TY - GEN
T1 - A parallel adaptive cartesian PDE solver using space-filling curves
AU - Bungartz, Hans Joachim
AU - Mehl, Miriam
AU - Weinzierl, Tobias
PY - 2006
Y1 - 2006
N2 - In this paper, we present a parallel multigrid PDE solver working on adaptive hierarchical cartesian grids. The presentation is restricted to the linear elliptic operator of second order, but extensions are possible and have already been realised as prototypes. Within the solver the handling of the vertices and the degrees of freedom associated to them is implemented solely using stacks and iterates of a Peano space-filling curve. Thus, due to the structuredness of the grid, two administrative bits per vertex are sufficient to store both geometry and grid refinement information. The implementation and parallel extension, using a space-filling curve to obtain a load balanced domain decomposition, will be formalised. In view of the fact that we are using a multigrid solver of linear complexity O(n), it has to be ensured that communication cost and, hence, the parallel algorithm's overall complexity do not exceed this linear behaviour.
AB - In this paper, we present a parallel multigrid PDE solver working on adaptive hierarchical cartesian grids. The presentation is restricted to the linear elliptic operator of second order, but extensions are possible and have already been realised as prototypes. Within the solver the handling of the vertices and the degrees of freedom associated to them is implemented solely using stacks and iterates of a Peano space-filling curve. Thus, due to the structuredness of the grid, two administrative bits per vertex are sufficient to store both geometry and grid refinement information. The implementation and parallel extension, using a space-filling curve to obtain a load balanced domain decomposition, will be formalised. In view of the fact that we are using a multigrid solver of linear complexity O(n), it has to be ensured that communication cost and, hence, the parallel algorithm's overall complexity do not exceed this linear behaviour.
UR - https://www.scopus.com/pages/publications/33749996686
U2 - 10.1007/11823285_112
DO - 10.1007/11823285_112
M3 - Conference contribution
AN - SCOPUS:33749996686
SN - 3540377832
SN - 9783540377832
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 1064
EP - 1074
BT - Euro-Par 2006 Parallel Processing - 12th International Euro-Par Conference, Proceedings
PB - Springer Verlag
T2 - 12th International Euro-Par Conference 2006
Y2 - 28 August 2006 through 1 September 2006
ER -