Description
Book SynopsisBoundary 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.
Table of ContentsPreface 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
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