FEM3D
Files Describing a 3D Finite Element Model

FEM3D is a data directory which contains examples of 3D FEM files, which define a 3D finite element model.

The FEM format is a simple dataset of several files that can be used to describe a finite element model.

The finite element model might include the following files:

• a node file, node coordinates (in 1D, 2D or 3D);
• an element file, elements defined by a sequence of node indices. For this simple format, we assume the elements are all of the same order, and the most common choices are linear or quadratic tetrahedrons;
• a value file, listing the values of one or more functions at each node.
• a boundary node mask file, listing for each node the value 1 if it is a boundary node, and 0 otherwise.
• a boundary node file, listing the coordinates of nodes that lie on the boundary.
• a boundary element file, listing the indices (from the boundary node file) of the nodes that form elements (of one dimension lower) lying on the boundary of the mesh.

FEM File Characteristics:

• ASCII
• Each line is one "record"
• Each record is either a comment record or a data record;
• Comment records begin with the "#" character;
• A data record records node coordinates for one node, or the node indices for one element, or the set of node data for one node;
• For a given file, each data record contains the same number of items, separated by blanks.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Related Data and Programs:

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

FEM2D, a data directory which contains examples of 2D FEM files, text files that describe a 2D finite element geometry;

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

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

FEM3D_SAMPLE, a FORTRAN90 program which evaluates a finite element function defined on 3D tetrahedral mesh.

Reference:

1. Hans Rudolf Schwarz,
   Methode der Finiten Elemente,
   Teubner Studienbuecher, 1980,
   ISBN: 3-519-02349-0.
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.

Sample Files:

BLOCK is 3D FEM data for the function f(x,y,z)=x^2+2*y^2-z^2, on a 5x5x5 grid of 125 nodes in the cube [0,4]x[0,4]x[0,4], organized into 384 linear tetrahedrons.

• block_nodes.txt, defines the nodes.
• block_elements.txt, defines the elements.
• block_values.txt, defines the nodal values.
• block_boundary_node_mask.txt, 0 for interior nodes, 1 for boundary nodes.
• block_boundary_nodes.txt, defines the boundary nodes.
• block_boundary_elements.txt, defines the boundary faces.
• block_boundary.png, an image of the triangulated surface of the boundary.

CASE1 is 3D FEM data for a 5x1x1 rectangular channel region using 8261 nodes and 5000 quadratic (ten node) tetrahedral elements.

• case1_nodes.txt, defines the nodes.
• case1_elements.txt, defines the elements.
• case1_values.txt, defines the nodal values U, V, W, and P (three velocity components and pressure).
• case1_boundary_node_mask.txt, 0 for interior nodes, 1 for boundary nodes.
• case1_boundary_nodes.txt, defines the boundary nodes.
• case1_boundary_elements.txt, defines the boundary faces.

CUBE is 3D FEM data for the unit cube, using 8 nodes, organized into 6 linear tetrahedrons.

• cube_nodes.txt, defines the nodes.
• cube_elements.txt, defines the elements.
• cube_boundary_node_mask.txt, 0 for interior nodes, 1 for boundary nodes.
• cube_boundary_nodes.txt, defines the boundary nodes.
• cube_boundary_elements.txt, defines the boundary faces.

P01 is 3D FEM data for a rectangular channel of dimensions 3x1x1 physical units, using 584 nodes and 2568 tetrahedral elements.

• p01_nodes.txt, defines the nodes.
• p01_elements.txt, defines the elements.
• p01_values.txt, defines the nodal values.
• p01.png, an image of the mesh.
• p01_boundary_node_mask.txt, 0 for interior nodes, 1 for boundary nodes.
• p01_boundary_nodes.txt, defines the boundary nodes.
• p01_boundary_elements.txt, defines the boundary faces.

P04 is 3D FEM data for a sphere, using 587 nodes and 2775 linear tetrahedral elements.

• p04_nodes.txt, defines the nodes.
• p04_elements.txt, defines the elements.
• p04.png, an image of the mesh.
• p04_boundary_node_mask.txt, 0 for interior nodes, 1 for boundary nodes.
• p04_boundary_nodes.txt, defines the boundary nodes.
• p04_boundary_elements.txt, defines the boundary faces.

You can go up one level to the DATA directory.