The hierarchial preconditioning on unstructured grids |
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Authors: | Gerhard Globisch Sergei V Nepomnyaschikh |
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Affiliation: | 1. Fakult?t für Mathematik, Technische Universit?t Chemnitz, D-09107, Chemnitz, Germany 2. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch Russian Academy of Sciences, 6 Lavrentiev av., 630090, Novosibirsk, Russia
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Abstract: | We present the implementation of two hierarchically preconditioned methods for the fast solution of mesh equations that approximate
2D-elliptic boundary value problems on unstructured quasi uniform triangulations. Based on the fictitious space approach the
original problem can be embedded into an auxiliary one, where both the hierarchical grid information and the preconditioner
are well defined. We implemented the corresponding Yserentant preconditioned conjugate gradient method as well as thebpx-preconditioned cg-iteration having optimal computational costs. Several numerical examples demonstrate the efficiency of
the artificially constructed hierarchical methods which can be of importance in industrial engineering, where often only the
nodal coordinates and the element connectivity of the underlying (fine) discretization are available. |
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Keywords: | 65N55 65N50 65N30 78A30 |
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