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The Boundary Element Method in Excel for Teaching Vector Calculus and Simulation
Authors: Stephen Kirkup
Abstract:This paper discusses the implementation of the boundary element method (BEM) on an Excel spreadsheet and how it can be used in teaching vector calculus and simulation. There are two separate spreadheets, within which Laplace equation is solved by the BEM in two dimensions (LIBEM2) and axisymmetric three dimensions (LBEMA). The main algorithms are implemented in the associated programming language within Excel, Visual Basic for Applications (VBA). The BEM only requires a boundary mesh and hence it is a relatively accessible method. The BEM in the open spreadsheet environment is demonstrated as being useful as an aid to teaching and learning. The application of the BEM implemented on a spreadsheet for educational purposes in introductory vector calculus and simulation is explored. The development of assignment work is discussed, and sample results from student work are given. The spreadsheets were found to be useful tools in developing the students’ understanding of vector calculus and in simulating heat conduction.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.2022753Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 448
 Leingme B, (2015) A Guide to Microsoft Excel 2013 for Scientists and Engineers. Academic Press, London, San Diego, Waltham and Oxford.
 Bourg D, (2006) Excel Scientific and Engineering Cookbook, O’Reilly Media, USA.
 Billo J, (2007) Excel for Scientists and Engineers: Numerical Methods, John Wiley and Sons, New Jersey, Canada. Available as a free ebook on-line www.cad-cam-cae.com/blog18/Billo.htm
 Niazkar M, Afzali F H, (2015) Application of Excel spreadsheet in engineering education, First International & Fourth National Conference on Engineering Education, Shiraz University.
 Peak M S, Varley M R, Picton, P D, (2005) Spreadsheet Software as a Teaching Tool in Technology, Proceedings of The International Symposium on Modern Applied Technology and Management, Beijing, China, 341-346.
 Varley M R, Peak M S, Picton P D, Hatfield F, (2010) Enhancing Student Understanding of Concepts in Engineering and other STEM Areas using Spreadsheets, International Conference on Engineering Education ICEE-2010 Gliwice, Poland. http://cad-cam-cae.com/blog18/Varley.htm.
 Numerical Methods website, www.numerical-methods.com.
 Fernandez S, Orose J A, Galan J J, (2012) A New Methodology to Teach Numerical Methods With MS Excel, J of Maritime Research, IX(2):29-32.
 Benacka J (2016) Numerical Modelling with Spreadsheets as a Means to Promote STEM to High School Students, Eurasia Journal of Mathematics, Science & Technology Education., 12(4), 947-964.
 Boundary Element Method website www.boundary-element-method.com.
 Davies A, Crann D, (1998) The boundary element method on a spreadsheet, Int. J. Math. Educ. Sci. Technol., 29(6), 851-865.
 Introduction to Boundary Element Method, LD College of Engineering, Ahmedabad, http://www.boundary-element-method.com/LDCE/.
 Kirkup S M, Henwood D J. An empirical analysis of the boundary element method applied to Laplace equation, Applied Mathematical Modelling. 1994;18(1):32–38.
 Kirkup S M. Fortran codes for computing the discrete Helmholtz integral operators, Advances in Computational Mathematics. 1998;9(3):391-409.
 Kirkup S M. The Boundary Element Method in Acoustics, Integrated Sound Software, UK; 1998, 2007.
 Kirkup S M, Yazdani J. A Gentle Introduction to the Boundary Element Method in Matlab/Freemat. WSEAS MAMECTIS conference, Corfu; 2008:46-52.