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<html>
<head>
<title>
FEM2D_PACK - Finite Element Routines
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
FEM2D_PACK <br> Finite Element Routines
</h1>
<hr>
<p>
<b>FEM2D_PACK</b>
is a FORTRAN90 library which
contains utility routines for 2D finite element calculations.
</p>
<p>
The emphasis is on simplicity and clarity.
Primarily, the 2D planar case is handled, with a choice
of low order triangular ("T") and quadrilateral ("Q") elements.
</p>
<p>
A few routines are included for computing a "sphere grid",
that is, a finite element mesh on the surface of a sphere.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>FEM2D_PACK</b> is available in
<a href = "../../cpp_src/fem2d_pack/fem2d_pack.html">a C++ version</a> and
<a href = "../../f77_src/fem2d_pack/fem2d_pack.html">a FORTRAN77 version</a> and
<a href = "../../f_src/fem2d_pack/fem2d_pack.html">a FORTRAN90 version</a> and
<a href = "../../m_src/fem2d_pack/fem2d_pack.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/fem_basis/fem_basis.html">
FEM_BASIS</a>,
a FORTRAN90 library which
can define and evaluate basis functions for any degree
in an M-dimensional simplex (1D interval, 2D triangle,
3D tetrahedron, and higher dimensional generalizations.)
</p>
<p>
<a href = "../../f_src/fem1d_pack/fem1d_pack.html">
FEM1D_PACK</a>,
a FORTRAN90 library which
contains utilities for 1D finite element calculations.
</p>
<p>
<a href = "../../data/fem2d/fem2d.html">
FEM2D</a>,
a data directory which
contains examples of 2D FEM files,
text files that describe a 2D finite element geometry
and associated nodal values;
</p>
<p>
<a href = "../../f_src/fem2d_heat/fem2d_heat.html">
FEM2D_HEAT</a>,
a FORTRAN90 program which
solves the 2D time dependent heat equation on the unit square.
</p>
<p>
<a href = "../../f_src/fem2d_poisson/fem2d_poisson.html">
FEM2D_POISSON</a>,
a FORTRAN90 program which
solves the 2D Poisson equation on a square, using the finite element method.
</p>
<p>
<a href = "../../f_src/fem2d_sample/fem2d_sample.html">
FEM2D_SAMPLE</a>,
a FORTRAN90 library which
evaluates a finite element function defined on an order 3 or order 6 triangulation.
</p>
<p>
<a href = "../../f_src/fem3d_pack/fem3d_pack.html">
FEM3D_PACK</a>,
a FORTRAN90 library which
contains utilities for 3D finite element calculations.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Milton Abramowitz, Irene Stegun,<br>
Handbook of Mathematical Functions,<br>
National Bureau of Standards, 1964,<br>
ISBN: 0-486-61272-4,<br>
LC: QA47.A34.
</li>
<li>
Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,<br>
LINPACK User's Guide,<br>
SIAM, 1979,<br>
ISBN13: 978-0-898711-72-1.
</li>
<li>
Vladimir Krylov,<br>
Approximate Calculation of Integrals,<br>
Dover, 2006,<br>
ISBN: 0486445798.
</li>
<li>
Hans Rudolf Schwarz,<br>
Finite Element Methods,<br>
Academic Press, 1988,<br>
ISBN: 0126330107,<br>
LC: TA347.F5.S3313.
</li>
<li>
Gilbert Strang, George Fix,<br>
An Analysis of the Finite Element Method,<br>
Cambridge, 1973,<br>
ISBN: 096140888X,<br>
LC: TA335.S77.
</li>
<li>
Arthur Stroud,<br>
Approximate Calculation of Multiple Integrals,<br>
Prentice Hall, 1971,<br>
ISBN: 0130438936,<br>
LC: QA311.S85.
</li>
<li>
Arthur Stroud, Don Secrest,<br>
Gaussian Quadrature Formulas,<br>
Prentice Hall, 1966,<br>
LC: QA299.4G3S7.
</li>
<li>
Olgierd Zienkiewicz,<br>
The Finite Element Method,<br>
Sixth Edition,<br>
Butterworth-Heinemann, 2005,<br>
ISBN: 0750663200,<br>
TA640.2.Z54.
