This module contains subroutines to generate the shape functions for multi dimensions. More...

Data Types
interface	xprod
	Performs the cross product of two vectors. More...

Functions/Subroutines
subroutine	quad_1d_shape (cv_ngi, cv_nloc, u_nloc, cvn, cvweigh, n, nlx, un, unlx)
	: For quadratic elements. Shape functions associated with volume integration using both CV basis functions CVN as well as FEM basis functions N (and its derivatives NLX, NLY, NLZ) More...

subroutine	quad_nd_shape (ndim, cv_ele_type, cv_ngi, cv_nloc, u_nloc, cvn, cvweigh, n, nlx, nly, nlz, un, unlx, unly, unlz)
	: For quadratic elements: Shape functions associated with volume integration using both CV (CVN) and FEM (N and its derivatives NLX/Y/Z) basis functions. More...

subroutine	quad_nd_shape_n (cv_ele_type, ndim, cv_ngi, cv_nloc, cvn, cvweigh, n, nlx, nly, nlz, cv_ngi_1d, cv_nloc_1d, cvn_1d, cvweigh_1d, n_1d, nlx_1d)
	: For quadatic elements – shape functions associated with volume integration using both CV basis functions CVN as well as FEM basis functions N (and its derivatives NLX, NLY, NLZ) More...

subroutine	vol_cv_tri_tet_shape (cv_ele_type, ndim, cv_ngi, cv_nloc, u_nloc, cvn, cvweigh, n, nlx, nly, nlz, un, unlx, unly, unlz)
	: Compute shape functions N, UN etc for linear trianles. Shape functions associated with volume integration using both CV basis functions CVN, as well as FEM basis functions N (and its derivatives NLX, NLY, NLZ). Also for velocity basis functions UN, UNLX, UNLY, UNLZ. More...

subroutine	new_pt_qua_vol_cv_tri_tet_shape (cv_ele_type, ndim, cv_ngi, cv_nloc, u_nloc, cvn, cvweigh, n, nlx, nly, nlz, un, unlx, unly, unlz)
	: new 1 or 4 pt quadrature set on each CV of a quadratic tetrahedra ..... Compute shape functions N, UN etc for linear trianles. Shape functions associated with volume integration using both CV basis functions CVN, as well as FEM basis functions N (and its derivatives NLX, NLY, NLZ). Also for velocity basis functions UN, UNLX, UNLY, UNLZ. More...

subroutine	test_quad_tet (cv_nloc, cv_ngi, cvn, n, nlx, nly, nlz, cvweight, x, y, z, x_nonods, x_ndgln2, totele)
	test the volumes of idealised triangle More...

subroutine	compute_xndgln_tritetquadhex (cv_ele_type, max_totele, max_x_nonods, quad_cv_nloc, totele, x_nonods, x_ndgln, lx, ly, lz, x, y, z, fem_nod, x_ideal, y_ideal, z_ideal, x_ndgln_ideal)
	Get the x_ndgln for the nodes of triangles or tetrahedra. More...

subroutine	suf_cv_tri_tet_shape (cv_ele_type, ndim, scvngi, cv_nloc, u_nloc, scvfeweigh, scvfen, scvfenlx, scvfenly, scvfenlz, scvfenslx, scvfensly, sufen, sufenlx, sufenly, sufenlz, sufenslx, sufensly, cv_neiloc, cvfem_neiloc, ufem_neiloc)
	: Compute shape functions N, UN etc for linear triangles. Shape functions associated with volume integration using both CV basis functions CVN, as well as FEM basis functions SN (and its derivatives SNLX, SNLY, SNLZ). Also for velocity basis functions SUN, SUNLX, SUNLY, SUNLZ. Also the derivatives along the CV faces: sufnlx, sufnly, sufunlx, sufunly More...

subroutine	james_quadrature_quad_tet (l1, l2, l3, l4, normx, normy, normz, sarea, X_LOC, Y_LOC, Z_LOC, CV_NEILOC, cv_nloc, scvngi)
	: the surface quadrature pts in local coord are l1, l2, l3, l4, and the associated normals normx, normy, normz and the surface area is sarea The position of the nodes of the tet are: (X_LOC, Y_LOC, Z_LOC) Calculate cv_neiloc: To get the neighbouring node for node ILOC and surface quadrature point SGI CV_JLOC = CV_NEILOC( CV_ILOC, SGI ) The number of quadrature points is 24 = 4 x 6 exterior faces (and quadrature points) and 36 = 4x6 + 6x4/2 = 60 pts. @WARNING: Disabled because it introduces errors More...

subroutine	get_tang_binorm (NX, NY, NZ, T1X, T1Y, T1Z, T2X, T2Y, T2Z, NNODRO)

subroutine	compute_surfaceshapefunctions_triangle_tetrahedron (cv_nloc_cells, cv_ele_type_cells, cv_ele_type, ndim, totele, cv_nloc, scvngi, x_nonods, quad_cv_nloc, x_ndgln, x, y, z, lx, ly, lz, fem_nod, sn, snlx, snly, snlz, sufnlx, sufnly, scvweigh, cv_neiloc_cells, cvfem_neiloc)
	: this subroutine calculates shape functions sn, snlx, snly, snlz, sufnlx, sufnly, their weights scvweigh and local connectivity cv_neiloc_cells, cvfem_neiloc on the boundaries of the cv_nloc_cells control volumes. The control volume types are defines using cv_ele_type_cells. cv_neiloc_cells is associated with the CV cells cvfem_neiloc is associated with the FEM basis SN etc. More...

subroutine	dummy_tri_tet (d1, d3, quad_cv_ngi, quad_cv_nloc, dummy_sngi, dummy_snloc, nwicel, cv_nloc, cv_sngi, totele, quad_u_loc_dummy, mloc, dummy_smloc, lowqua, npoly, npoly_ngi)
	Compute some local variables for suf_shape_tri_tet. More...

subroutine	shape_tri_tet (cv_ele_type_cells, cv_nloc_cells, cv_ele_type, ndim, totele, cv_nloc, cv_ngi, x_nonods, quad_cv_nloc, x_ndgln, x, y, z, lx, ly, lz, n, nlx, nly, nlz, cvweigh)
	: Determine the volume shape functions n, nlx, nly, nlz and weights cvweigh for the cv_nloc_cells CV cells. More...

subroutine	shatri_hex (l1, l2, l3, l4, weight, d3, nloc, ngi, n, nlx, nly, nlz, tri_tet)
	Get the shape functions on lines (in 2D) and quadrilateral surfaces in 3D. More...

subroutine	shatri (l1, l2, l3, l4, weight, d3, nloc, ngi, n, nlx, nly, nlz)
	get the shape functions for a triangle/tetrahedron More...

subroutine	shape_triangle_cubic (l1, l2, l3, l4, weight, d3, nloc, ngi, n, nlx, nly, nlz)
	Generates the shape functions of a cubic triangle. More...

subroutine	base_order_tri (n, nloc, ngi)
	order so that the 1st nodes are on the base for a quadratic triangle... More...

subroutine	base_order_tet (n, nloc, ngi)
	order so that the 1st nodes are on the base of tet for a quadratic tet... More...

subroutine	calc_cvn_tritetquadhex (cv_ele_type, totele, cv_nloc, cv_ngi, x_nonods, quad_cv_nloc, x_ndgln, fem_nod, cvn)
	Compute CVN (CV basis function) for triangles, tetrahedra, quadrilaterals and hexahedra. More...

subroutine	shape_l_q_quad (lowqua, ngi, nloc, mloc, sngi, snloc, smloc, m, mlx, mly, mlz, weight, n, nlx, nly, nlz, sweigh, sn, snlx, snly, sm, smlx, smly, nwicel, d3)
	This subrt computes shape functions. For now, let's just define for one element type. NB: N may overwrite M if we are not solving for pressure. More...

real function	volume_quad_map (cv_iloc, xgi, ygi, zgi, lx, ly, lz)
	Compute the cv_iloc^{th} shape function value at point (xgi, ygi, zgi) More...

real function	area_quad_map (cv_iloc, xgi, ygi, lx, ly)

real function	tet_vol (a, b, c, d)

real function	triareaf (x1, y1, x2, y2, x3, y3)

real function	triareaf_sign (x1, y1, x2, y2, x3, y3)

subroutine	crossproduct (n, cp, a, b)

subroutine	printoutfunmat (n, m, a)

subroutine	dgsdetnxloc2 (SNLOC, SNGI, XSL, YSL, ZSL, SN, SNLX, SNLY, SWEIGH, SDETWE, SAREA, D1, D3, DCYL, NORMXN, NORMYN, NORMZN, NORMX, NORMY, NORMZ)

subroutine	dgsdetnxloc2_all (SNLOC, SNGI, NDIM, XSL_ALL, SN, SNLX, SNLY, SWEIGH, SDETWE, SAREA, NORMXN_ALL, NORMX_ALL)

subroutine	normgi (NORMXN, NORMYN, NORMZN, DXDLX, DYDLX, DZDLX, DXDLY, DYDLY, DZDLY, NORMX, NORMY, NORMZ)
	Calculate the normal at the Gauss pts Perform x-product. N=T1 x T2. More...

