Parallelisation of Multiscale-Based Grid Adaptation using Space-Filling Curves

Free access article

Issue		ESAIM: Proc. Volume 29, 2009 Multiresolution and Adaptive Methods for Convection-Dominated Problems


Page(s)		108 - 129
DOI		http://dx.doi.org/10.1051/proc/2009058
Published online		10 December 2009

ESAIM: Proc., 2009, Vol. 29, pp. 108-129
DOI: 10.1051/proc/2009058

Parallelisation of Multiscale-Based Grid Adaptation using Space-Filling Curves

Kolja Brix¹, Silvia Sorana Melian¹, Siegfried Müller¹ and Gero Schieffer²

¹ Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany,
e-mail: {brix,melian,mueller}@igpm.rwth-aachen.de
² Lehrstuhl für Computergestützte Analyse Technischer Systeme, RWTH Aachen University, Steinbachstr. 53B, 52074 Aachen, Germany;
e-mail: schieffer@cats.rwth-aachen.de

Published online: 10 December 2009

Abstract
The concept of fully adaptive multiscale finite volume schemes has been developed and investigated during the past decade. By now it has been successfully employed in numerous applications arising in engineering. In order to perform 3D computations for complex geometries in reasonable CPU time, the underlying multiscale-based grid adaptation strategy has to be parallelised via MPI for distributed memory architectures. In view of a proper scaling of the computational performance with respect to CPU time and memory, the load of data has to be well-balanced and communication between processors has to be minimised. This has been realised using space-filling curves.

Résumé
Le concept des schémas de volumes finis multi-échelles et adaptatifs a été développé et étudié pendant les dix dernières années. Jusqu'à maintenant il a été utilisé avec succès dans de multiples applications provenant de l'ingéniérie. Dans le but de réaliser des simulations en 3D avec des géométries complexes en un temps de calcul raisonnable, la stratégie de maillage adaptatif multi-échelles a du $\hat{\mbox{e}}$ tre parallélisée via MPI pour des architectures à mémoires partagées. Pour de bonnes performances du point de vue du temps de calcul et de la gestion de la mémoire, la quantité de données doit $\hat{\mbox{e}}$ tre bien répartie et la communication entre les processeurs doit $\hat{\mbox{e}}$ tre minimisée. Ceci a été réalisé à l'aide des courbes remplissantes.

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