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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.
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LinksDownload the LIBEM2 Spreadsheet and Manual Included in the Researchgate project The Boundary Element Method on an Excel Spreadsheet Included in the Researchgate project Boundary Element Method Programs for the Solution of Laplace's Equation Included in the Researchgate project Teaching Numerical methods using Spreadsheets Stephen Kirkup's Research Papers Boundary Element Method website Boundary Element Method LinkedIn Group Spreadsheets in Science and Engineering LinkedIn Group Computational Mechanics Research LinkedIn Group Numerical Methods LinkedIn Group
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