subroutine	xprod1 (AX, AY, AZ, BX, BY, BZ, CX, CY, CZ)
	Perform the cross product of two vectors. More...

subroutine	xprod2 (A, B, C)
	Perform the cross product of two vectors. More...

subroutine	make_qtri (totele, x_nloc, max_x_nonods, x_nonods, x_ndgln, lx, ly, x, y, fem_nod)

subroutine	computing_small_qtriangles (ele_big, x_nloc_big, totele_big, x_nonods_big, increment_ele_big, x_ndgln_big, x_big, y_big)

subroutine	remaping_fields_qtriangles (ele_big, x_nloc_big, totele_big, x_nonods_big, x_ndgln_big, x_big, y_big, x_nonods, x_nloc, totele, x_ndgln, ele_ref, x, y)

subroutine	eliminating_repetitive_nodes (totele, x_nloc, x_nonods, over_all, x_ndgln, x, y)

subroutine	eliminating_repetitive_nodes_all (totele, x_nloc, x_nonods, mx_x_nonods, x_ndgln, x, y, z)

subroutine	adding_extra_parametric_nodes (totele, x_nloc, mx_x_nonods, x_ndgln, x, y)

subroutine	make_qtets (totele, quad_cv_nloc, x_nloc, max_x_nonods, x_nonods, x_ndgln_real, lx, ly, lz, x, y, z, fem_nod, xp2, yp2, zp2, x_ndgln_p2)
	This subrt creates the local coordinates and node points for: (a) quadratic tetrahedra of unit volume and (b) 27 points of the 8 hexahedra within the 8 linear tetrahedra. FEM_NOD is the local numbering of the FEM representation of the unit volume quadratic tetrahedron. More...

subroutine	make_linear_tetrahedron (ele, quad_cv_nloc, x_nloc, x_nonods, number_of_hexs, xp2, yp2, zp2, x, y, z, x_ndgln_p2, x_ndgln)

subroutine	make_bilinear_hexahedra (totele, number_of_hexs, quad_cv_nloc, x_nonods, x, y, z, x_ndgln)

subroutine	adding_parametric_nodes_hex (ele, ele_hex, totele, number_of_hexs, quad_cv_nloc, x_nonods, x, y, z, x_ndgln)

subroutine	shape_one_ele2 (ndim, cv_ele_type, cv_ngi, cv_nloc, u_nloc, cvweight, cvfen, cvfenlx, cvfenly, cvfenlz, ufen, ufenlx, ufenly, ufenlz, sbcvngi, sbcvfen, sbcvfenslx, sbcvfensly, sbcvfeweigh, sbufen, sbufenslx, sbufensly, nface, cv_sloclist, u_sloclist, cv_snloc, u_snloc)
	: This subrt defines the sub-control volume and FEM shape functions. Shape functions associated with volume integration using both CV basis functions CVN as well as FEM basis functions CVFEN (and its derivatives CVFENLX, CVFENLY, CVFENLZ) More...

subroutine	shape (LOWQUA, NGI, NLOC, MLOC, SNGI, SNLOC, SMLOC, M, MLX, MLY, MLZ, WEIGHT, N, NLX, NLY, NLZ, SWEIGH, SN, SNLX, SNLY, SM, SMLX, SMLY, NWICEL, D3)

subroutine	tr2or3dqu (NGI, NLOC, MLOC, M, MLX, MLY, MLZ, WEIGHT, N, NLX, NLY, NLZ, SNGI, SNLOC, SWEIGH, SN, SNLX, SNLY, SMLOC, SM, SMLX, SMLY, D3)
	:This subroutine defines the shape functions M and N and their derivatives at the Gauss points for quadratic elements. For 3-D FLOW. More...

subroutine	tr2d (LOWQUA, NGI, NLOC, MLOC, M, WEIGHT, N, NLX, NLY, SNGI, SNLOC, SWEIGH, SN, SNLX)
	This subroutine defines the shape functions M and N and their derivatives at the Gauss points For 3-D FLOW. More...

subroutine	shatrinew (L1, L2, L3, L4, WEIGHT, NLOC, NGI, N, NLX_ALL)
	: Work out the shape functions and their derivatives... More...

subroutine	shatriold (L1, L2, L3, L4, WEIGHT, D3, NLOC, NGI, N, NLX, NLY, NLZ)
	: Work out the shape functions and their derivatives... More...

subroutine	triquaold (L1, L2, L3, L4, WEIGHT, D3, NGI)
	: This sub calculates the local corrds L1, L2, L3, L4 and weights at the quadrature points. If D3 it does this for 3Dtetrahedra elements else triangular elements. More...

subroutine	spectr (NGI, NLOC, MLOC, M, WEIGHT, N, NLX, NLY, NLZ, D3, D2, IPOLY, IQADRA)
	This subroutine defines a spectal element. IPOLY defines the element type and IQADRA the quadrature. In 2-D the spectral local node numbering is as.. 7 8 9 4 5 6 1 2 3 For 3-D... lz=-1 3 4 1 2 and for lz=1 7 8 5 6. More...

subroutine	gtroot (IPOLY, IQADRA, WEIT, NODPOS, QUAPOS, NDGI, NDNOD)
	This sub returns the weights WEIT the quadrature points QUAPOS and the node points NODPOS. NODAL POISTIONS ****** NB if GETNDP then find the nodal positions. More...

real function	specfu (DIFF, LXGP, INOD, NDNOD, IPOLY, NODPOS)
	INOD contains the node at which the polynomial is associated with LXGP is the position at which the polynomial is to be avaluated.\ If(DIFF) then find the D poly/DX. More...

subroutine	cherot (WEIT, QUAPOS, NDGI, GETNDP)
	This computes the weight and points for Chebyshev-Gauss-Lobatto quadrature. See page 67 of:Spectral Methods in Fluid Dynamics, C.Canuto IF(GETNDP) then get the POSITION OF THE NODES AND DONT BOTHER WITH THE WEITS. More...

subroutine	legrot (WEIT, QUAPOS, NDGI, GETNDP)
	This computes the weight and points for Chebyshev-Gauss-Lobatto quadrature. See page 69 of:Spectral Methods in Fluid Dynamics, C.Canuto IF(GETNDP) then get the POSITION OF THE NODES AND DONT BOTHER WITH THE WEITS. More...

real function	plegen (LX, K)

real function	binomial_coefficient (K, L)
	Calculate binomial coefficients. More...

subroutine	lroots (QUAPOS, NDGI)
	This sub works out the Gauss-Lobatto-Legendre roots. More...

real function	cheby1 (DIFF, LX, INOD, NDNOD, NODPOS)
	If DIFF then returns the spectral function DIFFERENTIATED W.R.T X associated. This function returns the spectral function associated with node INOD at POINT LX NDNOD=no of nodes in 1-D. NDGI=no of Gauss pts in 1-D. NB The nodes are at the points COS(pie*J/2.) j=0,..,ndgi-1. More...

real function	cheby2 (DIFF, LX, INOD, NDNOD, NODPOS)
	If DIFF then returns the spectral function DIFFERENTIATED W.R.T X associated. This function returns the spectral function associated with node INOD at POINT LX NDNOD=no of nodes in 1-D. NDGI=no of Gauss pts in 1-D. NB The nodes are at the points COS(pie*J/2.) j=0,..,ndgi-1. More...

real function	tcheb (N, XPT, DIFF, DIFF2)
	If DIFF then return the n'th Chebyshef polynomial differentiated w.r.t x. If DIFF2 then form the 2'nd derivative. This sub returns the value of the K'th Chebyshef polynomial at a point XPT. More...

recursive integer function	factorial (n)
	Calculate n! More...

real function	legend (DIFF, LX, INOD, NDNOD, NODPOS)
	If DIFF then returns the spectral function DIFFERENTIATED W.R.T X associated. This function returns the spectral function associated with node INOD at POINT LX NDNOD=no of nodes in 1-D. NDGI=no of Gauss pts in 1-D. NB The nodes are at the points COS(pie*J/2.) j=0,..,ndgi-1. More...

subroutine	determin_sloclist (CV_SLOCLIST, CV_NLOC, CV_SNLOC, NFACE, ndim, cv_ele_type)
	determine CV_SLOCLIST More...

subroutine	jacobl (N, ALPHA, BETA, XJAC)
	COMPUTES THE GAUSS-LOBATTO COLLOCATION POINTS FOR JACOBI POLYNOMIALS. More...

subroutine	jacobf (N, POLY, PDER, POLYM1, PDERM1, POLYM2, PDERM2, X)
	COMPUTES THE JACOBI POLYNOMIAL (POLY) AND ITS DERIVATIVE (PDER) OF DEGREE N AT X. More...

real function	volume_tethex (hexs, x1, x2, x3, x4, y1, y2, y3, y4, z1, z2, z3, z4)

subroutine	get_cvn_compact_overlapping (cv_ele_type, ndim, cv_ngi, cv_nloc, cvn, cvweigh)
	: Calculates the CVN and CVWEIGH shape functions This subroutine is specially created to be used with compact_overlapping More...

integer function	get_nwicel (d3, nloc)
	: Provides a number defining the type of element we are dealing with 4,5 Linear tetrahedra, 10 quadratic tetrahedra; 3,4 Linear triangle, 5 quadratic triangle More...

