Applied Numerical Mathematics
Dendro: parallel algorithms for multigrid and AMR methods on 2:1 balanced octrees
Proceedings of the 2008 ACM/IEEE conference on Supercomputing
International Journal of Computational Science and Engineering
A blocking strategy on multicore architectures for dynamically adaptive PDE solvers
PPAM'09 Proceedings of the 8th international conference on Parallel processing and applied mathematics: Part I
Exploring a Novel Gathering Method for Finite Element Codes on the Cell/B.E. Architecture
Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
SIAM Journal on Scientific Computing
Towards multi-phase flow simulations in the PDE framework Peano
Computational Mechanics
HPCC'06 Proceedings of the Second international conference on High Performance Computing and Communications
Efficient storage and processing of adaptive triangular grids using sierpinski curves
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part I
A parallel adaptive cartesian PDE solver using space–filling curves
Euro-Par'06 Proceedings of the 12th international conference on Parallel Processing
Parallel geometric-algebraic multigrid on unstructured forests of octrees
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Euro-Par'12 Proceedings of the 18th international conference on Parallel processing workshops
11 PFLOP/s simulations of cloud cavitation collapse
SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
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Competitive numerical algorithms for solving partial differential equations have to work with the most efficient numerical methods like multigrid and adaptive grid refinement and thus with hierarchical data structures. Unfortunately, in most implementations, hierarchical data—typically stored in trees—cause a nonnegligible overhead in data access. To overcome this quandary—numerical efficiency versus efficient implementation—our algorithm uses space-filling curves to build up data structures which are processed linearly. In fact, the only kind of data structure used in our implementation is stacks. Thus, data access becomes very fast—even faster than the common access to nonhierarchical data stored in matrices—and, in particular, cache misses are reduced considerably. Furthermore, the implementation of multigrid cycles and/or higher order discretizations as well as the parallelization of the whole algorithm become very easy and straightforward on these data structures.