fem3d_pack

fem3d_pack, an Octave code which contains utility routines for 3D finite element method (FEM) calculations.

Licensing:

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

Languages:

fem3d_pack is available in a C++ version and a Fortran90 version and a MATLAB version and an Octave version.

Related Data and Programs:

fem3d_pack_test

fem_basis, an Octave code which can define and evaluate basis functions for any degree in an M-dimensional simplex (1D interval, 2D triangle, 3D tetrahedron, and higher dimensional generalizations.)

fem1d_pack, an Octave code which contains utilities for 1D finite element calculations.

fem2d_pack, an Octave code which contains utilities for 2D finite element calculations.

fem3d, a data directory which contains examples of 3D FEM files, three text files that describe a 3D finite element geometry;

fem3d_project, an Octave code 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, an Octave code which evaluates a finite element function defined on 3D tetrahedral mesh.

Reference:

1. Claudio Rocchini, Paolo Cignoni,
   Generating Random Points in a Tetrahedron,
   Journal of Graphics Tools,
   Volume 5, Number 4, 2000, pages 9-12.
2. Reuven Rubinstein,
   Monte Carlo Optimization, Simulation and Sensitivity of Queueing Networks,
   Krieger, 1992,
   ISBN: 0894647644,
   LC: QA298.R79.
3. Gilbert Strang, George Fix,
   An Analysis of the Finite Element Method,
   Cambridge, 1973,
   ISBN: 096140888X,
   LC: TA335.S77.
4. Olgierd Zienkiewicz,
   The Finite Element Method,
   Sixth Edition,
   Butterworth-Heinemann, 2005,
   ISBN: 0750663200,
   LC: TA640.2.Z54.

Source Code:

• bandwidth_mesh.m, bandwidth of finite element mesh.
• bandwidth_var.m, determines the bandwidth for finite element variables.
• basis_brick8.m, evaluates basis functions for a BRICK8 element.
• basis_brick20.m, evaluates basis functions for a BRICK20 element.
• basis_brick27.m, evaluates basis functions for a BRICK27 element.
• basis_mn_tet4.m, all bases at N points for a TET4 element.
• basis_mn_tet10.m, all bases at N points for a TET10 element.
• basis_mn_tet10_test.m, verifies BASIS_MN_TET10.
• nodes_brick8.m, returns the nodes of the BRICK8 element.
• nodes_brick20.m, returns the nodes of the BRICK20 element.
• nodes_brick27.m, returns the nodes of the BRICK27 element.
• physical_to_reference_tet4.m, maps TET4 physical points to reference points.
• r8mat_det_4d.m computed the determinant of a 4x4 R8MAT.
• r8mat_solve.m uses Gauss-Jordan elimination to solve an N by N linear system.
• reference_tet4_sample.m, returns nonuniform sample points from the reference tetrahedron.
• reference_tet4_uniform.m, returns uniform sample points from the reference tetrahedron.
• reference_tet4_uniform2.m, returns uniform sample points from the reference tetrahedron.
• reference_to_physical_tet4.m, maps TET4 reference points to physical points.
• tetrahedron_barycentric.m computes the barycentric coordinates of a point with respect to a tetrahedron.
• tetrahedron_volume.m computes the volume of a tetrahedron.