Detailed Description

This module contains subroutines to generate the shape functions for multi dimensions.

Function/Subroutine Documentation

◆ adding_extra_parametric_nodes()

subroutine shape_functions_ndim::adding_extra_parametric_nodes	(	integer, intent(in)	totele,
		integer, intent(in)	x_nloc,
		integer, intent(in)	mx_x_nonods,
		integer, dimension( : ), intent(inout)	x_ndgln,
		real, dimension( : ), intent(inout)	x,
		real, dimension( : ), intent(inout)	y
	)

Here is the caller graph for this function:

◆ adding_parametric_nodes_hex()

subroutine shape_functions_ndim::adding_parametric_nodes_hex	(	integer, intent(in)	ele,
		integer, intent(in)	ele_hex,
		integer, intent(in)	totele,
		integer, intent(in)	number_of_hexs,
		integer, intent(in)	quad_cv_nloc,
		integer, intent(in)	x_nonods,
		real, dimension( : ), intent(inout)	x,
		real, dimension( : ), intent(inout)	y,
		real, dimension( : ), intent(inout)	z,
		integer, dimension( : ), intent(inout)	x_ndgln
	)

Here is the caller graph for this function:

◆ area_quad_map()

real function shape_functions_ndim::area_quad_map	(	integer	cv_iloc,
		real	xgi,
		real	ygi,
		real, dimension( : )	lx,
		real, dimension( : )	ly
	)

Here is the call graph for this function:

Here is the caller graph for this function:

◆ base_order_tet()

subroutine shape_functions_ndim::base_order_tet	(	real, dimension( nloc, ngi ), intent(inout)	n,
		integer, intent(in)	nloc,
		integer, intent(in)	ngi
	)

order so that the 1st nodes are on the base of tet for a quadratic tet...

Here is the caller graph for this function:

◆ base_order_tri()

subroutine shape_functions_ndim::base_order_tri	(	real, dimension( nloc, ngi ), intent(inout)	n,
		integer, intent(in)	nloc,
		integer, intent(in)	ngi
	)

order so that the 1st nodes are on the base for a quadratic triangle...

Here is the caller graph for this function:

◆ binomial_coefficient()

real function shape_functions_ndim::binomial_coefficient	(	integer	K,
		integer	L
	)

Calculate binomial coefficients.

Here is the call graph for this function:

Here is the caller graph for this function:

◆ calc_cvn_tritetquadhex()

subroutine shape_functions_ndim::calc_cvn_tritetquadhex	(	integer, intent(in)	cv_ele_type,
		integer, intent(in)	totele,
		integer, intent(in)	cv_nloc,
		integer, intent(in)	cv_ngi,
		integer, intent(in)	x_nonods,
		integer, intent(in)	quad_cv_nloc,
		integer, dimension( : ), intent(in)	x_ndgln,
		integer, dimension( : ), intent(in)	fem_nod,
		real, dimension( :, : ), intent(inout)	cvn
	)

Compute CVN (CV basis function) for triangles, tetrahedra, quadrilaterals and hexahedra.

Here is the caller graph for this function:

◆ cheby1()

real function shape_functions_ndim::cheby1	(	logical, intent(inout)	DIFF,
		real, intent(inout)	LX,
		integer, intent(inout)	INOD,
		integer, intent(inout)	NDNOD,
		real, dimension(:), intent(inout)	NODPOS
	)

If DIFF then returns the spectral function DIFFERENTIATED W.R.T X associated. This function returns the spectral function associated with node INOD at POINT LX NDNOD=no of nodes in 1-D. NDGI=no of Gauss pts in 1-D. NB The nodes are at the points COS(pie*J/2.) j=0,..,ndgi-1.

Here is the call graph for this function:

Here is the caller graph for this function:

◆ cheby2()

real function shape_functions_ndim::cheby2	(	logical, intent(inout)	DIFF,
		real, intent(inout)	LX,
		integer, intent(inout)	INOD,
		integer, intent(inout)	NDNOD,
		real, dimension(:), intent(inout)	NODPOS
	)

If DIFF then returns the spectral function DIFFERENTIATED W.R.T X associated. This function returns the spectral function associated with node INOD at POINT LX NDNOD=no of nodes in 1-D. NDGI=no of Gauss pts in 1-D. NB The nodes are at the points COS(pie*J/2.) j=0,..,ndgi-1.

Here is the call graph for this function:

Here is the caller graph for this function:

◆ cherot()

subroutine shape_functions_ndim::cherot	(	real, dimension(:), intent(inout)	WEIT,
		real, dimension(:), intent(inout)	QUAPOS,
		integer, intent(inout)	NDGI,
		logical, intent(inout)	GETNDP
	)

This computes the weight and points for Chebyshev-Gauss-Lobatto quadrature. See page 67 of:Spectral Methods in Fluid Dynamics, C.Canuto IF(GETNDP) then get the POSITION OF THE NODES AND DONT BOTHER WITH THE WEITS.

Here is the caller graph for this function:

◆ compute_surfaceshapefunctions_triangle_tetrahedron()

subroutine shape_functions_ndim::compute_surfaceshapefunctions_triangle_tetrahedron	(	integer, intent(in)	cv_nloc_cells,
		integer, intent(in)	cv_ele_type_cells,
		integer, intent(in)	cv_ele_type,
		integer, intent(in)	ndim,
		integer, intent(in)	totele,
		integer, intent(in)	cv_nloc,
		integer, intent(in)	scvngi,
		integer, intent(in)	x_nonods,
		integer, intent(in)	quad_cv_nloc,
		integer, dimension( : ), intent(in)	x_ndgln,
		real, dimension( : ), intent(in)	x,
		real, dimension( : ), intent(in)	y,
		real, dimension( : ), intent(in)	z,
		real, dimension( : ), intent(in)	lx,
		real, dimension( : ), intent(in)	ly,
		real, dimension( : ), intent(in)	lz,
		integer, dimension( : ), intent(in)	fem_nod,
		real, dimension( :, : ), intent(inout)	sn,
		real, dimension( :, : ), intent(inout)	snlx,
		real, dimension( :, : ), intent(inout)	snly,
		real, dimension( :, : ), intent(inout)	snlz,
		real, dimension( :, : ), intent(inout)	sufnlx,
		real, dimension( :, : ), intent(inout)	sufnly,
		real, dimension( : ), intent(inout)	scvweigh,
		integer, dimension( :, : ), intent(inout)	cv_neiloc_cells,
		integer, dimension( :, : ), intent(inout)	cvfem_neiloc
	)

: this subroutine calculates shape functions sn, snlx, snly, snlz, sufnlx, sufnly, their weights scvweigh and local connectivity cv_neiloc_cells, cvfem_neiloc on the boundaries of the cv_nloc_cells control volumes. The control volume types are defines using cv_ele_type_cells. cv_neiloc_cells is associated with the CV cells cvfem_neiloc is associated with the FEM basis SN etc.

Here is the call graph for this function:

Here is the caller graph for this function:

◆ compute_xndgln_tritetquadhex()

subroutine shape_functions_ndim::compute_xndgln_tritetquadhex	(	integer, intent(in)	cv_ele_type,
		integer, intent(in)	max_totele,
		integer, intent(in)	max_x_nonods,
		integer, intent(in)	quad_cv_nloc,
		integer, intent(inout)	totele,
		integer, intent(inout)	x_nonods,
		integer, dimension( : ), intent(inout)	x_ndgln,
		real, dimension( : ), intent(inout)	lx,
		real, dimension( : ), intent(inout)	ly,
		real, dimension( : ), intent(inout)	lz,
		real, dimension( : ), intent(inout)	x,
		real, dimension( : ), intent(inout)	y,
		real, dimension( : ), intent(inout)	z,
		integer, dimension( : ), intent(inout)	fem_nod,
		real, dimension( : ), intent(inout)	x_ideal,
		real, dimension( : ), intent(inout)	y_ideal,
		real, dimension( : ), intent(inout)	z_ideal,
		integer, dimension( : ), intent(inout)	x_ndgln_ideal
	)

Get the x_ndgln for the nodes of triangles or tetrahedra.

