From the viewpoint of the adaptive solution of partial differential equations a finit
e element method on hierarchical triangular meshes is developed permitting hanging nodes
arising from nonuniform hierarchical refinement.
Construction, extension and restriction of the nonuniform hierarchical basis and the
accompanying mesh are described by graphs. The corresponding FE basis is generated by
hierarchical transformation. The characteristic feature of the generalizable concept is the
combination of the conforming hierarchical basis for easily defining and changing the FE
space with an accompanying nonconforming FE basis for the easy assembly of a FE
equations system. For an elliptic model the conforming FEM problem is solved by an iterative
method applied to this nonconforming FEM equations system and modified by
projection into the subspace of conforming basis functions. The iterative method used is the
Yserentant- or BPX-preconditioned conjugate gradient algorithm.
On a MIMD computer system the parallelization by domain decomposition is easy and
efficient to organize both for the generation and solution of the equations system and for
the change of basis and mesh.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:ch1-199801330 |
| Date | 30 October 1998 |
| Creators | Groh, U. |
| Contributors | TU Chemnitz, SFB 393 |
| Publisher | Universitätsbibliothek Chemnitz |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:preprint |
| Format | application/pdf, application/postscript, text/plain, application/zip |
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