FEM2D_SAMPLE
Evaluate a Finite Element Function of a 2D Argument
FEM2D_SAMPLE
is a C++ program which
can evaluate a finite element function of a 2D argument.
The current version of the program can only handle finite element
meshes which are made of piecewise linear triangles of order 3 or 6.
Usage:
fem2d_sample fem_prefix sample_prefix
where fem_prefix is the common prefix for the FEM files:

fem_prefix_nodes.txt, the node coordinates.

fem_prefix_elements.txt, the nodes that make up each element;

fem_prefix_values.txt, the values defined at each node.
and sample_prefix is the common prefix for the SAMPLE files,
for which the node file is input, and the values file is created by the program:

sample_prefix_nodes.txt, the node coordinates where samples are desired.

sample_prefix_values.txt, the values computed at each sample node.
Licensing:
The computer code and data files described and made available on this web page
are distributed under
the GNU LGPL license.
Languages:
FEM2D_SAMPLE is available in
a C++ version and
a FORTRAN90 version and
a MATLAB version.
Related Data and Programs:
FEM1D_SAMPLE,
a C++ program which
samples a scalar or vector finite element function of one variable,
defined by FEM files,
returning interpolated values at the sample points.
FEM2D,
a data directory which
contains examples of 2D FEM files,
three text files that describe a 2D finite element geometry;
FEM2D_HEAT,
a C++ program which
solves the
time dependent heat equation in the unit square.
FEM2D_PACK,
a C++ library which
includes utitlies for 2D finite element calculations.
FEM2D_POISSON,
a C++ program which
solves Poisson's equation
on a square, using the finite element method.
FEM2D_POISSON_LINEAR,
a C++ program which
solves the 2D Poisson equation on a rectangle, using the finite element method,
and piecewise linear triangular elements.
FEM2D_PROJECT,
a C++ program which
projects a function F(X,Y) into a given finite element space
of piecewise linear triangular elements.
FEM3D_SAMPLE,
a C++ program which
evaluates a finite element function defined on 3D tetrahedral mesh.
HISTOGRAM_DATA_2D_SAMPLE,
a C++ program which
demonstrates how to construct a Probability Density Function (PDF)
from a frequency table over a 2D domain, and then to use that PDF
to create new samples.
Reference:

Hans Rudolf Schwarz,
Finite Element Methods,
Academic Press, 1988,
ISBN: 0126330107,
LC: TA347.F5.S3313.

Gilbert Strang, George Fix,
An Analysis of the Finite Element Method,
Cambridge, 1973,
ISBN: 096140888X,
LC: TA335.S77.

Olgierd Zienkiewicz,
The Finite Element Method,
Sixth Edition,
ButterworthHeinemann, 2005,
ISBN: 0750663200,
LC: TA640.2.Z54.
Source Code:
Examples and Tests:
SQ is FEM data for the function f(x,y)=x^2+y^2, on a 5x5 grid
of nodes, organized into linear triangles. The sample data seeks the values
of this function on a 4x4 evenly spaced grid.
List of Routines:

MAIN is the main program for FEM2D_SAMPLE.

BASIS_MN_T3: all bases at N points for a T3 element.

BASIS_MN_T6: all bases at N points for a T6 element.

CH_CAP capitalizes a single character.

CH_EQI is true if two characters are equal, disregarding case.

CH_TO_DIGIT returns the integer value of a base 10 digit.

GRID_SAMPLE samples a (scalar) FE function on a T3 or T6 triangulation.

FILE_COLUMN_COUNT counts the number of columns in the first line of a file.

FILE_ROW_COUNT counts the number of row records in a file.

GET_SEED returns a random seed for the random number generator.

I4_MAX returns the maximum of two integers.

I4_MIN returns the smaller of two integers.

I4_UNIFORM returns a scaled pseudorandom I4.

I4COL_COMPARE compares columns I and J of an I4COL.

I4COL_SORT_A ascending sorts an I4COL.

I4COL_SWAP swaps two columns of an I4COL.

I4MAT_DATA_READ reads data from an I4MAT file.

I4MAT_HEADER_READ reads the header from an I4MAT file.

R4_ABS returns the absolute value of an R4.

R4_NINT returns the nearest integer to an R4.

R4_UNIFORM_01 returns a unit pseudorandom R4.

R8_HUGE returns a "huge" R8.

R8_MAX returns the maximum of two R8's.

R8_MIN returns the minimum of two R8's.

R8_NINT returns the nearest integer to an R8.

R8MAT_DATA_READ reads the data from an R8MAT file.

R8MAT_HEADER_READ reads the header from an R8MAT file.

R8MAT_WRITE writes an R8MAT file.

S_LEN_TRIM returns the length of a string to the last nonblank.

S_TO_I4 reads an I4 from a string.

S_TO_I4VEC reads an I4VEC from a string.

S_TO_R8 reads an R8 from a string.

S_TO_R8VEC reads an R8VEC from a string.

S_WORD_COUNT counts the number of "words" in a string.

SORT_HEAP_EXTERNAL externally sorts a list of items into ascending order.

TIMESTAMP prints the current YMDHMS date as a time stamp.

TRIANGULATION_ORDER3_NEIGHBOR_TRIANGLES determines triangle neighbors.

TRIANGULATION_ORDER6_NEIGHBOR_TRIANGLES determines triangle neighbors.

TRIANGULATION_SEARCH_DELAUNAY searches a triangulation for a point.
You can go up one level to
the C++ source codes.
Last revised on 08 August 2009.