fem2d_sample

fem2d_sample, a FORTRAN90 code which evaluates a finite element function of a 2D argument.

The current version of the code 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 codes:

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

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

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

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

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

fem2d_sample_test

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

HISTOGRAM_DATA_2D_SAMPLE, a FORTRAN90 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.

MESH_BANDWIDTH, a FORTRAN90 code 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.

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.
• fem2d_sample.sh, compiles the source code.