dp), intent(in)	w
	)

Gradient of wedges nodal basis at point (u,v,w)

References dwedgel(), messages::fatal(), and wedgel().

Referenced by elementdescription::nodalfirstderivatives().

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recursive function pelementbase::legendrep	(	integer, intent(in)	l,
		real (kind=dp), intent(in)	x
	)

Function LegendreP returns value of l,th Legendre polynomial for point x.

Value of legendre polynomial is precalculated for l=<20 and calculated from recursion for l>20, P(i+1,x)=1/(1+i)*((2*i+1)*x*P(i,x)+i*P(i-1,x)), where P(0,x)=1, P(1,x)=x.

References messages::fatal().

Referenced by dlegendrep(), dpyramidbubblepbasis(), dpyramidfacepbasis(), dtetrabubblepbasis(), dtetrafacepbasis(), dtriangleebubblepbasis(), dwedgebubblepbasis(), dwedgefacepbasis(), phi(), pyramidbubblepbasis(), pyramidfacepbasis(), tetrabubblepbasis(), tetrafacepbasis(), triangleebubblepbasis(), wedgebubblepbasis(), and wedgefacepbasis().

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real (kind=dp) function pelementbase::linebubblepbasis	(	integer, intent(in)	i,
		real (kind=dp), intent(in)	u,
		logical, optional	invertEdge
	)

Bubble function i of line element.

References phi().

Referenced by elementdescription::elementinfo().

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real (kind=dp) function pelementbase::linenodalpbasis	(	integer, intent(in)	node,
		real (kind=dp), intent(in)	u
	)

References messages::fatal().

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real (kind=dp) function pelementbase::phi	(	integer, intent(in)	i,
		real (kind=dp), intent(in)	x
	)

Phi function value at point x. Phi is defined as (Szabo & Babuska: Finite Element Analysis, p.38).

References messages::fatal(), legendrep(), and varphi().

Referenced by brickbubblepbasis(), brickedgepbasis(), brickfacepbasis(), checkcircleboundary(), dbrickbubblepbasis(), dbrickedgepbasis(), dbrickfacepbasis(), dquadbubblepbasis(), dquadedgepbasis(), dvarphi(), dwedgebubblepbasis(), dwedgeedgepbasis(), dwedgefacepbasis(), linebubblepbasis(), quadbubblepbasis(), quadedgepbasis(), varphi(), wedgebubblepbasis(), wedgeedgepbasis(), and wedgefacepbasis().

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real(kind=dp) function pelementbase::pyramidbubblepbasis	(	integer, intent(in)	i,
		integer, intent(in)	j,
		integer, intent(in)	k,
		real(kind=dp), intent(in)	u,
		real(kind=dp), intent(in)	v,
		real(kind=dp), intent(in)	w
	)

Pyramid bubble basis at point (u,v,w)

References legendrep(), and pyramidnodalpbasis().

Referenced by elementdescription::elementinfo().

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real(kind=dp) function pelementbase::pyramidedgepbasis	(	integer, intent(in)	edge,
		integer, intent(in)	i,
		real(kind=dp), intent(in)	u,
		real(kind=dp), intent(in)	v,
		real(kind=dp), intent(in)	w,
		logical, intent(in), optional	invertEdge
	)

Pyramid edge basis at point (u,v,w)

References messages::fatal(), pyramidnodalpbasis(), and varphi().

Referenced by elementdescription::elementinfo().

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real(kind=dp) function pelementbase::pyramidfacepbasis	(	integer, intent(in)	face,
		integer, intent(in)	i,
		integer, intent(in)	j,
		real(kind=dp), intent(in)	u,
		real(kind=dp), intent(in)	v,
		real(kind=dp), intent(in)	w,
		integer, dimension(4), intent(in), optional	localNumbers
	)

Pyramid face basis at point (u,v,w)

References messages::fatal(), pelementmaps::getpyramidfacemap(), legendrep(), pyramidl(), pyramidnodalpbasis(), and varphi().

Referenced by elementdescription::elementinfo().

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real(kind=dp) function pelementbase::pyramidl	(	integer, intent(in)	which,
		real(kind=dp), intent(in)	u,
		real(kind=dp), intent(in)	v
	)

References messages::fatal().

Referenced by dpyramidfacepbasis(), and pyramidfacepbasis().

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real(kind=dp) function pelementbase::pyramidnodalpbasis	(	integer, intent(in)	node,
		real(kind=dp), intent(in)	u,
		real(kind=dp), intent(in)	v,
		real(kind=dp), intent(in)	w
	)

Pyramid nodal basis at point (u,v,w)

References messages::fatal(), and pyramidt().

