**Author details**

boundary, LBEM3 for the general three-dimensional problem interior or exterior to a closed boundary, LBEMA for the axisymmetric three-dimensional problem interior or exterior to a closed boundary, LSEM3 for the general three-dimensional problem exterior to an open boundary and LSEMA for the axisymmetric threedimensional problem exterior to an open boundary. The linkage between these and

**File/code Purpose of module LIBEM2 LBEMA LBEM3 LSEMA LSEM3**

GEOM2D Geometrical operations (2D) X X X

GLRULES Gauss-Legendre quadrature rules X X X

VGEOMA Verifies the geometry (axisym) X X

L3ALCC Copy of L3ALC (to fake recursion) X X

VGEOM3 Verifies the geometry (3D) X X

GEOM3D Geometrical operations (3D) X X X X

X

X X

X X XX X

X X XX X

X X XX X

X X

X X

X X

L2LC Computes the discrete Laplace operators

*Numerical Modeling and Computer Simulation*

L3ALC Computes the discrete Laplace operators

L3LC Computes the discrete Laplace operators

GLS2 Solves a generalised linear system of

LUFAC Carries out LU factorisation of the

GLT7 7-point Gaussian quadrature rule for

GLT25 25-point Gaussian quadrature rule for

VGEOM2 Verifies the geometry (2D) X

VG2LC Verifies the use of the L2LC module X

LUFBSUB Carries out forward and back substitution

(2D)

(3D)

(axisym)

equations

matrix

triangle

triangle

*The main codes and supporting library.*

The main subroutines have the control parameters LSOL, LVALID and TOLGEOM. LSOL is set to TRUE if the full solution is sought and FALSE if the linear system is the output. LVALID is set to TRUE if validation is required and

The GLS algorithm in file GLS2 carries out a column-swapping method [31] in order to prepare the linear system for solution by a standard method. The standard method in this work is LU factorization and back substitution in files LUFAC and

the supporting codes in the library is shown in **Table 8**.

LUFBSUBS.

**16**

**Table 8.**

FALSE if it is not. TOLGEOM sets the geometrical tolerance.

Stephen Kirkup\* and Javad Yazdani University of Central Lancashire, Preston, UK

\*Address all correspondence to: smkirkup@uclan.ac.uk

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
