Boundary methods: elements, contours, and nodes

After introducing some novel topics related to the boundary element method (BEM), the authors focus on the boundary contour method (BCM)-a variant of the BEM that further reduces the dimensionality of a problem. The final section of the book explores the boundary node method, which combines the BEM with moving least-squares approximants to produce a mesh-free, boundary-only method.

The authors, who are also the primary developers of these methods, clearly introduce and develop each topic. In addition to numerical solutions of boundary value problems in potential theory and linear elasticity, they also discuss topics such as shape sensitivities, shape optimization, and adaptive meshing. Numerical results for selected problems appear throughout the book, as do extensive references. ---------------------Features--------------------- · Introduces novel computational methods that combine the advantages of the boundary element method with those of mesh-free methods · Includes numerical results for many of the problems discussed · Explores applications such as shape sensitivity analysis, shape optimization, and error estimation, analysis, and adaptivity ---------------------Contents--------------------- INTRODUCTION TO BOUNDARY METHODS

I SELECTED TOPICS IN BOUNDARY ELEMENT METHODS

BOUNDARY INTEGRAL EQUATIONS Potential Theory in Three Dimensions Linear Elasticity in Three Dimensions Nearly Singular Integrals in Linear Elasticity Finite Parts of Hypersingular Equations ERROR ESTIMATION Linear Operators Iterated HBIE and Error Estimation Element-Based Error Indicators Numeric