FEM3D_SAMPLE
Evaluate a Finite Element Function of a 3D Argument

FEM3D_SAMPLE is a MATLAB program which can evaluate a finite element function of a 3D argument.

The current version of the program can only handle tetrahedral finite element meshes using linear basis functions.

The current version of the program uses a NAIVE search algorithm to locate points within the mesh. It is intended that this search algorithm be replaced by a Delaunay search.

Usage:

fem3d_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:

FEM3D_SAMPLE is available in a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

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

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.

FEM2D_SAMPLE, a MATLAB program which samples a scalar or vector finite element function of 2 variables defined by FEM files, returning interpolated values at the sample points.

FEM3D, a data directory which contains examples of 3D FEM files, three text files that describe a 3D finite element geometry;

FEM3D_PACK, a MATLAB library which contains utilities for 3D finite element calculations.

FEM3D_PROJECT, a MATLAB program which projects a function F(X,Y,Z), given as a data, into a given finite element space of piecewise linear tetrahedral elements.

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:

• fem3d_sample.m, the source code.

Examples and Tests:

SQ is FEM data for the function f(x,y,z)=x^2+2*y^2-z^2, on a 5x5x5 grid of nodes in the cube [0,4]x[0,4]x[0,4], organized into linear linear tetrahedrons. The sample data seeks the values of this function on a 4x4x4 evenly spaced grid.

• fem_sq_nodes.txt, defines the FEM nodes.
• fem_sq_elements.txt, defines the FEM elements.
• fem_sq_values.txt, defines the FEM nodal values.
• sample_sq_nodes.txt, defines the sample nodes.
• sample_sq_values.txt, defines the sample nodal values.
• sample_sq_values_exact.txt, the exact values of the function at the sample nodes. This should be compared with the values determined from the FEM function.

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