Referenced by dpyramidbubblepbasis(), dpyramidedgepbasis(), dpyramidfacepbasis(), elementdescription::nodalbasisfunctions(), pyramidbubblepbasis(), pyramidedgepbasis(), and pyramidfacepbasis().

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real(kind=dp) function pelementbase::pyramidt	(	integer, intent(in)	which,
		real(kind=dp), intent(in)	c,
		real(kind=dp), intent(in)	t
	)

References messages::fatal().

Referenced by dpyramidnodalpbasis(), and pyramidnodalpbasis().

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real (kind=dp) function pelementbase::quadbubblepbasis	(	integer, intent(in)	i,
		integer, intent(in)	j,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v,
		integer, dimension(4), optional	localNumbers
	)

Quadrilateral bubble basis at point (u,v).

References phi(), and quadl().

Referenced by elementdescription::elementinfo().

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real (kind=dp) function pelementbase::quadedgepbasis	(	integer, intent(in)	edge,
		integer, intent(in)	i,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v,
		logical, optional	invertEdge
	)

Quadrilateral edge basis at point (u,v).

References messages::fatal(), and phi().

Referenced by elementdescription::elementinfo().

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real(kind=dp) function pelementbase::quadl	(	integer, intent(in)	which,
		real(kind=dp), intent(in)	u,
		real(kind=dp), intent(in)	v
	)

Defines linear functions for quadrilateral nodes. These are used in calculation of changing parameters for bubbles of quadrilateral if directional function values are requested.

References messages::fatal().

Referenced by dquadbubblepbasis(), dquadpyraedgepbasis(), quadbubblepbasis(), and quadpyraedgepbasis().

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real (kind=dp) function pelementbase::quadnodalpbasis	(	integer, intent(in)	node,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v
	)

Quadrilateral nodal basis at point (u,v).

References messages::fatal().

Referenced by dquadpyraedgepbasis(), elementdescription::nodalbasisfunctions(), and quadpyraedgepbasis().

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real (kind=dp) function pelementbase::quadpyraedgepbasis	(	integer, intent(in)	edge,
		integer, intent(in)	i,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v,
		logical, optional	invertEdge
	)

Quadrilateral edge basis at point (u,v), which is compatible with basis for pyramidal 3d element square face.

References messages::fatal(), pelementmaps::getquadedgemap(), quadl(), quadnodalpbasis(), and varphi().

Referenced by elementdescription::elementinfo().

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real (kind=dp) function pelementbase::tetrabubblepbasis	(	integer, intent(in)	i,
		integer, intent(in)	j,
		integer, intent(in)	k,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v,
		real (kind=dp), intent(in)	w
	)

Tetra bubble basis at point (u,v,w)

References legendrep(), and tetranodalpbasis().

Referenced by elementdescription::elementinfo().

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real (kind=dp) function pelementbase::tetraedgepbasis	(	integer, intent(in)	edge,
		integer, intent(in)	i,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v,
		real (kind=dp), intent(in)	w,
		integer, intent(in), optional	tetratype
	)

Tetra edge basis at point (u,v,w)

References messages::fatal(), tetranodalpbasis(), and varphi().

Referenced by elementdescription::elementinfo().

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real (kind=dp) function pelementbase::tetrafacepbasis	(	integer, intent(in)	face,
		integer, intent(in)	i,
		integer, intent(in)	j,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v,
		real (kind=dp), intent(in)	w,
		integer, intent(in), optional	tetratype
	)

Tetra face basis at point (u,v,w)

References messages::fatal(), legendrep(), and tetranodalpbasis().

Referenced by elementdescription::elementinfo().

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real (kind=dp) function pelementbase::tetranodalpbasis	(	integer, intent(in)	node,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v,
		real (kind=dp), intent(in)	w
	)

Tetrahedron nodal basis at point (u,v,w)

References messages::fatal().

Referenced by dtetrabubblepbasis(), dtetraedgepbasis(), dtetrafacepbasis(), elementdescription::nodalbasisfunctions(), elementdescription::rtandbdmelementinfo(), tetrabubblepbasis(), tetraedgepbasis(), and tetrafacepbasis().

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real(kind=dp) function pelementbase::toexp	(	real(kind=dp), intent(in)	x,
		integer, intent(in)	n
	)

Referenced by dtrianglebubblepbasis().

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real (kind=dp) function pelementbase::trianglebubblepbasis	(	integer, intent(in)	j,
		integer, intent(in)	n,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v,
		integer, dimension(3), optional	localNumbers
	)

Triangle bubble basis at point (u,v).

References trianglenodalpbasis().

Referenced by elementdescription::elementinfo().

