Mathematical and Computational Aspects

This book contains the edited versions of most of the papers presented at the 9th International Conference on Boundary Elements held at the University of Stuttgart, Germany from August 31st to September 4th, 1987, which was organized in co-operation with the Computational Mechanics Institute and GAMM (Society for Applied Mathematics and Mechanics). This Conference, as the previous ones, aimed to review the latest developments in technique and theory and point out new advanced future trends. The emphasis of the meeting was on the engineering advances versus mathematical formulations, in an effort to consolidate the basis of many new applications. Recently engineers have proposed different techniques to solve non-linear and time dependent problems and many of these formulations needed a better mathematical understanding. Furthermore, new approximate formulations have been proposed for boundary elements which appeared to work in engineering practice, but did not have a proper theoretical background. The Conference also discussed the engineering applications of the method and concentrated on a link between BEM practitioners, industrial users and researchers working on the latest development of the method. The editors would like to express their appreciation and thanks to Ms. Liz Newman and Mr. H. Schmitz for their unstinting work in the preparation of the Conference.

The Origin of the Boundary Element Method and its Variants (Opening address).- Mathematical Aspects.- Green’s Functions for the Boundary Element Method (Invited contribution).- Best Approximation of a Linear Operation Equation (Invited contribution).- On the Identification of Non-Linear Operators and its Application (Invited contribution).- Boundary Integral Equation Methods for Canonical Problems in Diffraction Theory (Invited contribution).- Methods of Construction of Fundamental Solutions of Decomposable Linear Differential Operators (Invited contribution).- A Generalized Approach to Transfer the Domain Integrals onto Boundary Ones for Potential Problems in BEM.- The Hybrid Boundary Element Method.- New Integral Equation Formulations for Continuum Mechanics.- Analyses of Infinite Reservoir Using the Boundary Element Method with Particular Integrals.- Convergence and Error Estimates.- Experimental Convergence of Boundary Element Methods for the Capacity of the Electrified Square Plate.- On the Stability of Boundary Element Methods for Integral Equations of the First Kind.- On Quadrature Methods and Spline Approximation of Singular Integral Equations.- Significance of Kernel Singularities for the Numerical Solution of Fredholm Integral Equations.- Accuracy and Efficiency of a Panel Method for Free Surface Flow Problem in Three Dimensions.- A-Posteriori Error Estimates and Adaptive Approaches for some Boundary Element Methods.- Numerical Aspects.- Adaptive Boundary Element Methods (Invited contribution).- A Comparison of the BEM and the T Matrix Methods (Invited contribution).- Construction of Equivalent Finite Element Functions Using BEM.- The Effect of Non-Convex Boundaries on Time Domain Boundary Element Solutions.- A New Numerical Algorithm for Solving FundamentalSolutions.- Adaptive Refinements in BEM.- Self-Adaptive P-Hierarchical Boundary Elements in Elastostatics.- A New Coordinate Transformation Method for Singular and Nearly Singular Integrals over General Curved Boundary Elements.- Development of Overhauser Splines as Boundary Elements.- Coupling Be/Fe Methods and Other Coupling Methods.- Symmetric Methods for the Coupling of Finite Elements and Boundary Elements (Invited contribution).- On Some Coupled Problems in Mechanics by the Coupling Technique of Boundary Element and Finite Element (Invited contribution).- On Coupling of the Boundary Element and R-Function Methods.- On Simplified Hybrid Methods for Coupling of Finite Elements and Boundary Elements.- Computational Aspects.- The Panel Clustering Technique for the Boundary Element Method (Invited contribution).- Multigrid Methods in Boundary Element Calculations (Invited contribution).- Linear Equations Solver for Large Block Matrices Arising in BEM.- Nonlinear Equations Solver for Large Equations Sets Arising When Using BEM in Inhomogenous Regions of Nonlinear Material.- Resolving Difficulties in the BIEM Caused by Geometric Corners and Discontinuous Boundary Conditions.- Software.- Industrial Application of the Boundary Element System BETSY.- Integrated Design and Analysis using the Boundary Element Method.- Boundary Elements on Personal Computers.- Murphy’s Law in Boundary Element Implementations.- Computer Programme KYOKAI.F for Viscous and Thermal Fluid Flow Problems.- DBETSY — Industrial Application of the BEM.