FEM1D_SAMPLE
Evaluate a Finite Element Function of a 1D Argument

FEM1D_SAMPLE is a C++ program which can evaluate a finite element function of one argument.

The current version of the program can only handle finite element meshes which are made of piecewise constant or piecewise linear basis functions.

Usage:

fem1d_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:

FEM1D_SAMPLE is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

DISCRETE_PDF_SAMPLE_2D, a C++ program which demonstrates how to construct a Probability Density Function (PDF) from a table of sample data, and then to use that PDF to create new samples.

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

FEM1D, a C++ program which applies the finite element method to a 1D linear two point boundary value problem.

FEM1D_ADAPTIVE, a C++ program which applies the finite element method to a 1D linear two point boundary value problem using adaptive refinement to improve the solution.

FEM1D_BVP_LINEAR, a C++ program which applies the finite element method, with piecewise linear elements, to a two point boundary value problem in one spatial dimension.

FEM1D_HEAT_STEADY, a C++ program which uses the finite element method to solve the steady (time independent) heat equation in 1D.

FEM1D_NONLINEAR, a C++ program which applies the finite element method to a 1D nonlinear two point boundary value problem.

FEM1D_PACK, a C++ library which contains utilities for 1D finite element calculations.

FEM1D_PMETHOD, a C++ program which applies the p-method version of the finite element method to a 1D linear two point boundary value problem.

FEM1D_PROJECT, a C++ program which projects data into a finite element space, including the least squares approximation of data, or the projection of a finite element solution from one mesh to another.

FEM2D_SAMPLE, a C++ library which evaluates a finite element function defined on an order 3 or order 6 triangulation.

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

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:

• fem1d_sample.cpp, the source code.
• fem1d_sample.sh, commands to compile the source code.

Examples and Tests:

P1 is FEM data for the vector function f(x)=[ 1, x, x^2], on a grid of 11 evenly spaced nodes from -5 to 5, using piecewise constant basis functions.

• p1_fem_nodes.txt, the FEM nodes.
• p1_fem_elements.txt, the FEM elements.
• p1_fem_values.txt, the FEM nodal values.
• p1_sample_nodes.txt, the sample nodes.
• p1_sample_values.txt, the sample nodal values.

P2 is FEM data for the vector function f(x)=[ 1, x, x^2], on a grid of 11 evenly spaced nodes from -5 to 5, using piecewise linear basis functions.

• p2_fem_nodes.txt, the FEM nodes.
• p2_fem_elements.txt, the FEM elements.
• p2_fem_values.txt, the FEM nodal values.
• p2_sample_nodes.txt, the sample nodes.
• p2_sample_values.txt, the sample nodal values.

List of Routines:

• MAIN is the main program for FEM1D_SAMPLE.
• CH_CAP capitalizes a single character.
• CH_EQI is true if two characters are equal, disregarding case.
• CH_TO_DIGIT returns the integer value of a base 10 digit.
• FEM1D_EVALUATE evaluates a 1D FEM function at sample points.
• FILE_COLUMN_COUNT counts the number of columns in the first line of a file.
• FILE_ROW_COUNT counts the number of row records in a file.
• I4MAT_DATA_READ reads data from an I4MAT file.
• I4MAT_HEADER_READ reads the header from an I4MAT file.
• R8MAT_DATA_READ reads the data from an R8MAT file.
• R8MAT_HEADER_READ reads the header from an R8MAT file.
• R8MAT_WRITE writes an R8MAT file.
• R8VEC_BRACKET4 finds the interval containing or nearest a given value.
• S_LEN_TRIM returns the length of a string to the last nonblank.
• S_TO_I4 reads an I4 from a string.
• S_TO_I4VEC reads an I4VEC from a string.
• S_TO_R8 reads an R8 from a string.
• S_TO_R8VEC reads an R8VEC from a string.
• S_WORD_COUNT counts the number of "words" in a string.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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