Numerical analysis and implementational aspects of a new multilevel grid deformation method

  • Recently, we introduced and mathematically analysed a new method for grid deformation (Grajewski et al., 2009) [15] we call basic deformation method (BDM) here. It generalises the method proposed by Liao et al. (Bochev et al., 1996; Cai et al., 2004; Liao and Anderson, 1992) [4], [6], [20]. In this article, we employ the BDM as core of a new multilevel deformation method (MDM) which leads to vast improvements regarding robustness, accuracy and speed. We achieve this by splitting up the deformation process in a sequence of easier subproblems and by exploiting grid hierarchy. Being of optimal asymptotic complexity, we experience speed-ups up to a factor of 15 in our test cases compared to the BDM. This gives our MDM the potential for tackling large grids and time-dependent problems, where possibly the grid must be dynamically deformed once per time step according to the user's needs. Moreover, we elaborate on implementational aspects, in particular efficient grid searching, which is a key ingredient of the BDM.

Export metadata

Additional Services

Share in X Search Google Scholar
Metadaten
Author:Matthias GrajewskiORCiD, Michael Köster, Stefam Turek
DOI:https://doi.org/10.1016/j.apnum.2010.03.017
ISSN:0168-9274
Parent Title (English):Applied Numerical Mathematics
Publisher:Elsevier
Place of publication:Amsterdam
Document Type:Article
Language:English
Year of Completion:2010
Date of the Publication (Server):2020/02/13
Volume:60
Issue:8
First Page:767
Last Page:781
Link:https://doi.org/10.1016/j.apnum.2010.03.017
Zugriffsart:campus
Institutes:FH Aachen / Fachbereich Medizintechnik und Technomathematik
collections:Verlag / Elsevier