FEM3D_PACK
3D Finite Element Method Utility Library

FEM3D_PACK is a C++ library which contains utility routines for 3D finite element calculations.

Licensing:

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

Languages:

FEM3D_PACK is available in a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

FEM_BASIS, a C++ library 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, a C++ library which contains utilities for 1D finite element calculations.

FEM2D_PACK, a C++ library which contains utilities for 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, 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 C++ program 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:

• fem3d_pack.cpp, the source code.
• fem3d_pack.hpp, the include file.

Examples and Tests:

• fem3d_pack_test.cpp, a sample calling program.
• fem3d_pack_test.sh, commands to compile and run the sample program.
• fem3d_pack_test.txt, the output file.

List of Routines:

• BANDWIDTH_MESH determines the bandwidth of the coefficient matrix.
• BANDWIDTH_VAR determines the bandwidth for finite element variables.
• BASIS_BRICK8: BRICK8 basis functions at natural coordinates.
• BASIS_BRICK8_TEST verifies BASIS_BRICK8.
• BASIS_BRICK20: BRICK20 basis functions at natural coordinates.
• BASIS_BRICK20_TEST verifies BASIS_BRICK20.
• BASIS_BRICK20: BRICK20 basis functions at natural coordinates.
• BASIS_BRICK27_TEST verifies BASIS_BRICK27.
• BASIS_MN_TET4: all bases at N points for a TET4 element.
• BASIS_MN_T4_TEST verifies BASIS_MN_TET4.
• BASIS_MN_TET10: all bases at N points for a TET10 element.
• BASIS_MN_TET10_TEST verifies BASIS_MN_TET10.
• I4_MAX returns the maximum of two I4's.
• NODES_BRICK8 returns the natural coordinates of the BRICK8 element.
• NODES_BRICK20 returns the natural coordinates of the BRICK20 element.
• NODES_BRICK27 returns the natural coordinates of the BRICK27 element.
• PHYSICAL_TO_REFERENCE_TET4 maps physical points to reference points.
• R8_ABS returns the absolute value of an R8.
• R8GE_FSS factors and solves multiple R8GE systems.
• R8MAT_COPY_NEW copies one R8MAT to a "new" R8MAT.
• R8MAT_DET_4D computes the determinant of a 4 by 4 R8MAT.
• R8MAT_MV multiplies a matrix times a vector.
• R8MAT_SOLVE uses Gauss-Jordan elimination to solve an N by N linear system.
• R8MAT_UNIFORM_01_NEW returns a new unit pseudorandom R8MAT.
• R8VEC_SUM returns the sum of an R8VEC.
• R8VEC_UNIFORM_01_NEW returns a new unit pseudorandom R8VEC.
• REFERENCE_TET4_SAMPLE: sample points in the reference tetrahedron.
• REFERENCE_TET4_UNIFORM: uniform sample points in the reference tetrahedron.
• REFERENCE_TET4_UNIFORM2: uniform sample points in the reference tetrahedron.
• REFERENCE_TO_PHYSICAL_TET4 maps TET4 reference points to physical points.
• TETRAHEDRON_BARYCENTRIC returns the barycentric coordinates of a point.
• TETRAHEDRON_VOLUME computes the volume of a tetrahedron in 3D.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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