Here is the call graph for this function:

Here is the caller graph for this function:

◆ computing_small_qtriangles()

subroutine shape_functions_ndim::computing_small_qtriangles	(	integer, intent(in)	ele_big,
		integer, intent(in)	x_nloc_big,
		integer, intent(in)	totele_big,
		integer, intent(in)	x_nonods_big,
		integer, intent(inout)	increment_ele_big,
		integer, dimension( : ), intent(inout)	x_ndgln_big,
		real, dimension( : ), intent(inout)	x_big,
		real, dimension( : ), intent(inout)	y_big
	)

Here is the caller graph for this function:

◆ crossproduct()

subroutine shape_functions_ndim::crossproduct	(	integer, intent(in)	n,
		real, dimension( : ), intent(inout)	cp,
		real, dimension( : ), intent(in)	a,
		real, dimension( : ), intent(in)	b
	)

Here is the caller graph for this function:

◆ determin_sloclist()

subroutine shape_functions_ndim::determin_sloclist	(	integer, dimension( :, : ), intent(inout)	CV_SLOCLIST,
		integer, intent(in)	CV_NLOC,
		integer, intent(in)	CV_SNLOC,
		integer, intent(in)	NFACE,
		integer, intent(in)	ndim,
		integer, intent(in)	cv_ele_type
	)

determine CV_SLOCLIST

Here is the caller graph for this function:

◆ dgsdetnxloc2()

subroutine shape_functions_ndim::dgsdetnxloc2	(	integer, intent(in)	SNLOC,
		integer, intent(in)	SNGI,
		real, dimension( : ), intent(in)	XSL,
		real, dimension( : ), intent(in)	YSL,
		real, dimension( : ), intent(in)	ZSL,
		real, dimension( :, : ), intent(in)	SN,
		real, dimension( :, : ), intent(in)	SNLX,
		real, dimension( :, : ), intent(in)	SNLY,
		real, dimension( : ), intent(in)	SWEIGH,
		real, dimension( : ), intent(inout)	SDETWE,
		real, intent(inout)	SAREA,
		logical, intent(in)	D1,
		logical, intent(in)	D3,
		logical, intent(in)	DCYL,
		real, dimension( : ), intent(inout)	NORMXN,
		real, dimension( : ), intent(inout)	NORMYN,
		real, dimension( : ), intent(inout)	NORMZN,
		real, intent(in)	NORMX,
		real, intent(in)	NORMY,
		real, intent(in)	NORMZ
	)

Here is the call graph for this function:

Here is the caller graph for this function:

◆ dgsdetnxloc2_all()

subroutine shape_functions_ndim::dgsdetnxloc2_all	(	integer, intent(in)	SNLOC,
		integer, intent(in)	SNGI,
		integer, intent(in)	NDIM,
		real, dimension( ndim, snloc ), intent(in)	XSL_ALL,
		real, dimension( snloc, sngi ), intent(in)	SN,
		real, dimension( snloc, sngi ), intent(in)	SNLX,
		real, dimension( snloc, sngi ), intent(in)	SNLY,
		real, dimension( sngi ), intent(in)	SWEIGH,
		real, dimension( sngi ), intent(inout)	SDETWE,
		real, intent(inout)	SAREA,
		real, dimension( ndim, sngi ), intent(inout)	NORMXN_ALL,
		real, dimension( ndim ), intent(in)	NORMX_ALL
	)

Here is the call graph for this function:

Here is the caller graph for this function:

◆ dummy_tri_tet()

subroutine shape_functions_ndim::dummy_tri_tet	(	logical, intent(in)	d1,
		logical, intent(in)	d3,
		integer, intent(inout)	quad_cv_ngi,
		integer, intent(in)	quad_cv_nloc,
		integer, intent(inout)	dummy_sngi,
		integer, intent(inout)	dummy_snloc,
		integer, intent(inout)	nwicel,
		integer, intent(in)	cv_nloc,
		integer, intent(in)	cv_sngi,
		integer, intent(in)	totele,
		integer, intent(inout)	quad_u_loc_dummy,
		integer, intent(inout)	mloc,
		integer, intent(inout)	dummy_smloc,
		logical, intent(inout)	lowqua,
		integer, intent(inout)	npoly,
		integer, intent(inout)	npoly_ngi
	)

Compute some local variables for suf_shape_tri_tet.

Here is the caller graph for this function:

◆ eliminating_repetitive_nodes()

subroutine shape_functions_ndim::eliminating_repetitive_nodes	(	integer, intent(in)	totele,
		integer, intent(in)	x_nloc,
		integer, intent(in)	x_nonods,
		logical, intent(in)	over_all,
		integer, dimension( : ), intent(inout)	x_ndgln,
		real, dimension( : ), intent(in)	x,
		real, dimension( : ), intent(in)	y
	)

Here is the caller graph for this function:

◆ eliminating_repetitive_nodes_all()

subroutine shape_functions_ndim::eliminating_repetitive_nodes_all	(	integer, intent(in)	totele,
		integer, intent(in)	x_nloc,
		integer, intent(inout)	x_nonods,
		integer, intent(in)	mx_x_nonods,
		integer, dimension( : ), intent(inout)	x_ndgln,
		real, dimension( : ), intent(inout)	x,
		real, dimension( : ), intent(inout)	y,
		real, dimension( : ), intent(inout), optional	z
	)

Here is the caller graph for this function:

◆ factorial()

recursive integer function shape_functions_ndim::factorial ( integer, intent(in) n )

Calculate n!

Here is the caller graph for this function:

◆ get_cvn_compact_overlapping()

subroutine shape_functions_ndim::get_cvn_compact_overlapping	(	integer, intent(in)	cv_ele_type,
		integer, intent(in)	ndim,
		integer, intent(in)	cv_ngi,
		integer, intent(in)	cv_nloc,
		real, dimension( :, : ), intent(inout)	cvn,
		real, dimension( : ), intent(inout)	cvweigh
	)

: Calculates the CVN and CVWEIGH shape functions This subroutine is specially created to be used with compact_overlapping

Here is the call graph for this function:

◆ get_nwicel()

integer function shape_functions_ndim::get_nwicel	(	logical	d3,
		integer	nloc
	)

: Provides a number defining the type of element we are dealing with 4,5 Linear tetrahedra, 10 quadratic tetrahedra; 3,4 Linear triangle, 5 quadratic triangle

Here is the caller graph for this function:

◆ get_tang_binorm()

subroutine shape_functions_ndim::get_tang_binorm	(	real, dimension( nnodro ), intent(in)	NX,
		real, dimension( nnodro ), intent(in)	NY,
		real, dimension( nnodro ), intent(in)	NZ,
		real, dimension( nnodro ), intent(inout)	T1X,
		real, dimension( nnodro ), intent(inout)	T1Y,
		real, dimension( nnodro ), intent(inout)	T1Z,
		real, dimension( nnodro ), intent(inout)	T2X,
		real, dimension( nnodro ), intent(inout)	T2Y,
		real, dimension( nnodro ), intent(inout)	T2Z,
		integer, intent(in)	NNODRO
	)

Here is the caller graph for this function:

◆ gtroot()

subroutine shape_functions_ndim::gtroot	(	integer, intent(inout)	IPOLY,
		integer, intent(inout)	IQADRA,
		real, dimension(:), intent(inout)	WEIT,
		real, dimension(:), intent(inout)	NODPOS,
		real, dimension(:), intent(inout)	QUAPOS,
		integer, intent(inout)	NDGI,
		integer, intent(inout)	NDNOD
	)

This sub returns the weights WEIT the quadrature points QUAPOS and the node points NODPOS. NODAL POISTIONS ****** NB if GETNDP then find the nodal positions.

Here is the call graph for this function:

Here is the caller graph for this function:

◆ jacobf()

subroutine shape_functions_ndim::jacobf	(	integer, intent(in)	N,
		real, intent(inout)	POLY,
		real, intent(inout)	PDER,
		real, intent(inout)	POLYM1,
		real, intent(inout)	PDERM1,
		real, intent(inout)	POLYM2,
		real, intent(inout)	PDERM2,
		real, intent(in)	X
	)

COMPUTES THE JACOBI POLYNOMIAL (POLY) AND ITS DERIVATIVE (PDER) OF DEGREE N AT X.

Here is the caller graph for this function:

◆ jacobl()

subroutine shape_functions_ndim::jacobl	(	integer, intent(in)	N,
		real, intent(inout)	ALPHA,
		real, intent(inout)	BETA,
		real, dimension(: )	XJAC
	)

COMPUTES THE GAUSS-LOBATTO COLLOCATION POINTS FOR JACOBI POLYNOMIALS.

