**4.3 LSEM3 module, test problem and results**

The LSEM3 module solves Laplace's equation exterior to a thin shell in three dimensions. The subroutine call has the following form:

LSEM3(MAXNODES,NNODE,NODES,MAXPANELS,NPANEL,PANELS,


The definition of the important parameters can be found from the previous notes on LBEM3 and LSEMA. The test problem is in the file LSEM3\_T, and it is similar to the test problem for LSEMA. This time, the open boundaries are two unit square plates of in *x* � *y* planes. The two squares are 0.1 apart: one is at a potential of zero and the other is at a potential of one. The squares are each divided into 32 panels. The results at points between the squares, along a central axis, are shown in **Table 7**.


**Table 6.**

*The results from the axisymmetric shell problem.*

*A Pilot Fortran Software Library for the Solution of Laplace's Equation by the Boundary… DOI: http://dx.doi.org/10.5772/intechopen.86507*


**Table 7.**

The module LSEMA has the form:

*Numerical Modeling and Computer Simulation*

\* AMAT,BMAT,L\_EH, M\_EH,

*<sup>Φ</sup>*^ *<sup>Γ</sup>*; VELDIF, *<sup>ν</sup>*^*Γ*; VELAV, *<sup>V</sup>*^ *<sup>Γ</sup>*; and PPHI, *<sup>φ</sup>*^*E*.

**4.3 LSEM3 module, test problem and results**

\* MAXPOINTS,NPOINT,POINTS, \* HA,HB,HF,HAA,HBB,HFF, \* HINPHI,HINVEL,PINPHI, \* LSOL,LVALID,TOLGEOM,

\* AMAT,BMAT,L\_EH,M\_EH,

*The results from the axisymmetric shell problem.*

dimensions. The subroutine call has the following form:

\* PHIDIF,PHIAV,VELDIF,VELAV,PPHI,

\* PERM,XORY,C,WKSPC1,WKSPC2,WKSPC3)

**Table 6**.

**Table 7**.

**Table 6.**

**14**

\* MAXPOINTS,NPOINT,POINTS, \* HA,HB,HF,HAA,HBB,HFF, \* HIPHI,HIVEL,PINPHI, \* LSOL,LVALID,TOLGEOM,

\* PHIDIF,PHIAV,VELDIF,VELAV,PPHI,

\* PERM,XORY,C,WKSPC1,WKSPC2,WKSPC3).

LSEMA(MAXNODES,NNODE,NODES,MAXPANELS,NPANEL,PANELS,

The LSEMA parameters are similar to the LBEMA ones. However the expres-

HA stores the values of *α* on the shell panels, similarly HB, *β*; HAA, *A*; and HBB,

The test problem is in file LSEMA\_T. It consists of two circular coaxial parallel plates in the *r, θ* plane, of radius 1.0 and a distance of 0.1 apart in the planes where *z* ¼ 0*:*0 and *z* ¼ 0*:*1*:* A Dirichlet boundary condition is applied to both plates. On the plate at *z* ¼ 0*:*0, the potential of 0.0 is applied, and a potential (*δ* = 0, *Φ* ¼ 0) of 1.0 is applied on the other plate (*δ* = 0, *Φ* ¼ 1). A complete analytic solution is not available. However in the central region between the plates, a simple gradient of potential is intuitive, as discussed. The results from the test problem are listed in

The LSEM3 module solves Laplace's equation exterior to a thin shell in three

LSEM3(MAXNODES,NNODE,NODES,MAXPANELS,NPANEL,PANELS,

The definition of the important parameters can be found from the previous notes on LBEM3 and LSEMA. The test problem is in the file LSEM3\_T, and it is similar to the test problem for LSEMA. This time, the open boundaries are two unit square plates of in *x* � *y* planes. The two squares are 0.1 apart: one is at a potential of zero and the other is at a potential of one. The squares are each divided into 32 panels. The results at points between the squares, along a central axis, are shown in

**Index Point Expected (4 d.p.) Computed (4 d.p.)** (0.0, 0.025) 0.25 0.2495 (0.0, 0.05) 0.5 0.5000 (0.0, 0.075) 0.75 0.7506

^*Γ*; PHIAV,

sions of the boundary condition and the boundary function are different.

*B:* The main output from the subroutine is PHIDIF that corresponds to *δ*

*The results from the three-dimensional shell problem.*
