1 / 18
Télécharger la présentation

Boundary Element Method in Engineering: Numerical Solutions for Partial Differential Equations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Introduction Stephen Kirkup School of Engineering, University of Central Lancashire, England

  2. UK to India image by dentistindelhi.co.in

  3. UK and me • Grew up on a farm in Co. Durham • Studied BSc Mathematics at the University of Newcastle • Studied MSc Numerical Analysis and Programming at the University of Dundee • Studied PhD “Solution of Exterior Acoustic problems by the Boundary Element Method” at the University of Brighton • Mostly worked in universities in the North West of the England (Historically Lancashire). Universities of Salford, Liverpool, Blackburn and UCLan http://www.map-of-uk.com/

  4. Around UCLan, Preston

  5. Lancashire and the Industrial Revolution

  6. Lancashire and the Industrial Revolution C N Trueman "Lancashire and the Industrial Revolution"historylearningsite.co.uk. The History Learning Site, 31 Mar 2015. 16 Aug 2016. C N Trueman "Lancashire and the Industrial Revolution"historylearningsite.co.uk. The History Learning Site, 31 Mar 2015. 16 Aug 2016. C N Trueman "Lancashire and the Industrial Revolution"historylearningsite.co.uk. The History Learning Site, 31 Mar 2015. 16 Aug 2016. • Lancashire Today • Manufacturing hub of UK • Engineering – Particularly Aerospace

  7. UCLan – University of Central Lancashire • About UCLan • Engineering Innovation Centre • Engineering Degrees BEng and MEng • Aerospace Engineering • Mechanical Engineering • Energy Engineering • Motorsports Engineering • Computer-Aided Engineering • Postgraduate degrees and research • See website for more information www.uclan.ac.uk

  8. Teaching • My teaching is currently focussed on mathematics for engineers, • Year 1 to year 3 of engineering degrees. • Year 2 and year 3 modules are rather “mathematics and simulation” modules • In the past I have also taught • Computer Science (Year 1 to Year 3 of BSc course) • Programming and object-oriented software engineering (Java) • Formal Computer Science • Analytic Engineering • Dynamics • Control • Sustainablity in construction and nuclear industry • Current Focus • Use existing and develop on-line resources for teaching maths • Handouts (egwww.mathcentre.ac.uk) • Software (eg spreadsheets, matlab codes (freemat/octave,Simulink)) • Develop students towards technological solutions to maths problems to support pen-and-paper solutions (egmatlab-mupad, mathematica, maxsyma (free)) • Accessibilty and empowerment (VLE, available technologies) (Example – inverting a matrix)

  9. Brief Introduction on BEM from Speaker • Worked in the BEM – amongst many other things – for 30 years • Started as a mathematician but became also interested in programming (software design), engineering and education • Book “The Boundary Element Method in Acoustics” and accompanying Fortran library 1998/2007 • Mainly worked in Helmholtz Equations (Acoustics) and Laplace Equation • Website : www.boundary-element-method.com which has published ‘open source’ software and educational materials • This presentation can be downloaded from www.kirkup.info/LDCE • Most of my publications and projects can be found on Researchgate • Member of LinkedIn • User groups : Boundary Element Method, Computational Mechanics, Applied Mathematical Modelling

  10. Purpose • The Boundary Element Method is a Numerical Method • From a mathematical viewpoint the BEM finds an approximate solution to a partial differential equation (PDE) governing a domain • For an engineer the BEM can be used to simulate the properties of a design before committing the building the prototype • Domain of ‘just about any reasonable’ shape and general conditions • Analytic methods only work for simple separable geometries - eg circles, squares, spheres and cylinders. Useful for generating test problems.

  11. Boundary Value Problem - Boundary • The BEM solves a PDE a boundary value problem • Domain is OR

  12. Boundary Value Problem - Conditions • The BEM solves a PDE with boundary conditions; a boundary value problem α Robin eg impedance Dirichlet or Essential Neuman or flux • Note: Exterior problems also have a condition at ∞, that is in the far-field • Game is : Given the PDE, the boundary and the boundary condition, we need to find in the domain • To solve the boundary value problem

  13. Summary of my BEM work • Practical Problems • Computer-Aided Analysis of Engine Noise (1992) • Computational methods for the acoustic modal analysis of an enclosed fluid with application to a loudspeaker cabinet (1997) • DC capacitor simulation by the boundary element method (2006) • Simulation of the Acoustic Field of a Horn Loudspeaker by the Boundary Element–Rayleigh Integral Method (2013) • General method development and analysis • Modal analysis of acoustically-loaded structures via integral equation methods (1991) • The computational modelling of acoustic shields by the boundary and shell element method (1992) • Computational solution of acoustic radiation problems by Kussmaul's boundary element method (1992) • Methods for Speeding Up the Boundary Element Solution of Acoustic Radiation Problems (1992) • The influence of the weighting parameter on the improved boundary element solution of the exterior Helmholtz equation (1992) • Solution of the Helmholtz eigenvalue problem via the boundary element method (1993)

  14. Summary of my BEM work (continued) • General method development and analysis (continued) • Computational solution of the acoustic field surrounding a baffled panel by the Rayleigh integral method (1994) • An empirical analysis of the boundary element method applied to Laplace's equation (1994) • Solution of Helmholtz Equation in the Exterior Domain by Elementary Boundary Integral Methods (1995) • Solution of discontinuous interior Helmholtz problems by the boundary and shell element method (1997) • Software • Fortran codes for computing the discrete Helmholtz integral operators (1998) • Educational/Developmental • A Gentle Introduction to the Boundary Element Method in Matlab/Freemat(2008)

  15. SIMS analysis and Inverse Problems • SIMS experiment • Concentration-depth profiles of the original material structure are given in the top diagram • Material (semiconductor) is bombarded with ions. • Simulation of outcome is given in lower figure • Surface recedes • Atoms are mixed within the material structure • Sputtering is related to the surface concentrations

  16. SIMS analysis and Inverse Problems (continued) • Simulation of the ‘forward problem’ • Convection-diffusion equations • Finite difference methods • Computational solution of the atomic mixing equations (1998) • Computational solution of the atomic mixing equations: Special methods and algorithm of IMPETUS II (1998) • Quantification Problem • Finding the initial material structure from the SIMS profiles • Inverse / ill-posed problem • Inverse Diffusion problem : Classically the Backward Heat conduction problem

  17. FDTD Method for Electromagnetic Simulation in Java www.kirkup.info/FDTD

  18. This week • Develop the BEM for the solution of Laplace’s equation • Simplest equation to which the BEM can be applied • Is widely applicable in physics and engineering: ‘potential’ problems • The model equation for the BEM • Most problems you find with the application of the BEM to any other problem area will be found in this one • It is the best equation with which we learn and teach the BEM and …. • Develop the BEM for the solution of the Helmholtz Equation • Acoustics • Eigenvalue Problems • Fluid-Structure Interaction • Other methods, depending on time etc • Tutorial Today • Download Excel spreadsheet and User Guide

More Related