N: DEGREE OF APPROXIMATION ALPHA: PARAMETER IN JACOBI WEIGHT BETA: PARAMETER IN JACOBI WEIGHT

XJAC: OUTPUT ARRAY WITH THE GAUSS-LOBATTO ROOTS THEY ARE ORDERED FROM LARGEST (+1.0) TO SMALLEST (-1.0)

Here is the call graph for this function:

Here is the caller graph for this function:

◆ james_quadrature_quad_tet()

subroutine shape_functions_ndim::james_quadrature_quad_tet	(	real, dimension( scvngi ), intent(inout)	l1,
		real, dimension( scvngi ), intent(inout)	l2,
		real, dimension( scvngi ), intent(inout)	l3,
		real, dimension( scvngi ), intent(inout)	l4,
		real, dimension( scvngi ), intent(inout)	normx,
		real, dimension( scvngi ), intent(inout)	normy,
		real, dimension( scvngi ), intent(inout)	normz,
		real, dimension( scvngi ), intent(inout)	sarea,
		real, dimension( cv_nloc ), intent(inout)	X_LOC,
		real, dimension( cv_nloc ), intent(inout)	Y_LOC,
		real, dimension( cv_nloc ), intent(inout)	Z_LOC,
		integer, dimension( cv_nloc, scvngi ), intent(inout)	CV_NEILOC,
		integer, intent(in)	cv_nloc,
		integer, intent(in)	scvngi
	)

: the surface quadrature pts in local coord are l1, l2, l3, l4, and the associated normals normx, normy, normz and the surface area is sarea The position of the nodes of the tet are: (X_LOC, Y_LOC, Z_LOC) Calculate cv_neiloc: To get the neighbouring node for node ILOC and surface quadrature point SGI CV_JLOC = CV_NEILOC( CV_ILOC, SGI ) The number of quadrature points is 24 = 4 x 6 exterior faces (and quadrature points) and 36 = 4x6 + 6x4/2 = 60 pts. @WARNING: Disabled because it introduces errors

Here is the call graph for this function:

Here is the caller graph for this function:

◆ legend()

real function shape_functions_ndim::legend	(	logical, intent(inout)	DIFF,
		real, intent(inout)	LX,
		integer, intent(inout)	INOD,
		integer, intent(inout)	NDNOD,
		real, dimension(:), intent(inout)	NODPOS
	)

If DIFF then returns the spectral function DIFFERENTIATED W.R.T X associated. This function returns the spectral function associated with node INOD at POINT LX NDNOD=no of nodes in 1-D. NDGI=no of Gauss pts in 1-D. NB The nodes are at the points COS(pie*J/2.) j=0,..,ndgi-1.

Here is the caller graph for this function:

◆ legrot()

subroutine shape_functions_ndim::legrot	(	real, dimension(:), intent(inout)	WEIT,
		real, dimension(:), intent(inout)	QUAPOS,
		integer, intent(inout)	NDGI,
		logical, intent(inout)	GETNDP
	)

This computes the weight and points for Chebyshev-Gauss-Lobatto quadrature. See page 69 of:Spectral Methods in Fluid Dynamics, C.Canuto IF(GETNDP) then get the POSITION OF THE NODES AND DONT BOTHER WITH THE WEITS.

Here is the call graph for this function:

Here is the caller graph for this function:

◆ lroots()

subroutine shape_functions_ndim::lroots	(	real, dimension(:), intent(inout)	QUAPOS,
		integer	NDGI
	)

This sub works out the Gauss-Lobatto-Legendre roots.

Here is the call graph for this function:

Here is the caller graph for this function:

◆ make_bilinear_hexahedra()

subroutine shape_functions_ndim::make_bilinear_hexahedra	(	integer, intent(in)	totele,
		integer, intent(in)	number_of_hexs,
		integer, intent(in)	quad_cv_nloc,
		integer, intent(inout)	x_nonods,
		real, dimension( : ), intent(inout)	x,
		real, dimension( : ), intent(inout)	y,
		real, dimension( : ), intent(inout)	z,
		integer, dimension( : ), intent(inout)	x_ndgln
	)

Here is the call graph for this function:

Here is the caller graph for this function:

◆ make_linear_tetrahedron()

subroutine shape_functions_ndim::make_linear_tetrahedron	(	integer, intent(in)	ele,
		integer, intent(in)	quad_cv_nloc,
		integer, intent(in)	x_nloc,
		integer, intent(in)	x_nonods,
		integer, intent(in)	number_of_hexs,
		real, dimension( 10 ), intent(in)	xp2,
		real, dimension( 10 ), intent(in)	yp2,
		real, dimension( 10 ), intent(in)	zp2,
		real, dimension( : ), intent(inout)	x,
		real, dimension( : ), intent(inout)	y,
		real, dimension( : ), intent(inout)	z,
		integer, dimension( : ), intent(in)	x_ndgln_p2,
		integer, dimension( : ), intent(inout)	x_ndgln
	)

Here is the caller graph for this function:

◆ make_qtets()

subroutine shape_functions_ndim::make_qtets	(	integer, intent(inout)	totele,
		integer, intent(in)	quad_cv_nloc,
		integer, intent(in)	x_nloc,
		integer, intent(in)	max_x_nonods,
		integer, intent(inout)	x_nonods,
		integer, dimension( : ), intent(inout)	x_ndgln_real,
		real, dimension( : ), intent(inout)	lx,
		real, dimension( : ), intent(inout)	ly,
		real, dimension( : ), intent(inout)	lz,
		real, dimension( : ), intent(inout)	x,
		real, dimension( : ), intent(inout)	y,
		real, dimension( : ), intent(inout)	z,
		integer, dimension( : ), intent(inout)	fem_nod,
		real, dimension( : ), intent(inout)	xp2,
		real, dimension( : ), intent(inout)	yp2,
		real, dimension( : ), intent(inout)	zp2,
		integer, dimension( : ), intent(inout)	x_ndgln_p2
	)

This subrt creates the local coordinates and node points for: (a) quadratic tetrahedra of unit volume and (b) 27 points of the 8 hexahedra within the 8 linear tetrahedra. FEM_NOD is the local numbering of the FEM representation of the unit volume quadratic tetrahedron.

Here is the call graph for this function:

Here is the caller graph for this function:

◆ make_qtri()

subroutine shape_functions_ndim::make_qtri	(	integer, intent(in)	totele,
		integer, intent(in)	x_nloc,
		integer, intent(in)	max_x_nonods,
		integer, intent(inout)	x_nonods,
		integer, dimension( : ), intent(inout)	x_ndgln,
		real, dimension( : ), intent(inout)	lx,
		real, dimension( : ), intent(inout)	ly,
		real, dimension( : ), intent(inout)	x,
		real, dimension( : ), intent(inout)	y,
		integer, dimension( : ), intent(inout)	fem_nod
	)

Here is the call graph for this function:

Here is the caller graph for this function:

◆ new_pt_qua_vol_cv_tri_tet_shape()

subroutine shape_functions_ndim::new_pt_qua_vol_cv_tri_tet_shape	(	integer, intent(in)	cv_ele_type,
		integer, intent(in)	ndim,
		integer, intent(in)	cv_ngi,
		integer, intent(in)	cv_nloc,
		integer, intent(in)	u_nloc,
		real, dimension( :, : ), intent(inout)	cvn,
		real, dimension( : ), intent(inout)	cvweigh,
		real, dimension( :, : ), intent(inout)	n,
		real, dimension( :, : ), intent(inout)	nlx,
		real, dimension( :, : ), intent(inout)	nly,
		real, dimension( :, : ), intent(inout)	nlz,
		real, dimension( :, : ), intent(inout)	un,
		real, dimension( :, : ), intent(inout)	unlx,
		real, dimension( :, : ), intent(inout)	unly,
		real, dimension( :, : ), intent(inout)	unlz
	)

: new 1 or 4 pt quadrature set on each CV of a quadratic tetrahedra ..... Compute shape functions N, UN etc for linear trianles. Shape functions associated with volume integration using both CV basis functions CVN, as well as FEM basis functions N (and its derivatives NLX, NLY, NLZ). Also for velocity basis functions UN, UNLX, UNLY, UNLZ.

Here is the call graph for this function:

Here is the caller graph for this function:

◆ normgi()

subroutine shape_functions_ndim::normgi	(	real, intent(inout)	NORMXN,
		real, intent(inout)	NORMYN,
		real, intent(inout)	NORMZN,
		real, intent(in)	DXDLX,
		real, intent(in)	DYDLX,
		real, intent(in)	DZDLX,
		real, intent(in)	DXDLY,
		real, intent(in)	DYDLY,
		real, intent(in)	DZDLY,
		real, intent(in)	NORMX,
		real, intent(in)	NORMY,
		real, intent(in)	NORMZ
	)

Calculate the normal at the Gauss pts Perform x-product. N=T1 x T2.

Here is the caller graph for this function:

◆ plegen()

real function shape_functions_ndim::plegen	(	real, intent(in)	LX,
		integer, intent(in)	K
	)

Here is the call graph for this function:

Here is the caller graph for this function:

◆ printoutfunmat()

subroutine shape_functions_ndim::printoutfunmat	(	integer, intent(in)	n,
		integer, intent(in)	m,
		real, dimension( :,: ), intent(in)	a
	)

◆ quad_1d_shape()

subroutine shape_functions_ndim::quad_1d_shape	(	integer, intent(in)	cv_ngi,
		integer, intent(in)	cv_nloc,
		integer, intent(in)	u_nloc,
		real, dimension( :, : ), intent(inout)	cvn,
		real, dimension( : ), intent(inout)	cvweigh,
		real, dimension( :, : ), intent(inout)	n,
		real, dimension( :, : ), intent(inout)	nlx,
		real, dimension( :, : ), intent(inout)	un,
		real, dimension( :, : ), intent(inout)	unlx
	)

: For quadratic elements. Shape functions associated with volume integration using both CV basis functions CVN as well as FEM basis functions N (and its derivatives NLX, NLY, NLZ)

Here is the call graph for this function:

Here is the caller graph for this function:

◆ quad_nd_shape()

subroutine shape_functions_ndim::quad_nd_shape	(	integer, intent(in)	ndim,
		integer, intent(in)	cv_ele_type,
		integer, intent(in)	cv_ngi,
		integer, intent(in)	cv_nloc,
		integer, intent(in)	u_nloc,
		real, dimension( :, : ), intent(inout)	cvn,
		real, dimension( : ), intent(inout)	cvweigh,
		real, dimension( :, : ), intent(inout)	n,
		real, dimension( :, : ), intent(inout)	nlx,
		real, dimension( :, : ), intent(inout)	nly,
		real, dimension( :, : ), intent(inout)	nlz,
		real, dimension( :, : ), intent(inout)	un,
		real, dimension( :, : ), intent(inout)	unlx,
		real, dimension( :, : ), intent(inout)	unly,
		real, dimension( :, : ), intent(inout)	unlz
	)

: For quadratic elements: Shape functions associated with volume integration using both CV (CVN) and FEM (N and its derivatives NLX/Y/Z) basis functions.

Here is the call graph for this function:

Here is the caller graph for this function:

◆ quad_nd_shape_n()

subroutine shape_functions_ndim::quad_nd_shape_n	(	integer, intent(in)	cv_ele_type,
		integer, intent(in)	ndim,
		integer, intent(in)	cv_ngi,
		integer, intent(in)	cv_nloc,
		real, dimension( :, : ), intent(inout)	cvn,
		real, dimension( : ), intent(inout)	cvweigh,
		real, dimension( :, : ), intent(inout)	n,
		real, dimension( :, : ), intent(inout)	nlx,
		real, dimension( :, : ), intent(inout)	nly,
		real, dimension( :, : ), intent(inout)	nlz,
		integer, intent(in)	cv_ngi_1d,
		integer, intent(in)	cv_nloc_1d,
		real, dimension( :, : ), intent(in)	cvn_1d,
		real, dimension( : ), intent(in)	cvweigh_1d,
		real, dimension( :, : ), intent(in)	n_1d,
		real, dimension( :, : ), intent(in)	nlx_1d
	)

: For quadatic elements – shape functions associated with volume integration using both CV basis functions CVN as well as FEM basis functions N (and its derivatives NLX, NLY, NLZ)

Here is the caller graph for this function:

◆ remaping_fields_qtriangles()

subroutine shape_functions_ndim::remaping_fields_qtriangles	(	integer, intent(in)	ele_big,
		integer, intent(in)	x_nloc_big,
		integer, intent(in)	totele_big,
		integer, intent(in)	x_nonods_big,
		integer, dimension(: ), intent(in)	x_ndgln_big,
		real, dimension( : ), intent(in)	x_big,
		real, dimension( : ), intent(in)	y_big,
		integer, intent(in)	x_nonods,
		integer, intent(in)	x_nloc,
		integer, intent(in)	totele,
		integer, dimension( : ), intent(inout)	x_ndgln,
		integer, intent(inout)	ele_ref,
		real, dimension( : ), intent(inout)	x,
		real, dimension( : ), intent(inout)	y
	)

Here is the caller graph for this function:

◆ shape()

subroutine shape_functions_ndim::shape	(	logical, intent(in)	LOWQUA,
		integer, intent(in)	NGI,
		integer, intent(in)	NLOC,
		integer, intent(in)	MLOC,
		integer, intent(in)	SNGI,
		integer, intent(in)	SNLOC,
		integer, intent(in)	SMLOC,
		real, dimension(:,:), intent(out)	M,
		real, dimension(:,:), intent(out)	MLX,
		real, dimension(:,:), intent(out)	MLY,
		real, dimension(:,:), intent(out)	MLZ,
		real, dimension(:), intent(out)	WEIGHT,
		real, dimension(:,:), intent(out)	N,
		real, dimension(:,:), intent(out)	NLX,
		real, dimension(:,:), intent(out)	NLY,
		real, dimension(:,:), intent(out)	NLZ,
		real, dimension(:), intent(out)	SWEIGH,
		real, dimension(:,:), intent(out)	SN,
		real, dimension(:,:), intent(out)	SNLX,
		real, dimension(:,:), intent(out)	SNLY,
		real, dimension(:,:), intent(out)	SM,
		real, dimension(:,:), intent(out)	SMLX,
		real, dimension(:,:), intent(out)	SMLY,
		integer, intent(in)	NWICEL,
		logical, intent(in)	D3
	)

Here is the call graph for this function:

Here is the caller graph for this function:

◆ shape_l_q_quad()

subroutine shape_functions_ndim::shape_l_q_quad	(	logical, intent(in)	lowqua,
		integer, intent(in)	ngi,
		integer, intent(in)	nloc,
		integer, intent(in)	mloc,
		integer, intent(in)	sngi,
		integer, intent(in)	snloc,
		integer, intent(in)	smloc,
		real, dimension( :, : ), intent(inout)	m,
		real, dimension( :, : ), intent(inout)	mlx,
		real, dimension( :, : ), intent(inout)	mly,
		real, dimension( :, : ), intent(inout)	mlz,
		real, dimension( : ), intent(inout)	weight,
		real, dimension( :, : ), intent(inout)	n,
		real, dimension( :, : ), intent(inout)	nlx,
		real, dimension( :, : ), intent(inout)	nly,
		real, dimension( :, : ), intent(inout)	nlz,
		real, dimension( : ), intent(inout)	sweigh,
		real, dimension( :, : ), intent(inout)	sn,
		real, dimension( :, : ), intent(inout)	snlx,
		real, dimension( :, : ), intent(inout)	snly,
		real, dimension( :, : ), intent(inout)	sm,
		real, dimension( :, : ), intent(inout)	smlx,
		real, dimension( :, : ), intent(inout)	smly,
		integer, intent(in)	nwicel,
		logical, intent(in)	d3
	)

This subrt computes shape functions. For now, let's just define for one element type. NB: N may overwrite M if we are not solving for pressure.

Here is the call graph for this function:

Here is the caller graph for this function:

◆ shape_one_ele2()

subroutine shape_functions_ndim::shape_one_ele2	(	integer, intent(in)	ndim,
		integer, intent(in)	cv_ele_type,
		integer, intent(in)	cv_ngi,
		integer, intent(in)	cv_nloc,
		integer, intent(in)	u_nloc,
		real, dimension( : ), intent(inout)	cvweight,
		real, dimension( :, : ), intent(inout)	cvfen,
		real, dimension( :, : ), intent(inout)	cvfenlx,
		real, dimension( :, : ), intent(inout)	cvfenly,
		real, dimension( :, : ), intent(inout)	cvfenlz,
		real, dimension( :, : ), intent(inout)	ufen,
		real, dimension( :, : ), intent(inout)	ufenlx,
		real, dimension( :, : ), intent(inout)	ufenly,
		real, dimension( :, : ), intent(inout)	ufenlz,
		integer, intent(in)	sbcvngi,
		real, dimension( :, : ), intent(inout)	sbcvfen,
		real, dimension( :, : ), intent(inout)	sbcvfenslx,
		real, dimension( :, : ), intent(inout)	sbcvfensly,
		real, dimension( : ), intent(inout)	sbcvfeweigh,
		real, dimension( :, : ), intent(inout)	sbufen,
		real, dimension( :, : ), intent(inout)	sbufenslx,
		real, dimension( :, : ), intent(inout)	sbufensly,
		integer, intent(in)	nface,
		integer, dimension( :, : ), intent(inout)	cv_sloclist,
		integer, dimension( :, : ), intent(inout)	u_sloclist,
		integer, intent(in)	cv_snloc,
		integer, intent(in)	u_snloc
	)

: This subrt defines the sub-control volume and FEM shape functions. Shape functions associated with volume integration using both CV basis functions CVN as well as FEM basis functions CVFEN (and its derivatives CVFENLX, CVFENLY, CVFENLZ)

Here is the call graph for this function:

Here is the caller graph for this function:

◆ shape_tri_tet()

subroutine shape_functions_ndim::shape_tri_tet	(	integer, intent(in)	cv_ele_type_cells,
		integer, intent(in)	cv_nloc_cells,
		integer, intent(in)	cv_ele_type,
		integer, intent(in)	ndim,
		integer, intent(in)	totele,
		integer, intent(in)	cv_nloc,
		integer, intent(in)	cv_ngi,
		integer, intent(in)	x_nonods,
		integer, intent(in)	quad_cv_nloc,
		integer, dimension( : ), intent(in)	x_ndgln,
		real, dimension( : ), intent(in)	x,
		real, dimension( : ), intent(in)	y,
		real, dimension( : ), intent(in)	z,
		real, dimension( : ), intent(in)	lx,
		real, dimension( : ), intent(in)	ly,
		real, dimension( : ), intent(in)	lz,
		real, dimension( :, : ), intent(inout)	n,
		real, dimension( :, : ), intent(inout)	nlx,
		real, dimension( :, : ), intent(inout)	nly,
		real, dimension( :, : ), intent(inout)	nlz,
		real, dimension( : ), intent(inout)	cvweigh
	)

: Determine the volume shape functions n, nlx, nly, nlz and weights cvweigh for the cv_nloc_cells CV cells.

