LIBEMA - Solution of the Axisymmetric Interior 3D Laplace Equation in Microsoft Excel by the Boundary Element Method


The LIBEMA.xlsm spreadsheet solves the axisymmetric three-dimensional interior Laplace equation, with a generalised (Robin or mixed) boundary condition (which includes the special cases of the Dirichlet (essential) and the Neumann (derivative or flux) condition) by the Boundary Element Method. The closed boundary may be any axisymmetric 3D shape and it is represented or approximated by a set of truncated conical panels. The boundary functions are approximated by a constant on each panel; this is the simplest form of the boundary element method in 3D with axisymmetry. The solution may be found at any set of points within the interior domain.

The input data is displayed on the sheets of the spreadsheet and the steps in the boundary element method may be activated by buttons on the spreadsheet. The results are also displayed on the sheets of the spreadsheet. The standard 'direct' and 'indirect' methods may be applied by activating the appropriate button. It is shown how the interim results from one run can be re-used in another run of the code, and hence how the computational cost or computer time used in simulations may be managed.

There is a guide for using the method and the simple test problem covered within the spreadsheet is that of a square with a simple linear solution. The stages of the boundary element method are explained and each macro has a guiding document to explain what each is doing.

The software is able to sketch the generator of the boundary and domain points. For example for the cylidrical test problem the generator of the boundary and the domain points are sketched in the diagram.

The spreadsheet may be downloadeed from LIBEMA 1.xlsm LIBEMA 1 Excel Spreadsheet

and the initial guide may be downloaded from LIBEMA_xls 1.pdf LIBEMA Guide Homepage