In this paper matrix compression techniques in the
context of wavelet Galerkin schemes for boundary
integral equations are developed and analyzed that
exhibit optimal complexity in the following sense.
The fully discrete scheme produces approximate
solutions within discretization error accuracy
offered by the underlying Galerkin method at a
computational expense that is proven to stay
proportional to the number of unknowns.
Key issues are the second compression, that
reduces the near field complexity significantly,
and an additional a-posteriori compression.
The latter one is based on a general result
concerning an optimal work balance, that applies,
in particular, to the quadrature used to compute
the compressed stiffness matrix with sufficient
accuracy in linear time. The theoretical results
are illustrated by a 3D example on a nontrivial
domain.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:18485 |
| Date | 05 April 2006 |
| Creators | Dahmen, Wolfgang, Harbrecht, Helmut, Schneider, Reinhold |
| Publisher | Technische Universität Chemnitz |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:preprint, info:eu-repo/semantics/preprint, doc-type:Text |
| Source | Preprintreihe des Chemnitzer SFB 393, 02-06 |
| Rights | info:eu-repo/semantics/openAccess |
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