Here is the call graph for this function:

Here is the caller graph for this function:

◆ shape_triangle_cubic()

subroutine shape_functions_ndim::shape_triangle_cubic	(	real, dimension( : ), intent(in)	l1,
		real, dimension( : ), intent(in)	l2,
		real, dimension( : ), intent(in)	l3,
		real, dimension( : ), intent(in)	l4,
		real, dimension( : ), intent(in)	weight,
		logical, intent(in)	d3,
		integer, intent(in)	nloc,
		integer, intent(in)	ngi,
		real, dimension( :, : ), intent(inout)	n,
		real, dimension( :, : ), intent(inout)	nlx,
		real, dimension( :, : ), intent(inout)	nly,
		real, dimension( :, : ), intent(inout)	nlz
	)

Generates the shape functions of a cubic triangle.

Here is the caller graph for this function:

◆ shatri()

subroutine shape_functions_ndim::shatri	(	real, dimension( : ), intent(in)	l1,
		real, dimension( : ), intent(in)	l2,
		real, dimension( : ), intent(in)	l3,
		real, dimension( : ), intent(in)	l4,
		real, dimension( : ), intent(in)	weight,
		logical, intent(in)	d3,
		integer, intent(in)	nloc,
		integer, intent(in)	ngi,
		real, dimension( :, : ), intent(inout)	n,
		real, dimension( :, : ), intent(inout)	nlx,
		real, dimension( :, : ), intent(inout)	nly,
		real, dimension( :, : ), intent(inout)	nlz
	)

get the shape functions for a triangle/tetrahedron

Here is the call graph for this function:

Here is the caller graph for this function:

◆ shatri_hex()

subroutine shape_functions_ndim::shatri_hex	(	real, dimension( : ), intent(in)	l1,
		real, dimension( : ), intent(in)	l2,
		real, dimension( : ), intent(in)	l3,
		real, dimension( : ), intent(in)	l4,
		real, dimension( : ), intent(inout)	weight,
		logical, intent(in)	d3,
		integer, intent(in)	nloc,
		integer, intent(in)	ngi,
		real, dimension( :, : ), intent(inout)	n,
		real, dimension( :, : ), intent(inout)	nlx,
		real, dimension( :, : ), intent(inout)	nly,
		real, dimension( :, : ), intent(inout)	nlz,
		logical, intent(in)	tri_tet
	)

Get the shape functions on lines (in 2D) and quadrilateral surfaces in 3D.

Here is the call graph for this function:

Here is the caller graph for this function:

◆ shatrinew()

subroutine shape_functions_ndim::shatrinew	(	real, dimension(:), intent(in)	L1,
		real, dimension(:), intent(in)	L2,
		real, dimension(:), intent(in)	L3,
		real, dimension(:), intent(in)	L4,
		real, dimension(:), intent(inout)	WEIGHT,
		integer, intent(in)	NLOC,
		integer, intent(in)	NGI,
		real, dimension(:, : ), intent(inout)	N,
		real, dimension (:,:,:), intent(inout)	NLX_ALL
	)

: Work out the shape functions and their derivatives...

Here is the call graph for this function:

Here is the caller graph for this function:

◆ shatriold()

subroutine shape_functions_ndim::shatriold	(	real, dimension(:), intent(in)	L1,
		real, dimension(:), intent(in)	L2,
		real, dimension(:), intent(in)	L3,
		real, dimension(:), intent(in)	L4,
		real, dimension(:), intent(inout)	WEIGHT,
		logical, intent(in)	D3,
		integer, intent(in)	NLOC,
		integer, intent(in)	NGI,
		real, dimension(:, : ), intent(inout)	N,
		real, dimension(:, : ), intent(inout)	NLX,
		real, dimension(:, : ), intent(inout)	NLY,
		real, dimension(:, : ), intent(inout)	NLZ
	)

: Work out the shape functions and their derivatives...

Here is the call graph for this function:

Here is the caller graph for this function:

◆ specfu()

real function shape_functions_ndim::specfu	(	logical	DIFF,
		real	LXGP,
		integer	INOD,
		integer	NDNOD,
		integer	IPOLY,
		real, dimension(:)	NODPOS
	)

INOD contains the node at which the polynomial is associated with LXGP is the position at which the polynomial is to be avaluated.\ If(DIFF) then find the D poly/DX.

Here is the call graph for this function:

Here is the caller graph for this function:

◆ spectr()

subroutine shape_functions_ndim::spectr	(	integer, intent(in)	NGI,
		integer, intent(in)	NLOC,
		integer, intent(in)	MLOC,
		real, dimension(:,:), intent(inout)	M,
		real, dimension(:), intent(inout)	WEIGHT,
		real, dimension(:,:), intent(inout)	N,
		real, dimension(:,:), intent(inout)	NLX,
		real, dimension(:,:), intent(inout)	NLY,
		real, dimension(:,:), intent(inout)	NLZ,
		logical	D3,
		logical	D2,
		integer, intent(inout)	IPOLY,
		integer, intent(inout)	IQADRA
	)

This subroutine defines a spectal element. IPOLY defines the element type and IQADRA the quadrature. In 2-D the spectral local node numbering is as.. 7 8 9 4 5 6 1 2 3 For 3-D... lz=-1 3 4 1 2 and for lz=1 7 8 5 6.

Here is the call graph for this function:

Here is the caller graph for this function:

◆ suf_cv_tri_tet_shape()

subroutine shape_functions_ndim::suf_cv_tri_tet_shape	(	integer, intent(in)	cv_ele_type,
		integer, intent(in)	ndim,
		integer, intent(in)	scvngi,
		integer, intent(in)	cv_nloc,
		integer, intent(in)	u_nloc,
		real, dimension( : ), intent(inout)	scvfeweigh,
		real, dimension( :, : ), intent(inout)	scvfen,
		real, dimension( :, : ), intent(inout)	scvfenlx,
		real, dimension( :, : ), intent(inout)	scvfenly,
		real, dimension( :, : ), intent(inout)	scvfenlz,
		real, dimension( :, : ), intent(inout)	scvfenslx,
		real, dimension( :, : ), intent(inout)	scvfensly,
		real, dimension( :, : ), intent(inout)	sufen,
		real, dimension( :, : ), intent(inout)	sufenlx,
		real, dimension( :, : ), intent(inout)	sufenly,
		real, dimension( :, : ), intent(inout)	sufenlz,
		real, dimension( :, : ), intent(inout)	sufenslx,
		real, dimension( :, : ), intent(inout)	sufensly,
		integer, dimension( :, : ), intent(inout)	cv_neiloc,
		integer, dimension( :, : ), intent(inout)	cvfem_neiloc,
		integer, dimension( :, : ), intent(inout)	ufem_neiloc
	)

: Compute shape functions N, UN etc for linear triangles. Shape functions associated with volume integration using both CV basis functions CVN, as well as FEM basis functions SN (and its derivatives SNLX, SNLY, SNLZ). Also for velocity basis functions SUN, SUNLX, SUNLY, SUNLZ. Also the derivatives along the CV faces: sufnlx, sufnly, sufunlx, sufunly

Here is the call graph for this function:

Here is the caller graph for this function:

◆ tcheb()

real function shape_functions_ndim::tcheb	(	integer, intent(in)	N,
		real, intent(in)	XPT,
		logical, intent(in)	DIFF,
		logical, intent(in)	DIFF2
	)

If DIFF then return the n'th Chebyshef polynomial differentiated w.r.t x. If DIFF2 then form the 2'nd derivative. This sub returns the value of the K'th Chebyshef polynomial at a point XPT.

