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A Symmetric Hybrid Boundary Element Method for Acoustical Problems

  • Lothar Gaul
  • Marcus Wagner
  • Wolfgang Wenzel
Part of the International Centre for Mechanical Sciences book series (CISM, volume 433)

Abstract

The boundary element method (BEM) can be effectively used to solve mixed boundary value problems, as well as fluid-structure interaction problems. Among the advantages of BEM are the reduction of the problem dimension by one, high accuracy and the efficient treatment of problems with infinite domains. The direct BEM leads to a system of equations with dense and unsymmetric matrices. Thus, coupling with symmetric domain discretization techniques, such as finite element methods, is numerically inefficient. For this reason, alternative approaches are use herein derived from variational principles leading to symmetry by construction. By relaxing continuity between the fields on the boundary and those in the domain two multi-field variational principles have been formulated. Emerging from these variational principles, two Hybrid Boundary Element Methods (HBEM) were developed, the Hybrid Displacement Method and the Hybrid Stress Method, respectively. The choice of weighted fundamental solutions as domain approximations selected independently from polynomial approximations of boundary variables allow to map domain integrals in boundary integrals. Symmetric sytems of equations for frequency and time domain are obtained.

Keywords

Fundamental Solution Boundary Element Method Acoustical Problem Domain Approximation Boundary Integral Formulation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Wien 2002

Authors and Affiliations

  • Lothar Gaul
    • 1
  • Marcus Wagner
    • 1
  • Wolfgang Wenzel
    • 1
  1. 1.Institute A of MechanicsUniversity of StuttgartGermany

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