LIBEM2 - Solution of the 2D Laplace Equation in Microsoft Excel by the Boundary Element Method

The LIBEM2.xlsm spreadsheet solves the two-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 shape and it is represented or approximated by a set of straight line panels. The boundary functions are approximated by a constant on each panel; this is the simplest form of the boundary element method in 2D. 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 new verson of the software is able to sketch the boundary and domain points and has more helpful error messages. For example the square boundary and domain points are sketched in the diagram. The spreadsheet may be downloaded from LIBEM2 1_5.xlsm LIBEM2 1.5 Excel Spreadsheet and the initial guide may be downloaded from LIBEM2_xls 1.5.pdf LIBEM2 Guide www.boundary-element-method.com Homepage