Elmer FEM solver Elmer is an open source finite element software for multiphysical problems
pelementbase Module Reference

## 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().

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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.

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).

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().

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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().

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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)

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().

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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.

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)

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().

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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().

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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().

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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)

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().

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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().

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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)

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().

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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().

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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.

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().

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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().

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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().

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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)

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().

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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: