fem1d_sample

fem1d_sample, a FORTRAN90 code which can evaluate a finite element function of a 1D argument.

The current version of the code 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 MIT license

Languages:

fem1d_sample is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and codes:

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

FEM1D, a FORTRAN90 code which applies the finite element method to a 1D linear two point boundary value problem.

FEM1D_ADAPTIVE, a FORTRAN90 code 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 FORTRAN90 code 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 FORTRAN90 code which uses the finite element method to solve the steady (time independent) heat equation in 1D.

FEM1D_NONLINEAR, a FORTRAN90 code which applies the finite element method to a 1D nonlinear two point boundary value problem.

FEM1D_PACK, a FORTRAN90 code which contains utilities for 1D finite element calculations.

FEM1D_PMETHOD, a FORTRAN90 code which applies the p-method version of the finite element method to a 1D linear two point boundary value problem.

FEM1D_PROJECT, a FORTRAN90 code 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.

fem1d_sample_test

FEM2D_SAMPLE, a FORTRAN90 code which evaluates a finite element function defined on an order 3 or order 6 triangulation.

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

HISTOGRAM_DATA_2D_SAMPLE, a FORTRAN90 code 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.

PIECEWISE_LINEAR_PRODUCT_INTEGRAL, a FORTRAN90 code which calculates the exact value of the integral of the product of two piecewise linear functions F(X) and G(X).

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.f90, the source code.
• fem1d_sample.sh, compiles the source code.