FEM1D_SAMPLE
Evaluate a Finite Element Function of a 1D Argument

FEM1D_SAMPLE is a FORTRAN90 program which can evaluate a finite element function of a 1D argument.

The current version of the program can only handle finite element meshes which are made of piecewise constant or piecewise linear basis functions.

Usage:

fem1d_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.

Related Data and Programs:

DISCRETE_PDF_SAMPLE a MATLAB program which demonstrates how to construct a Probability Density Function (PDF) from a table of sample data, and then to use that PDF to create new samples.

FEM is a data directory which contains a description and examples of files that describe a finite element model.

FEM1D is a FORTRAN90 program which applies the finite element method to a 1D linear two point boundary value problem.

FEM1D_ADAPTIVE is a FORTRAN90 program which applies the finite element method to a 1D linear two point boundary value problem using adaptive refinement to improve the solution.

FEM1D_NONLINEAR is a FORTRAN90 program which applies the finite element method to a 1D nonlinear two point boundary value problem.

FEM1D_PMETHOD is a FORTRAN90 program which applies the p-method version of the finite element method to a 1D linear two point boundary value problem.

FEM1D_PROJECT is a FORTRAN90 program which projects data into a finite element space, including the least squares approximation of data, or the projection of a finite element solution from one mesh to another.

FEM1D_SAMPLE is available in a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

FEM2D_SAMPLE is a FORTRAN90 program which evaluates a finite element function defined on an order 3 or order 6 triangulation.

PIECEWISE_LINEAR_PRODUCT_INTEGRAL is a FORTRAN90 library which calculates the exact value of the integral of the product of two piecewise linear functions F(X) and G(X).

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:

• fem1d_sample.f90, the source code.
• fem1d_sample.csh, commands to compile the source code.

Examples and Tests:

P1 is FEM data for the vector function f(x)=[ 1, x, x^2], on a grid of 11 evenly spaced nodes from -5 to 5, using piecewise constant basis functions.

• p1_fem_nodes.txt, the FEM nodes.
• p1_fem_elements.txt, the FEM elements.
• p1_fem_values.txt, the FEM nodal values.
• p1_sample_nodes.txt, the sample nodes.
• p1_sample_values.txt, the sample nodal values.

P2 is FEM data for the vector function f(x)=[ 1, x, x^2], on a grid of 11 evenly spaced nodes from -5 to 5, using piecewise linear basis functions.

• p2_fem_nodes.txt, the FEM nodes.
• p2_fem_elements.txt, the FEM elements.
• p2_fem_values.txt, the FEM nodal values.
• p2_sample_nodes.txt, the sample nodes.
• p2_sample_values.txt, the sample nodal values.

List of Routines:

• MAIN is the main program for FEM1D_SAMPLE.
• CH_CAP capitalizes a single character.
• CH_EQI is a case insensitive comparison of two characters for equality.
• CH_TO_DIGIT returns the integer value of a base 10 digit.
• DTABLE_DATA_READ reads data from a DTABLE file.
• DTABLE_HEADER_READ reads the header from a DTABLE file.
• DTABLE_WRITE0 writes a DTABLE file with no headers.
• FEM1D_EVALUATE evaluates a 1D FEM function at sample points.
• 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_UNIT returns a free FORTRAN unit number.
• ITABLE_DATA_READ reads data from an ITABLE file.
• ITABLE_HEADER_READ reads the header from an integer table file.
• R8VEC_BRACKET4 finds the nearest interval to each of a vector of values.
• 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.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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