</li>
<li>
Daniel Zwillinger, editor,<br>
CRC Standard Mathematical Tables and Formulae,<br>
30th Edition,<br>
CRC Press, 1996,<br>
ISBN: 0-8493-2479-3.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "fem2d_pack.f90">fem2d_pack.f90</a>, the source code;
</li>
<li>
<a href = "fem2d_pack.sh">fem2d_pack.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "fem2d_pack_prb.f90">fem2d_pack_prb.f90</a>, the calling program;
</li>
<li>
<a href = "fem2d_pack_prb.sh">fem2d_pack_prb.sh</a>,
commands to compile, link and run the calling program;
</li>
<li>
<a href = "fem2d_pack_prb_output.txt">fem2d_pack_prb_output.txt</a>,
the output file.
</li>
<li>
<a href = "fem2d_pack_prb_q4.png">fem2d_pack_prb_q4.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
a Q4 mesh.
</li>
<li>
<a href = "fem2d_pack_prb_t3.png">fem2d_pack_prb_t3.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
a T3 mesh.
</li>
<li>
<a href = "fem2d_pack_prb_t4.png">fem2d_pack_prb_t4.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
a T4 mesh.
</li>
<li>
<a href = "fem2d_pack_prb_t6.png">fem2d_pack_prb_t6.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
a T6 mesh.
</li>
<li>
<a href = "sphere_q4_nodes.txt">sphere_q4_nodes.txt</a>,
a node file for a Q4 mesh, which is also a
<a href = "../../data/polygonal_surface/polygonal_surface.html">
polygonal surface,</a>
that approximates a sphere.
</li>
<li>
<a href = "sphere_q4_elements.txt">sphere_q4_elements.txt</a>,
an element file for a Q4 mesh, which is also a
<a href = "../../data/polygonal_surface/polygonal_surface.html">
polygonal surface,</a>
that approximates a sphere.
</li>
<li>
<a href = "sphere_q9_nodes.txt">sphere_q9_nodes.txt</a>,
a node file for a Q9 mesh
that approximates a sphere.
</li>
<li>
<a href = "sphere_q9_elements.txt">sphere_q9_elements.txt</a>,
an element file for a Q9 mesh
that approximates a sphere.
</li>
<li>
<a href = "sphere_q16_nodes.txt">sphere_q16_nodes.txt</a>,
a node file for a Q16 mesh
that approximates a sphere.
</li>
<li>
<a href = "sphere_q16_elements.txt">sphere_q16_elements.txt</a>,
an element file for a Q16 mesh
that approximates a sphere.
</li>
<li>
<a href = "sphere_t3_nodes.txt">sphere_t3_nodes.txt</a>,
a node file for a T3 mesh, which is also a
<a href = "../../data/polygonal_surface/polygonal_surface.html">
polygonal surface,</a>
that approximates a sphere.
</li>
<li>
<a href = "sphere_t3_elements.txt">sphere_t3_elements.txt</a>,
an element file for a T3 mesh, which is also a
<a href = "../../data/polygonal_surface/polygonal_surface.html">
polygonal surface,</a>
that approximates a sphere.
</li>
<li>
<a href = "sphere_t6_nodes.txt">sphere_t6_nodes.txt</a>,
a node file for a T6 mesh
that approximates a sphere.
</li>
<li>
<a href = "sphere_t6_elements.txt">sphere_t6_elements.txt</a>,
an element file for a T6 mesh
that approximates a sphere.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>BANDWIDTH_MESH:</b> bandwidth of finite element mesh.
</li>
<li>
<b>BANDWIDTH_VAR</b> determines the bandwidth for finite element variables.
</li>
<li>
<b>BASIS_11_Q4:</b> one basis at one point for a Q4 element.
</li>
<li>
<b>BASIS_11_Q4_TEST</b> verifies BASIS_11_Q4.
</li>
<li>
<b>BASIS_11_T3:</b> one basis at one point for the T3 element.
</li>
<li>
<b>BASIS_11_T3_TEST</b> verifies BASIS_11_T3.
</li>
<li>
<b>BASIS_11_T4:</b> one basis at one point for a T4 element.
</li>
<li>
<b>BASIS_11_T4_TEST</b> verifies BASIS_11_T4.
</li>
<li>
<b>BASIS_11_T6:</b> one basis at one point for the T6 element.
</li>
<li>
<b>BASIS_11_T6_TEST</b> verifies BASIS_11_T6.
</li>
<li>
<b>BASIS_MN_Q4:</b> all bases at N points for a Q4 element.
</li>
<li>
<b>BASIS_MN_Q4_TEST</b> verifies BASIS_MN_Q4.
