Mathematical Aspects of Boundary Element Methods

by Marc Bonnet

Overview

Boundary element methods relate to a wide range of engineering applications, including fluid flow, fracture analysis, geomechanics, elasticity, and heat transfer. Thus, new results in the field hold great importance not only to researchers in mathematics, but to applied mathematicians, physicists, and engineers.

A two-day minisymposium Mathematical Aspects of Boundary Element Methods at the IABEM conference in May 1998 brought together top rate researchers from around the world, including Vladimir Maz’ya, to whom the conference was dedicated. Focusing on the mathematical and numerical analysis of boundary integral operators, this volume presents 25 papers contributed to the symposium.

Mathematical Aspects of Boundary Element Methods provides up-to-date research results from the point of view of both mathematics and engineering. The authors detail new results, such as on nonsmooth boundaries, and new methods, including domain decomposition and parallelization, preconditioned iterative techniques, multipole expansions, higher order boundary elements, and approximate approximations. Together they illustrate the connections between the modeling of applied problems, the derivation and analysis of corresponding boundary integral equations, and their efficient numerical solutions.

Product Details

ISBN-13:	9781000673142
Publisher:	CRC Press
Publication date:	07/05/2024
Series:	Chapman & Hall/CRC Research Notes in Mathematics Series
Sold by:	Barnes & Noble
Format:	eBook
Pages:	312
File size:	3 MB

About the Author

Marc Bonnet, Anna-Margarete Sandig, Wolfgang L Wendland

Table of Contents

Preface Coupling Integral Equation Method and Finite Volume Elements for the Resolution of the Leontovich Boundary Value Problem for the Time-Harmonic Maxwell Equations in Three Dimensional Herterogeneous Media Smoothness Properties of Solutions to Variational Inequalities Describing Propagation of Mode-1 Cracks Edge Singularities and Kutta Condition for 3D Unsteady Flows in Aerodynamics Approximation Using Diagonal-Plus-Skeleton Matrices Variational Integral Formulation in the Problem of Elastic Scattering by a Buried Obstacle Sensitivity Analysis for Elastic Fields in Non Smooth Domains A Formulation for Crack Shape Sensitivity Analysis Based on Galeerking BIE, Domain Differentiation, and Adjoint Variable Periodic and Stochastic BEM for Large Structures Embedded in an Elastic Half-Space Self-Regularized Hypersingular BEM for Laplace’s Equation An Adaptive Boundary Element Method for Contact Problems Fast Summation Methods and Integral Equations Hybrid Galerkin Boundary Elements on Degenerate Meshes The Poincaré-Steklov Operator within Countably Normed Spaces Boundary Layer Approximate Approximations for the Cubature of Potentials A Simplified Approach to the Semi-Discrete Galerking Method for the Single-Layer Equation for a Plate Construction of Basis Functions for High Order Approximate Approximations Lp-Theory of Direct Boundary Integral Equations on a Contour with Peak Essential Norms of the Integral Operator Correspondng to the Neumann Problem for the Laplace Equations Polynomial Collocation Methods for 1D Intergral Equations with Nonsmooth Solutions Singularities in Discretized BIE’s for Laplace’s Equation; Trailin-Edge Conditions in Aerodynamics Fluid-Structure Interaction Problems Extraction, Higher Order Boundary Element Methods, and Adaptivity Asymptotic Solution of Boundary Integral Equations Sobolev Multipliers in the Theory of Integral Convolution Operators Stable Boundary Element Approximations of Steklov-Poincaré Operators

Editorial Reviews

A minisymposium at the IABEM conference in May 1998 (no other details are provided) brought together researchers from around the world, including Russian emigr<'e> Maz'ya (Link<:o>ping U., Sweden) to whom this volume is dedicated. Focusing on new methods and new results in the mathematical and numerical analysis of boundary integral operators, 25 papers illustrate connections between the modeling of applied problems, the derivation and analysis of corresponding boundary integral equations, and their efficient numerical solutions. Includes a bibliography of works by Maz'ya and a couple of photos of him. Of interest to engineers and physicists as well as mathematicians, pure and applied. Lacks an index. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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