fem1d_sample

fem1d_sample, a MATLAB code 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 MIT 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 code which applies the finite element method to a 1d linear two point boundary value problem.

fem1d_adaptive, a MATLAB code 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 code which reads three files defining a 1d arbitrary degree finite element function, and displays a plot.

fem1d_nonlinear, a MATLAB code which applies the finite element method to a 1d nonlinear two point boundary value problem.

fem1d_pmethod, a MATLAB code which applies the p-method version of the finite element method to a 1d linear two point boundary value problem.

fem1d_sample_test

fem2d_sample, a MATLAB code which evaluates a finite element function defined on an order 3 or order 6 triangulation.

fem3d_sample, a MATLAB code which evaluates a finite element function defined on 3d tetrahedral mesh.

histogram_data_2d_sample, a MATLAB code 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 code 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 code 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.