</li>
<li>
<b>BASIS_MN_T3:</b> all bases at N points for a T3 element.
</li>
<li>
<b>BASIS_MN_T3_TEST</b> verifies BASIS_MN_T3.
</li>
<li>
<b>BASIS_MN_T4:</b> all bases at N points for a T4 element.
</li>
<li>
<b>BASIS_MN_T4_TEST</b> verifies BASIS_MN_T4.
</li>
<li>
<b>BASIS_MN_T6:</b> all bases at N points for a T6 element.
</li>
<li>
<b>BASIS_MN_T6_TEST</b> verifies BASIS_MN_T6.
</li>
<li>
<b>CH_CAP</b> capitalizes a single character.
</li>
<li>
<b>DEGREES_TO_RADIANS</b> converts an angle from degrees to radians.
</li>
<li>
<b>DERIVATIVE_AVERAGE_T3</b> averages derivatives at the nodes of a T3 mesh.
</li>
<li>
<b>DERIVATIVE_AVERAGE_T6</b> averages derivatives at the nodes of a T6 mesh.
</li>
<li>
<b>DIV_Q4</b> estimates the divergence and vorticity of a discrete field.
</li>
<li>
<b>DIV_T3</b> estimates the divergence and vorticity of a discrete field.
</li>
<li>
<b>ELEMENT_CODE</b> returns the code for each element.
</li>
<li>
<b>ELEMENTS_EPS</b> creates an EPS file image of the elements of a grid.
</li>
<li>
<b>GET_UNIT</b> returns a free FORTRAN unit number.
</li>
<li>
<b>GRID_ELEMENT</b> returns the element grid associated with any available element.
</li>
<li>
<b>GRID_ELEMENT_NUM</b> returns the number of elements in a grid.
</li>
<li>
<b>GRID_NODE_NUM</b> returns the number of nodes in a grid.
</li>
<li>
<b>GRID_NODES_01</b> returns an equally spaced rectangular grid in the unit square.
</li>
<li>
<b>GRID_PRINT</b> prints the elements that form a grid.
</li>
<li>
<b>GRID_Q4_ELEMENT</b> produces an element grid of 4 node quadrilaterals.
</li>
<li>
<b>GRID_Q4_ELEMENT_NUM</b> counts the elements in a grid of 4 node quadrilaterals.
</li>
<li>
<b>GRID_Q4_NODE_NUM</b> counts the nodes in a grid of 4 node quadrilaterals.
</li>
<li>
<b>GRID_Q8_ELEMENT</b> produces an element grid of 8 node quadrilaterals.
</li>
<li>
<b>GRID_Q8_ELEMENT_NUM</b> counts the elements in a grid of 8 node quadrilaterals.
</li>
<li>
<b>GRID_Q8_NODE_NUM</b> counts the nodes in a grid of 8 node quadrilaterals.
</li>
<li>
<b>GRID_Q9_ELEMENT</b> produces an element grid of 9 node quadrilaterals.
</li>
<li>
<b>GRID_Q9_ELEMENT_NUM</b> counts the elements in a grid of 9 node quadrilaterals.
</li>
<li>
<b>GRID_Q9_NODE_NUM</b> counts the nodes in a grid of 9 node quadrilaterals.
</li>
<li>
<b>GRID_Q12_ELEMENT</b> produces an element grid of 12 node quadrilaterals.
</li>
<li>
<b>GRID_Q12_ELEMENT_NUM</b> counts the elements in a grid of 12 node quadrilaterals.
</li>
<li>
<b>GRID_Q12_NODE_NUM</b> counts the nodes in a grid of 12 node quadrilaterals.
</li>
<li>
<b>GRID_Q16_ELEMENT</b> produces an element grid of 16 node quadrilaterals.
</li>
<li>
<b>GRID_Q16_ELEMENT_NUM</b> counts the elements in a grid of 16 node quadrilaterals.
</li>
<li>
<b>GRID_Q16_NODE_NUM</b> counts the nodes in a grid of 16 node quadrilaterals.
</li>
<li>
<b>GRID_QL_ELEMENT</b> produces an element grid of 6 node quadratics/linears.
</li>
<li>
<b>GRID_QL_ELEMENT_NUM</b> counts the elements in a grid of QL quadrilaterals.
</li>
<li>
<b>GRID_QL_NODE_NUM</b> counts the nodes in a grid of QL quadrilaterals.
