FEM1D_SAMPLE
Evaluate a Finite Element Function of a 1D Argument

FEM1D_SAMPLE, a MATLAB program which can evaluate a finite element function of one 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.

Languages:

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

Related Data and Programs:

FEM1D, a data directory which contains examples of 1D FEM files, three text files that describe a 1D finite element model;

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

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

FEM1D_DISPLAY, a MATLAB program which reads three files defining a 1D arbitrary degree finite element function, and displays a plot.

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

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

fem1d_sample, a MATLAB program which samples a scalar or vector finite element function of one variable, defined by FEM files, returning interpolated values at the sample points.

fem1d_sample_test

FEM2D_SAMPLE, a MATLAB library which evaluates a finite element function defined on an order 3 or order 6 triangulation.

FEM3D_SAMPLE, a MATLAB program which evaluates a finite element function defined on 3D tetrahedral mesh.

HISTOGRAM_DATA_2D_SAMPLE, a MATLAB 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.

HISTOGRAM_PDF_SAMPLE, a MATLAB library which demonstrates how sampling can be done by starting with the formula for a PDF, creating a histogram, constructing a histogram for the CDF, and then sampling.

REJECTION_SAMPLE, a MATLAB library which demonstrates acceptance/rejection sampling.

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.m the source code.
• timestamp.m prints the YMDHMS date as a timestamp.

Examples and Tests:

• fem1d_sample_test.m calls all the tests.
• fem1d_sample_test.sh runs all the tests.
• fem1d_sample_test.txt the output file.

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.