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real (kind=dp) function pelementbase::triangleebubblepbasis	(	integer, intent(in)	i,
		integer, intent(in)	j,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v,
		integer, dimension(3), optional	localNumbers
	)

References legendrep(), and trianglenodalpbasis().

Referenced by elementdescription::elementinfo().

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real (kind=dp) function pelementbase::triangleedgepbasis	(	integer, intent(in)	edge,
		integer, intent(in)	i,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v,
		logical, intent(in), optional	invertEdge
	)

Triangle edge basis at point (u,v).

References messages::fatal(), trianglenodalpbasis(), and varphi().

Referenced by elementdescription::elementinfo().

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real (kind=dp) function pelementbase::trianglenodalpbasis	(	integer, intent(in)	node,
		real (kind=dp), intent(in)	u,
		real (kind=dp), intent(in)	v
	)

Triangle nodal basis at point (u,v).

References messages::fatal().

Referenced by dtrianglebubblepbasis(), dtriangleebubblepbasis(), dtriangleedgepbasis(), elementdescription::nodalbasisfunctions(), elementdescription::rtandbdmelementinfo(), trianglebubblepbasis(), triangleebubblepbasis(), and triangleedgepbasis().

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real (kind=dp) function pelementbase::varphi	(	integer, intent(in)	i,
		real (kind=dp), intent(in)	x
	)

varPhi function value at point x. Phi is defined as (Szabo & Babuska: Finite Element Analysis, p. 103). Phi(i,x)=1/4*(1-x^2)*varPhi(i,x)

References messages::fatal(), and phi().

Referenced by brickpyraedgepbasis(), dbrickpyraedgepbasis(), dpyramidedgepbasis(), dpyramidfacepbasis(), dquadpyraedgepbasis(), dtetraedgepbasis(), dtriangleedgepbasis(), dwedgeedgepbasis(), dwedgefacepbasis(), phi(), pyramidedgepbasis(), pyramidfacepbasis(), quadpyraedgepbasis(), tetraedgepbasis(), triangleedgepbasis(), wedgeedgepbasis(), and wedgefacepbasis().

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real(kind=dp) function pelementbase::wedgebubblepbasis	(	integer, intent(in)	i,
		integer, intent(in)	j,
		integer, intent(in)	k,
		real(kind=dp), intent(in)	u,
		real(kind=dp), intent(in)	v,
		real(kind=dp), intent(in)	w
	)

Wedge bubble basis at point (u,v,w)

References legendrep(), phi(), and wedgel().

Referenced by elementdescription::elementinfo().

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real(kind=dp) function pelementbase::wedgeedgepbasis	(	integer, intent(in)	edge,
		integer, intent(in)	i,
		real(kind=dp), intent(in)	u,
		real(kind=dp), intent(in)	v,
		real(kind=dp), intent(in)	w,
		logical, optional	invertEdge
	)

Wedge edge basis at point (u,v,w)

References messages::fatal(), phi(), varphi(), and wedgel().

Referenced by elementdescription::elementinfo().

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real(kind=dp) function pelementbase::wedgefacepbasis	(	integer, intent(in)	face,
		integer, intent(in)	i,
		integer, intent(in)	j,
		real(kind=dp), intent(in)	u,
		real(kind=dp), intent(in)	v,
		real(kind=dp), intent(in)	w,
		integer, dimension(4), optional	localNumbers
	)

Wedge face basis at point (u,v,w)

References messages::fatal(), pelementmaps::getwedgefacemap(), legendrep(), phi(), varphi(), wedgeh(), and wedgel().

Referenced by elementdescription::elementinfo().

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real(kind=dp) function pelementbase::wedgeh	(	integer, intent(in)	which,
		real(kind=dp), intent(in)	w
	)

References messages::fatal().

Referenced by dwedgefacepbasis(), and wedgefacepbasis().

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real(kind=dp) function pelementbase::wedgel	(	integer, intent(in)	which,
		real(kind=dp), intent(in)	u,
		real(kind=dp), intent(in)	v
	)

References messages::fatal().

Referenced by dwedgebubblepbasis(), dwedgeedgepbasis(), dwedgefacepbasis(), dwedgenodalpbasis(), wedgebubblepbasis(), wedgeedgepbasis(), wedgefacepbasis(), and wedgenodalpbasis().

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real(kind=dp) function pelementbase::wedgenodalpbasis	(	integer, intent(in)	node,
		real(kind=dp), intent(in)	u,
		real(kind=dp), intent(in)	v,
		real(kind=dp), intent(in)	w
	)

Wedge nodal basis at point (u,v,w)

References messages::fatal(), and wedgel().

Referenced by elementdescription::nodalbasisfunctions().

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The documentation for this module was generated from the following file:

PElementBase.src

Public Member Functions

Member Function/Subroutine Documentation