Boundary Element Topics

The so-called boundary element methods BEM, i.e. finite element approxima tions of boundary integral equations have been improved recently even more vividly then ever before and found some remarkable support by the German Research Foundation DFG in the just finished Priority Research Program "boundary element methods" . When this program began, we could start from several already existing particular activities which then during the six years initiated many new re sults and decisive new developments in theory and algorithms. The program was started due to encouragement by E. Stein, when most of the later par ticipants met in Stuttgart at a Boundary Element Conference 1987. Then W. Hackbusch, G. Kuhn, S. Wagner and W. Wendland were entrusted with writing the proposal which was 1988 presented at the German Research Foun dation and started in 1989 with 14 projects at 11 different universities. After German unification, the program was heavily extended by six more projects, four of which located in Eastern Germany. When we started, we were longing for the following goals: 1. Mathematicians and engineers should do joint research. 2. Methods and computational algorithms should be streamlined with re spect to the new computer architectures of vector and parallel computers. 3. The asymptotic error analysis of boundary element methods should be further developed. 4. Non-linear material laws should be taken care of by boundary element methods for crack-mechanics. 5. The coupling of finite boundary elements should be improved.

Klappentext

The volume contains papers presented at the final conference of the DFG Research Program in Boundary Element Methods. The contributions deal with and offer solutions for problems arising in the application of BEM to engineering tasks.

Inhalt
Efficient Calculation of Acoustic Fields by Boundary Element Method.- A Boundary Element Formulation for Generalized Viscoelastic Solids in Time Domain.- On the Efficient Realization of Sparse Matrix Techniques for Integral Equations with Focus on Panel Clustering, Cubature and Software Design Aspects.- Bimetal Problems.- Analysis of 3D Elastoplastic Notch and Crack Problems using Boundary Element Method.- Adaptive Domain Decomposition Methods for Finite and Boundary Element Equations.- On the Use of a BEM Time-Stepping Procedure for Nonlinear and Unsteady Wave-Structure Interaction.- Integral Equations arising from Instationary Flows around Thin Wings.- Multiscale Methods for the Solution of the Helmholtz and Laplace Equations.- Galerkin-Type Boundary Element Analysis for 3D Elasticity Problems.- Parallel Coupling of FEM and BEM for 3D Elasticity Problems.- Coupling of BEM and FEM for Elastic Structures.- Fast Algorithms for the Solution of Pseudodifferential Equations.- Different Methodologies for Coupled BEM and FEM with Implementation on Parallel Computers.- Error Analysis for the BEM on Nonsmooth Curves.- The hp-Version of the BEM with Geometric Meshes in 3D.- A Transonic Panel Method for Helicopter Flows.- Interpolation, Triangulation and Numerical Integration on Closed Manifolds.- Asymptotic Expansions of Elastic Fields in Domains with Boundary and Structural Singularities.- Local, Residual-Based A Posteriori Error Estimates Forcing Adaptive Boundary Element Methods.- Domain Decomposition and Preconditioning Techniques in Boundary Element Methods.- Benchmark Problems for Boundary Element Methods.