This formula can be found in:Spectral Methods for Fluid Dynamics, page 66

Here is the call graph for this function:

Here is the caller graph for this function:

◆ test_quad_tet()

subroutine shape_functions_ndim::test_quad_tet	(	integer, intent(in)	cv_nloc,
		integer, intent(in)	cv_ngi,
		real, dimension( :,: ), intent(in)	cvn,
		real, dimension( :, : ), intent(in)	n,
		real, dimension( :, : ), intent(in)	nlx,
		real, dimension( :, : ), intent(in)	nly,
		real, dimension( :, : ), intent(in)	nlz,
		real, dimension( : ), intent(in)	cvweight,
		real, dimension( : ), intent(in)	x,
		real, dimension( : ), intent(in)	y,
		real, dimension( : ), intent(in)	z,
		integer, intent(in)	x_nonods,
		integer, dimension( : ), intent(in)	x_ndgln2,
		integer, intent(in)	totele
	)

test the volumes of idealised triangle

◆ tet_vol()

real function shape_functions_ndim::tet_vol	(	real, dimension( : ), intent(in)	a,
		real, dimension( : ), intent(in)	b,
		real, dimension( : ), intent(in)	c,
		real, dimension( : ), intent(in)	d
	)

Here is the call graph for this function:

Here is the caller graph for this function:

◆ tr2d()

subroutine shape_functions_ndim::tr2d	(	logical	LOWQUA,
		integer, intent(in)	NGI,
		integer, intent(in)	NLOC,
		integer, intent(in)	MLOC,
		real, dimension(:,:), intent(inout)	M,
		real, dimension(:), intent(inout)	WEIGHT,
		real, dimension(:,:), intent(inout)	N,
		real, dimension(:,:), intent(inout)	NLX,
		real, dimension(:,:), intent(inout)	NLY,
		integer, intent(in)	SNGI,
		integer, intent(in)	SNLOC,
		real, dimension(:), intent(inout)	SWEIGH,
		real, dimension(:,:), intent(inout)	SN,
		real, dimension(:,:), intent(inout)	SNLX
	)

This subroutine defines the shape functions M and N and their derivatives at the Gauss points For 3-D FLOW.

◆ tr2or3dqu()

subroutine shape_functions_ndim::tr2or3dqu	(	integer, intent(in)	NGI,
		integer, intent(in)	NLOC,
		integer, intent(in)	MLOC,
		real, dimension(:,:), intent(inout)	M,
		real, dimension(:,:), intent(inout)	MLX,
		real, dimension(:,:), intent(inout)	MLY,
		real, dimension(:,:), intent(inout)	MLZ,
		real, dimension(:), intent(inout)	WEIGHT,
		real, dimension(:,:), intent(inout)	N,
		real, dimension(:,:), intent(inout)	NLX,
		real, dimension(:,:), intent(inout)	NLY,
		real, dimension(:,:), intent(inout)	NLZ,
		integer, intent(in)	SNGI,
		integer, intent(in)	SNLOC,
		real, dimension(:), intent(inout)	SWEIGH,
		real, dimension(:,:), intent(inout)	SN,
		real, dimension(:,:), intent(inout)	SNLX,
		real, dimension(:,:), intent(inout)	SNLY,
		integer, intent(in)	SMLOC,
		real, dimension(:,:), intent(inout)	SM,
		real, dimension(:,:), intent(inout)	SMLX,
		real, dimension(:,:), intent(inout)	SMLY,
		logical, intent(in)	D3
	)

:This subroutine defines the shape functions M and N and their derivatives at the Gauss points for quadratic elements. For 3-D FLOW.

Here is the call graph for this function:

Here is the caller graph for this function:

◆ triareaf()

real function shape_functions_ndim::triareaf	(	real, intent(in)	x1,
		real, intent(in)	y1,
		real, intent(in)	x2,
		real, intent(in)	y2,
		real, intent(in)	x3,
		real, intent(in)	y3
	)

Here is the caller graph for this function:

◆ triareaf_sign()

real function shape_functions_ndim::triareaf_sign	(	real	x1,
		real	y1,
		real	x2,
		real	y2,
		real	x3,
		real	y3
	)

Here is the caller graph for this function:

◆ triquaold()

subroutine shape_functions_ndim::triquaold	(	real, dimension(:), intent(inout)	L1,
		real, dimension(:), intent(inout)	L2,
		real, dimension(:), intent(inout)	L3,
		real, dimension(:), intent(inout)	L4,
		real, dimension(:), intent(inout)	WEIGHT,
		logical, intent(in)	D3,
		integer, intent(in)	NGI
	)

: This sub calculates the local corrds L1, L2, L3, L4 and weights at the quadrature points. If D3 it does this for 3Dtetrahedra elements else triangular elements.

Here is the caller graph for this function:

◆ vol_cv_tri_tet_shape()

subroutine shape_functions_ndim::vol_cv_tri_tet_shape	(	integer, intent(in)	cv_ele_type,
		integer, intent(in)	ndim,
		integer, intent(in)	cv_ngi,
		integer, intent(in)	cv_nloc,
		integer, intent(in)	u_nloc,
		real, dimension( :, : ), intent(inout)	cvn,
		real, dimension( : ), intent(inout)	cvweigh,
		real, dimension( :, : ), intent(inout)	n,
		real, dimension( :, : ), intent(inout)	nlx,
		real, dimension( :, : ), intent(inout)	nly,
		real, dimension( :, : ), intent(inout)	nlz,
		real, dimension( :, : ), intent(inout)	un,
		real, dimension( :, : ), intent(inout)	unlx,
		real, dimension( :, : ), intent(inout)	unly,
		real, dimension( :, : ), intent(inout)	unlz
	)

: Compute shape functions N, UN etc for linear trianles. Shape functions associated with volume integration using both CV basis functions CVN, as well as FEM basis functions N (and its derivatives NLX, NLY, NLZ). Also for velocity basis functions UN, UNLX, UNLY, UNLZ.

Here is the call graph for this function:

Here is the caller graph for this function:

◆ volume_quad_map()

real function shape_functions_ndim::volume_quad_map	(	integer, intent(in)	cv_iloc,
		real, intent(in)	xgi,
		real, intent(in)	ygi,
		real, intent(in)	zgi,
		real, dimension( : ), intent(in)	lx,
		real, dimension( : ), intent(in)	ly,
		real, dimension( : ), intent(in)	lz
	)

Compute the cv_iloc^{th} shape function value at point (xgi, ygi, zgi)

Here is the call graph for this function:

Here is the caller graph for this function:

◆ volume_tethex()

real function shape_functions_ndim::volume_tethex	(	logical, intent(in)	hexs,
		real, intent(in)	x1,
		real, intent(in)	x2,
		real, intent(in)	x3,
		real, intent(in)	x4,
		real, intent(in)	y1,
		real, intent(in)	y2,
		real, intent(in)	y3,
		real, intent(in)	y4,
		real, intent(in)	z1,
		real, intent(in)	z2,
		real, intent(in)	z3,
		real, intent(in)	z4
	)

Here is the caller graph for this function:

◆ xprod1()

subroutine shape_functions_ndim::xprod1	(	real, intent(inout)	AX,
		real, intent(inout)	AY,
		real, intent(inout)	AZ,
		real, intent(in)	BX,
		real, intent(in)	BY,
		real, intent(in)	BZ,
		real, intent(in)	CX,
		real, intent(in)	CY,
		real, intent(in)	CZ
	)

Perform the cross product of two vectors.

◆ xprod2()

subroutine shape_functions_ndim::xprod2	(	real, dimension(:), intent(inout)	A,
		real, dimension(:), intent(in)	B,
		real, dimension(:), intent(in)	C
	)

Perform the cross product of two vectors.

Data Types

Functions/Subroutines

Detailed Description

Function/Subroutine Documentation

◆ adding_extra_parametric_nodes()

◆ adding_parametric_nodes_hex()

◆ area_quad_map()

◆ base_order_tet()

◆ base_order_tri()

◆ binomial_coefficient()

◆ calc_cvn_tritetquadhex()

◆ cheby1()

◆ cheby2()

◆ cherot()

◆ compute_surfaceshapefunctions_triangle_tetrahedron()

◆ compute_xndgln_tritetquadhex()

◆ computing_small_qtriangles()

◆ crossproduct()

◆ determin_sloclist()

◆ dgsdetnxloc2()

◆ dgsdetnxloc2_all()

◆ dummy_tri_tet()

◆ eliminating_repetitive_nodes()

◆ eliminating_repetitive_nodes_all()

◆ factorial()

◆ get_cvn_compact_overlapping()

◆ get_nwicel()

◆ get_tang_binorm()

◆ gtroot()

◆ jacobf()

◆ jacobl()

◆ james_quadrature_quad_tet()

◆ legend()

◆ legrot()

◆ lroots()

◆ make_bilinear_hexahedra()

◆ make_linear_tetrahedron()

◆ make_qtets()

◆ make_qtri()

◆ new_pt_qua_vol_cv_tri_tet_shape()

◆ normgi()

◆ plegen()

◆ printoutfunmat()

◆ quad_1d_shape()

◆ quad_nd_shape()

◆ quad_nd_shape_n()

◆ remaping_fields_qtriangles()

◆ shape()

◆ shape_l_q_quad()

◆ shape_one_ele2()

◆ shape_tri_tet()

◆ shape_triangle_cubic()

◆ shatri()

◆ shatri_hex()

◆ shatrinew()

◆ shatriold()

◆ specfu()

◆ spectr()

◆ suf_cv_tri_tet_shape()

◆ tcheb()

◆ test_quad_tet()

◆ tet_vol()

◆ tr2d()

◆ tr2or3dqu()

◆ triareaf()

◆ triareaf_sign()

◆ triquaold()

◆ vol_cv_tri_tet_shape()

◆ volume_quad_map()

◆ volume_tethex()

◆ xprod1()

◆ xprod2()