FEM3D_SAMPLE
Evaluate a Finite Element Function of a 3D Argument


FEM3D_SAMPLE is a C++ 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
where fem_prefix is the common prefix for the FEM files: and sample_prefix is the common prefix for the SAMPLE files, for which the node file is input, and the values file is created by the program:

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

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

FEM1D_SAMPLE, a C++ 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 C++ 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 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.

HISTOGRAM_DATA_2D_SAMPLE, a C++ program 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.

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:

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.

List of Routines:

You can go up one level to the C++ source codes.


Last revised on 07 August 2009.