FEM2D_SAMPLE
Evaluate a Finite Element Function of a 2D Argument

FEM2D_SAMPLE is a FORTRAN90 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

• 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.

• 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:

FEM_BASIS_T3_DISPLAY, a MATLAB program which displays a basis function associated with a linear triangle ("T3") mesh.

FEM_BASIS_T6_DISPLAY, a MATLAB program which displays a basis function associated with a quadratic triangle ("T6") mesh.

FEM_IO, a FORTRAN90 library which reads or writes node, element and data files defining a finite element model.

FEM_TO_TEC, a MATLAB program which converts FEM models into TEC graphics files.

FEM1D_SAMPLE, a FORTRAN90 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, text files that describe a 2D finite element geometry and associated nodal values;

FEM2D_HEAT, a FORTRAN90 program which solves the 2D time dependent heat equation on the unit square.

FEM2D_PACK, a FORTRAN90 library which contains utilities for 2D finite element calculations.

FEM2D_POISSON, a FORTRAN90 program which solves the 2D Poisson equation on a square, using the finite element method.

FEM2D_PROJECT, a FORTRAN90 program which projects a function F(X,Y) into a given finite element space of piecewise linear triangular elements.

FEM3D_SAMPLE, a FORTRAN90 program which samples a finite element function of three variables, returning interpolated values at the sample points.

HISTOGRAM_DATA_2D_SAMPLE, a FORTRAN90 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.

MESH_BANDWIDTH, a FORTRAN90 program which returns the geometric bandwidth associated with a mesh of elements of any order and in a space of arbitrary dimension.

TRIANGULATION_ORDER3, a data directory which contains a description and examples of how an order 3 (linear) triangulation is defined by a node and element file.

TRIANGULATION_ORDER6, a data directory which contains a description and examples of how an order 6 (quadratic) triangulation is defined by a node and element file.

TRIANGULATION_ORDER6_CONTOUR, a MATLAB program which makes contours of a scalar quantity defined on the nodes of an order 6 triangulation.

Reference:

1. Hans Rudolf Schwarz,
   Finite Element Methods,
   Academic Press, 1988,
   ISBN: 0126330107,
   LC: TA347.F5.S3313.
2. Gilbert Strang, George Fix,
   An Analysis of the Finite Element Method,
   Cambridge, 1973,
   ISBN: 096140888X,
   LC: TA335.S77.
3. Olgierd Zienkiewicz,
   The Finite Element Method,
   Sixth Edition,
   Butterworth-Heinemann, 2005,
   ISBN: 0750663200,
   LC: TA640.2.Z54.

Source Code:

• fem2d_sample.f90, the 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.

• fem_sq_nodes.txt, defines the FEM nodes.
• fem_sq_elements.txt, defines the FEM elements.
• fem_sq_values.txt, defines the FEM nodal values.
• sample_sq_nodes.txt, defines the sample nodes.
• sample_sq_values.txt, defines the sample nodal values.

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 a case insensitive comparison of two characters for equality.
• CH_TO_DIGIT returns the integer ( kind = 4 ) value of a base 10 digit.
• FEM2D_EVALUATE samples an FEM 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 seed for the random number generator.
• GET_UNIT returns a free FORTRAN unit number.
• 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 columns I and J of an I4COL.
• I4MAT_DATA_READ reads data from an I4MAT file.
• I4MAT_HEADER_READ reads the header from an I4MAT.
• R8MAT_DATA_READ reads data from an R8MAT file.
• R8MAT_HEADER_READ reads the header from an R8MAT file.
• R8MAT_WRITE writes an R8MAT file.
• S_TO_I4 reads an integer ( kind = 4 ) value from a string.
• S_TO_I4VEC reads an integer ( kind = 4 ) vector 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 Delaunay triangulation for a point.

You can go up one level to the FORTRAN90 source codes.