In the last years multilevel preconditioners like BPX became more and more
popular for solving second-order elliptic finite element discretizations by iterative
methods. P. Oswald has adapted these methods for discretizations of the fourth
order biharmonic problem by rectangular conforming Bogner-Fox-Schmidt elements
and nonconforming Adini elements and has derived optimal estimates for the
condition numbers of the preconditioned linear systems. In this paper we generalize
the results from Oswald to the construction of BPX and Multilevel Diagonal
Scaling (MDS-BPX) preconditioners for the elasticity problem of thin smooth shells of
arbitrary forms where we use Koiter's equations of equilibrium for an homogeneous
and isotropic thin shell, clamped on a part of its boundary and loaded by a
resultant on its middle surface. We use the two discretizations mentioned above and the
preconditioned conjugate gradient method as iterative method. The parallelization
concept is based on a non-overlapping domain decomposition data structure. We
describe the implementations of the multilevel preconditioners. Finally, we show
numerical results for some classes of shells like plates, cylinders, and hyperboloids.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:17518 |
| Date | 30 October 1998 |
| Creators | Thess, M. |
| 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 |
| Rights | info:eu-repo/semantics/openAccess |
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