fem2d_sample

fem2d_sample, a C++ code which evaluates 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 MIT 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++ code 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++ code which solves the time dependent heat equation in the unit square.

FEM2D_PACK, a C++ code which includes utitlies for 2D finite element calculations.

fem2d_poisson_rectangle_linear, a C++ code which solves the 2D Poisson equation on a rectangle, using the finite element method, and piecewise linear triangular elements.

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

fem2d_sample_test

FEM3D_SAMPLE, a C++ code which evaluates a finite element function defined on 3D tetrahedral mesh.

HISTOGRAM_DATA_2D_SAMPLE, a C++ 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.

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.cpp, the source code.
• fem2d_sample.sh, compiles the source code.