FEM1D_PACK
1D Finite Element Routines

FEM1D_PACK is a C++ library which contains utilities for implementing the finite element method in a 1D region.

Licensing:

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

Languages:

FEM1D_PACK is available in a C version and a C++ version and a FORTRAN90 version and a FORTRAN77 version and a MATLAB version.

Related Data and Programs:

FEM1D, a data directory which contains examples of 1D FEM files, text files that describe a 1D finite element model and associated nodal values.

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_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.

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_PACK, a C++ library which contains utilities for 2D finite element calculations.

FEM3D_PACK, a C++ library which contains utilities for 3D finite element calculations.

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_pack.cpp, the source code.
• fem1d_pack.hpp, the include file.
• fem1d_pack.sh, BASH commands to compile the source code.

Examples and Tests:

• fem1d_pack_prb.cpp, a sample calling program.
• fem1d_pack_prb.sh, BASH commands to compile and run the sample program.
• fem1d_pack_prb_output.txt, the output file.

List of Routines:

• BANDWIDTH_MESH determines the bandwidth of the coefficient matrix.
• I4_MAX returns the maximum of two I4's.
• I4_MIN returns the minimum of two I4's.
• LEGENDRE_COM computes abscissas and weights for Gauss-Legendre quadrature.
• LOCAL_BASIS_1D evaluates the basis functions in an element.
• LOCAL_BASIS_PRIME_1D evaluates the basis function derivatives in an element.
• LOCAL_FEM_1D evaluates a local finite element function.
• R8_UNIFORM returns a scaled pseudorandom R8.
• R8MAT_PRINT prints an R8MAT.
• R8MAT_PRINT_SOME prints some of an R8MAT.
• R8VEC_DOT_PRODUCT computes the dot product of a pair of R8VEC's.
• R8VEC_SUM returns the sum of an R8VEC.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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