Mathematical Aspects of Boundary Element Methods

Mathematical Aspects of Boundary Element Methods : Dedicated to Vladimir Maz'ya on the Occasion of His 60th Birthday

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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.
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Product details

  • Paperback | 312 pages
  • 156.2 x 234.4 x 14.2mm | 408.24g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 2003.
  • 10 black & white tables, 3 black & white halftones
  • 1584880066
  • 9781584880066

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, H. Ammari and J.-C. Nedelec Smoothness Properties of Solutions to Variational Inequalities Describing Propagation of Mode-1 Cracks, M. Bach and S.A. Nazarov Edge Singularities and Kutta Condition for 3D Unsteady Flows in Aerodynamics, P. Bassanini, C.M. Casciola, M.R. Lancia, and R. Piva Approximation Using Diagonal-Plus-Skeleton Matrices, M. Bebendorf, S. Rjasanow, and E.E. Tyrtyshnikov Variational Integral Formulation in the Problem of Elastic Scattering by a Buried Obstacle, M. Ben Tahar, C. Granat, and T. Ha-Duong Sensitivity Analysis for Elastic Fields in Non Smooth Domains, M. Bochniak and A.-M. Sandig A Formulation for Crack Shape Sensitivity Analysis Based on Galeerking BIE, Domain Differentiation, and Adjoint Variable, M. Bonnet Periodic and Stochastic BEM for Large Structures Embedded in an Elastic Half-Space, D. Clouteau, D. Aubry, M.L. Elhabre, and E. Savin Self-Regularized Hypersingular BEM for Laplace's Equation, T.A. Cruse and J.D. Richardson An Adaptive Boundary Element Method for Contact Problems, C. Eck and W.L. Wendland Fast Summation Methods and Integral Equations, Y. Fu, J.R. Overfelt, and G.J. Rodin Hybrid Galerkin Boundary Elements on Degenerate Meshes, I.B. Ghraham, W. Hackbusch, and S.A. Sauter The Poincare-Steklov Operator within Countably Normed Spaces, N. Heuer and E.P. Stephan Boundary Layer Approximate Approximations for the Cubature of Potentials, T. Ivanov, V. Maz'ya, and G. Schmidt A Simplified Approach to the Semi-Discrete Galerking Method for the Single-Layer Equation for a Plate, D. Mauersberger and I.H. Sloan Construction of Basis Functions for High Order Approximate Approximations, V. Maz'ya and A. Soloviev Lp-Theory of Direct Boundary Integral Equations on a Contour with Peak, V. Maz'ya and A. Soloviev Essential Norms of the Integral Operator Correspondng to the Neumann Problem for the Laplace Equations, D. Medkova and J. Kral Polynomial Collocation Methods for 1D Intergral Equations with Nonsmooth Solutions, G. Monegato and L. Scuderi Singularities in Discretized BIE's for Laplace's Equation; Trailin-Edge Conditions in Aerodynamics, O. Morino and G. Bernardini Fluid-Structure Interaction Problems, D. Natroshvili, A.-M. Sandig, and W.L Wendland Extraction, Higher Order Boundary Element Methods, and Adaptivity, H. Schulz, Ch. Schwab, and W.L. Wendland Asymptotic Solution of Boundary Integral Equations, A. Sellier Sobolev Multipliers in the Theory of Integral Convolution Operators, T. Shaposhnikova Stable Boundary Element Approximations of Steklov-Poincare Operators, O. Steinbach
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