</li>
<li>
<b>GRID_SHAPE_2D</b> guesses the shape N1 by N2 of a vector of data.
</li>
<li>
<b>GRID_T3_ELEMENT</b> produces an element grid of pairs of 3 node triangles.
</li>
<li>
<b>GRID_T3_ELEMENT_NUM</b> counts the elements in a grid of 3 node triangles.
</li>
<li>
<b>GRID_T3_NODE_NUM</b> counts the nodes in a grid of 3 node triangles.
</li>
<li>
<b>GRID_T4_ELEMENT</b> produces an element grid of pairs of 4 node triangles.
</li>
<li>
<b>GRID_T4_ELEMENT_NUM</b> counts the elements in a grid of 4 node triangles.
</li>
<li>
<b>GRID_T4_NODE_NUM</b> counts the nodes in a grid of 4 node triangles.
</li>
<li>
<b>GRID_T6_ELEMENT</b> produces an element grid of pairs of 6 node triangles.
</li>
<li>
<b>GRID_T6_ELEMENT_NUM</b> counts the elements in a grid of 6 node triangles.
</li>
<li>
<b>GRID_T6_NODE_NUM</b> counts the nodes in a grid of 6 node triangles.
</li>
<li>
<b>GRID_T10_ELEMENT</b> produces an element grid of pairs of 10 node triangles.
</li>
<li>
<b>GRID_T10_ELEMENT_NUM</b> counts the elements in a grid of 10 node triangles.
</li>
<li>
<b>GRID_T10_NODE_NUM</b> counts the nodes in a grid of 10 node triangles.
</li>
<li>
<b>GRID_TEST</b> tests the grid element routines.
</li>
<li>
<b>GRID_WIDTH</b> computes the width of a given grid.
</li>
<li>
<b>I4_MODP</b> returns the nonnegative remainder of integer division.
</li>
<li>
<b>I4_WRAP</b> forces an integer to lie between given limits by wrapping.
</li>
<li>
<b>I4MAT_WRITE</b> writes an I4MAT file.
</li>
<li>
<b>I4VEC_PRINT</b> prints an I4VEC.
</li>
<li>
<b>INTERP</b> interpolates a quantity in an element from basis node values.
</li>
<li>
<b>INTERP_TEST</b> tests the interpolation property of an element.
</li>
<li>
<b>LEGENDRE_COM</b> computes abscissas and weights for Gauss-Legendre quadrature.
</li>
<li>
<b>LEGENDRE_SET</b> sets abscissas and weights for Gauss-Legendre quadrature.
</li>
<li>
<b>MAP</b> returns the interpolation matrix for any available element.
</li>
<li>
<b>MAP_TEST</b> tests the map routines.
</li>
<li>
<b>MASS_MATRIX_T6</b> computes the mass matrix, using 6-node triangles.
</li>
<li>
<b>NEXT_BOUNDARY_NODE</b> returns the next boundary node in any element.
</li>
<li>
<b>NEXT_BOUNDARY_NODE_Q4</b> returns the next boundary node in a Q4 element.
</li>
<li>
<b>NEXT_BOUNDARY_NODE_Q8</b> returns the next boundary node in a Q8 element.
</li>
<li>
<b>NEXT_BOUNDARY_NODE_Q9</b> returns the next boundary node in a Q9 element.
</li>
<li>
<b>NEXT_BOUNDARY_NODE_Q12</b> returns the next boundary node in a Q12 element.
</li>
<li>
<b>NEXT_BOUNDARY_NODE_Q16</b> returns the next boundary node in a Q16 element.
</li>
<li>
<b>NEXT_BOUNDARY_NODE_QL</b> returns the next boundary node in a QL element.
</li>
<li>
<b>NEXT_BOUNDARY_NODE_T3</b> returns the next boundary node in a T3 element.
</li>
<li>
<b>NEXT_BOUNDARY_NODE_T4</b> returns the next boundary node in a T4 element.
</li>
<li>
<b>NEXT_BOUNDARY_NODE_T6</b> returns the next boundary node in a T6 element.
</li>
<li>
<b>NEXT_BOUNDARY_NODE_T10</b> returns the next boundary node in a T10 element.
</li>
<li>
<b>NODE_REFERENCE</b> returns the basis nodes for any available element.
</li>
<li>
<b>NODE_REFERENCE_Q4</b> returns the basis nodes for a 4 node quadrilateral.
