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Computational Mechanics

, 44:247 | Cite as

An alternative collocation boundary element method for static and dynamic problems

  • Thomas Rüberg
  • Martin SchanzEmail author
Original Paper

Abstract

A collocation boundary element formulation is presented which is based on a mixed approximation formulation similar to the Galerkin boundary element method presented by Steinbach (SIAM J Numer Anal 38:401–413, 2000) for the solution of Laplace’s equation. The method is also applicable to vector problems such as elasticity. Moreover, dynamic problems of acoustics and elastodynamics are included. The resulting system matrices have an ordered structure and small condition numbers in comparison to the standard collocation approach. Moreover, the employment of Robin boundary conditions is easily included in this formulation. Details on the numerical integration of the occurring regular and singular integrals and on the solution of the arising systems of equations are given. Numerical experiments have been carried out for different reference problems. In these experiments, the presented approach is compared to the common nodal collocation method with respect to accuracy, condition numbers, and stability in the dynamic case.

Keywords

Collocation boundary element method Discontinuous elements Elastodynamics Robin boundary conditions 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Institute for Structural AnalysisGraz University of TechnologyGrazAustria
  2. 2.Institute of Applied MechanicsGraz University of TechnologyGrazAustria

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