, Volume 77, Issue 3, pp 253–273 | Cite as

Coarsening of Boundary-element Spaces

  • W. HackbuschEmail author
  • M. Löhndorf
  • S. A. Sauter


In this paper, we will present composite boundary elements (CBE) for classical Fredholm boundary integral equations. These new boundary elements allow the low-dimensional discretisation of boundary integral equations where the minimal number of degrees of freedom is independent of the, possibly, huge number of charts which are necessary to describe a complicated surface.

The applications are threefold: (a) The coarse-grid discretisation by composite boundary elements allow the use of multigrid algorithms for solving the fine-grid discretisation independently of the number of patches which are necessary to describe the surface. (b) If the accuracy requirements are moderate, the composite boundary elements allow the low-dimensional discretisation of the integral equation. (c) A posteriori error indicators can be applied already to a low-dimensional discretisation, which do not resolve the domain, to obtain a problem-adapted discretisation.

AMS Subject Classifications

65N38 74S15 78H15 80M15 


Boundary-element method multigrid algebraic multigrid 


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Copyright information

© Springer-Verlag Wien 2006

Authors and Affiliations

  1. 1.Max-Planck-Institut für Mathematik in den NaturwissenschaftenLeipzigGermany
  2. 2.Advanced Computer Vision GmbH – ACV Tech Gate ViennaWienAustria
  3. 3.Institut für Mathematik, Universität ZürichZürichSwitzerland

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