</li>
<li>
<b>NODE_REFERENCE_Q8</b> returns the basis nodes for an 8 node quadrilateral.
</li>
<li>
<b>NODE_REFERENCE_Q9</b> returns the basis nodes for a 9 node quadrilateral.
</li>
<li>
<b>NODE_REFERENCE_Q12</b> returns the basis nodes for a 12 node quadrilateral.
</li>
<li>
<b>NODE_REFERENCE_Q16</b> returns the basis nodes for a 16 node quadrilateral.
</li>
<li>
<b>NODE_REFERENCE_QL</b> returns the basis nodes for a quadratic/linear.
</li>
<li>
<b>NODE_REFERENCE_T3</b> returns the basis nodes for the 3 node triangle.
</li>
<li>
<b>NODE_REFERENCE_T4</b> returns the basis nodes for the 4 node triangle.
</li>
<li>
<b>NODE_REFERENCE_T6</b> returns the basis nodes for a 6 node triangle.
</li>
<li>
<b>NODE_REFERENCE_T10</b> returns the basis nodes for a 10 node triangle.
</li>
<li>
<b>NS_T6_VAR_COUNT</b> counts the Navier Stokes variables on a T6 grid.
</li>
<li>
<b>NS_T6_VAR_SET</b> sets the Navier Stokes variables on a T6 grid.
</li>
<li>
<b>ORDER_CODE</b> returns the order for each element.
</li>
<li>
<b>PHYSICAL_TO_REFERENCE_T3</b> maps physical points to reference points.
</li>
<li>
<b>POINTS_PLOT</b> plots a pointset.
</li>
<li>
<b>POLY</b> returns the polynomial terms associated with any available element.
</li>
<li>
<b>POLY_Q4</b> returns the monomials associated with a 4 node quadrilateral.
</li>
<li>
<b>POLY_Q8</b> returns the monomials associated with an 8 node quadrilateral.
</li>
<li>
<b>POLY_Q9</b> returns the monomials associated with a 9 node quadrilateral.
</li>
<li>
<b>POLY_Q12</b> returns the monomials associated with a 12 node quadrilateral.
</li>
<li>
<b>POLY_Q16</b> returns the monomials associated with a 16 node quadrilateral.
</li>
<li>
<b>POLY_QL</b> returns the monomials for a quadratic/linear quadrilateral.
</li>
<li>
<b>POLY_T3</b> returns the monomials associated with a 3 node triangle.
</li>
<li>
<b>POLY_T6</b> returns the monomials associated with a 6 node triangle.
</li>
<li>
<b>POLY_T10</b> returns the monomials associated with a 10 node triangle.
</li>
<li>
<b>R8_HUGE</b> returns the largest legal R8.
</li>
<li>
<b>R8_POWER</b> computes the P-th power of R.
</li>
<li>
<b>R8_SWAP</b> switches two R8's.
</li>
<li>
<b>R8_UNIFORM_01</b> returns a unit pseudorandom R8.
</li>
<li>
<b>R8GE_FA</b> performs a LINPACK style PLU factorization of an R8GE matrix.
</li>
<li>
<b>R8GE_INVERSE</b> computes the inverse of a matrix factored by R8GE_FA.
</li>
<li>
<b>R8MAT_PRINT</b> prints an R8MAT.
</li>
<li>
<b>R8MAT_PRINT_SOME</b> prints some of an R8MAT.
</li>
<li>
<b>R8MAT_WRITE</b> writes an R8MAT file.
</li>
<li>
<b>REFERENCE_SAMPLE</b> samples a reference element.
</li>
<li>
<b>REFERENCE_TO_PHYSICAL_Q4</b> maps Q4 reference points to physical points.
</li>
<li>
<b>REFERENCE_TO_PHYSICAL_T3</b> maps T3 reference points to physical points.
</li>
<li>
<b>REFERENCE_TO_PHYSICAL_T6</b> maps T6 reference points to physical points.
</li>
<li>
<b>S_BLANK_DELETE</b> removes blanks from a string, left justifying the remainder.
</li>
<li>
<b>S_EQI</b> is a case insensitive comparison of two strings for equality.
</li>
<li>
<b>S_L2NORM</b> computes the "big" L2 norm of a scalar function over a region.
</li>
<li>
<b>SERENE</b> interpolates data using a Q8 element.
</li>
<li>
<b>SHAPE</b> evaluates shape functions for any available reference element.
