Abstract. A fully adaptive numerical scheme for solving PDEs based on a finite volume discretization with explicit time discretization is presented. The local grid refinement is triggered by a multiresolution strategy which allows to control the approximation error in space. The costly fluxes are evaluated on the adaptive grid only. For automatic time step control a Runge–Kutta–Fehlberg method is used. A dynamic tree data structure allows memory compression and CPU time reduction. For validation different classical test problems are computed. The gain in memory and CPU time with respect to the finite volume scheme on a regular grid is reported and demonstrates the efficiency of the new method. Résumé. Nousprésentons ici une méthode numérique entièrement adaptative pour les EDP, basée sur une discrétisation spatiale en volumes finis et une intégration temporelle explicite de type Runge-Kutta. Une stratégie de type multi-résolution permet d’adapter localement le maillage tout en contrôlant l’erreur d’approximation en espace. Les flux sont évalués sur la grille adaptative uniquement. Une méthode de type Runge-Kutta-Fehlberg est employée afin de choisir automatiquement le pas de temps tout en contrôlant l’erreur d’approximation. Nous proposons en outre une méthode où lepasdetemps dépend de l’échelle, afin d’éviter d’utiliser sur tous les niveaux le pas de temps qui garantit la stabilité numérique sur le niveau de grille le plus fin. La structure de données est organisée en arbre graduel,

Abstract. On cc-NUMA multi-processors, the non-uniformity of main memory latencies motivates the need for co-location of threads and data. We call this special form of data locality, geographical locality. In this article, we study the performance of a parallel PDE solver with adaptive mesh refinement. The solver is parallelized using OpenMP and the adaptive mesh refinement makes dynamic load balancing necessary. Due to the dynamically changing memory access pattern caused by the runtime adaption, it is a challenging task to achieve a high degree of geographical locality. The main conclusions of the study are: (1) that geographical locality is very important for the performance of the solver, (2) that the performance can be improved significantly using dynamic page migration of misplaced data, (3) that a migrate-on-next-touch directive works well whereas the first-touch strategy is less advantageous for programs exhibiting a dynamically changing memory access patterns, and (4) that the overhead for such migration is low compared to the total execution time. 1