</li>
<li>
<b>SHAPE_Q4</b> evaluates shape functions for a 4 node reference quadrilateral.
</li>
<li>
<b>SHAPE_Q8</b> evaluates shape functions for an 8 node reference quadrilateral.
</li>
<li>
<b>SHAPE_Q9</b> evaluates shape functions for a 9 node reference quadrilateral.
</li>
<li>
<b>SHAPE_Q12</b> evaluates shape functions for a 12 node reference quadrilateral.
</li>
<li>
<b>SHAPE_Q16</b> evaluates shape functions for a 16 node reference quadrilateral.
</li>
<li>
<b>SHAPE_QL</b> evaluates shape functions for a 6 node quadratic/linear.
</li>
<li>
<b>SHAPE_T3</b> evaluates shape functions for a 3 node reference triangle.
</li>
<li>
<b>SHAPE_T4</b> evaluates shape functions for a 4 node reference triangle.
</li>
<li>
<b>SHAPE_T6</b> evaluates shape functions for a 6 node reference triangle.
</li>
<li>
<b>SHAPE_T10</b> evaluates shape functions for a 10 node reference triangle.
</li>
<li>
<b>SHAPE_TEST</b> verifies the shape function values at the basis nodes.
</li>
<li>
<b>SPHERE_GRID_ELEMENT_NUM</b> returns the number of elements in a sphere grid.
</li>
<li>
<b>SPHERE_GRID_NODE_NUM</b> returns the number of nodes in a sphere grid.
</li>
<li>
<b>SPHERE_GRID_Q4_ELEMENT</b> produces a Q4 sphere grid.
</li>
<li>
<b>SPHERE_GRID_Q4_ELEMENT_NUM</b> counts the elements in a Q4 sphere grid.
</li>
<li>
<b>SPHERE_GRID_Q4_NODE_NUM</b> counts nodes in a Q4 sphere grid.
</li>
<li>
<b>SPHERE_GRID_Q4_NODE_XYZ</b> produces node coordinates for a Q4 sphere grid.
</li>
<li>
<b>SPHERE_GRID_Q9_ELEMENT</b> produces a Q9 sphere grid.
</li>
<li>
<b>SPHERE_GRID_Q9_ELEMENT_NUM</b> counts the elements in a Q9 sphere grid.
</li>
<li>
<b>SPHERE_GRID_Q9_NODE_NUM</b> counts nodes in a Q9 sphere grid.
</li>
<li>
<b>SPHERE_GRID_Q9_NODE_XYZ</b> produces node coordinates for a Q9 sphere grid.
</li>
<li>
<b>SPHERE_GRID_Q16_ELEMENT</b> produces a Q16 sphere grid.
</li>
<li>
<b>SPHERE_GRID_Q16_ELEMENT_NUM</b> counts the elements in a Q16 sphere grid.
</li>
<li>
<b>SPHERE_GRID_Q16_NODE_NUM</b> counts nodes in a Q16 sphere grid.
</li>
<li>
<b>SPHERE_GRID_Q16_NODE_XYZ</b> produces node coordinates for a Q16 sphere grid.
</li>
<li>
<b>SPHERE_GRID_T3_ELEMENT</b> produces a T3 sphere grid.
</li>
<li>
<b>SPHERE_GRID_T3_ELEMENT_NUM</b> counts the elements in a T3 sphere grid.
</li>
<li>
<b>SPHERE_GRID_T3_NODE_NUM</b> counts nodes in a T3 sphere grid.
</li>
<li>
<b>SPHERE_GRID_T3_NODE_XYZ</b> produces node coordinates for a T3 sphere grid.
</li>
<li>
<b>SPHERE_GRID_T6_ELEMENT</b> produces a T6 sphere grid.
</li>
<li>
<b>SPHERE_GRID_T6_ELEMENT_NUM</b> counts the elements in a T6 sphere grid.
</li>
<li>
<b>SPHERE_GRID_T6_NODE_NUM</b> counts nodes in a T6 sphere grid.
</li>
<li>
<b>SPHERE_GRID_T6_NODE_XYZ</b> produces node coordinates for a T6 sphere grid.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TRIANGLE_UNIT_SET</b> sets a quadrature rule in the unit triangle.
</li>
<li>
<b>TRIANGLE_UNIT_SIZE</b> returns the "size" of a unit triangle quadrature rule.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 16 August 2009.
</i>
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