Journal of Parallel and Distributed Computing - Special issue on dynamic load balancing
A parallel algorithm for multilevel graph partitioning and sparse matrix ordering
Journal of Parallel and Distributed Computing
Parallel Computing - special issue on parallel computing for irregular applications
Proceedings of the 2000 ACM/IEEE conference on Supercomputing
Proceedings of the 2001 ACM/IEEE conference on Supercomputing
Status and Directions for the PYRAMID Parallel Unstructured AMR Library
IPDPS '01 Proceedings of the 15th International Parallel & Distributed Processing Symposium
Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries
Journal of Computational Physics
A framework approach for developing parallel adaptive multiphysics applications
Finite Elements in Analysis and Design - Special issue: The fifteenth annual Robert J. Melosh competition
High Resolution Forward And Inverse Earthquake Modeling on Terascale Computers
Proceedings of the 2003 ACM/IEEE conference on Supercomputing
Scalable Parallel Octree Meshing for TeraScale Applications
SC '05 Proceedings of the 2005 ACM/IEEE conference on Supercomputing
Is 1.7 x 10^10 Unknowns the Largest Finite Element System that Can Be Solved Today?
SC '05 Proceedings of the 2005 ACM/IEEE conference on Supercomputing
From mesh generation to scientific visualization: an end-to-end approach to parallel supercomputing
Proceedings of the 2006 ACM/IEEE conference on Supercomputing
ParFUM: a parallel framework for unstructured meshes for scalable dynamic physics applications
Engineering with Computers
libMesh: a C++ library for parallel adaptive mesh refinement/coarsening simulations
Engineering with Computers
deal.II—A general-purpose object-oriented finite element library
ACM Transactions on Mathematical Software (TOMS)
Low-constant parallel algorithms for finite element simulations using linear octrees
Proceedings of the 2007 ACM/IEEE conference on Supercomputing
Bottom-Up Construction and 2:1 Balance Refinement of Linear Octrees in Parallel
SIAM Journal on Scientific Computing
Dendro: parallel algorithms for multigrid and AMR methods on 2:1 balanced octrees
Proceedings of the 2008 ACM/IEEE conference on Supercomputing
Scalable adaptive mantle convection simulation on petascale supercomputers
Proceedings of the 2008 ACM/IEEE conference on Supercomputing
New challenges in dynamic load balancing
Applied Numerical Mathematics - Adaptive methods for partial differential equations and large-scale computation
A parallel direct solver for the self-adaptive hp Finite Element Method
Journal of Parallel and Distributed Computing
The cactus framework and toolkit: design and applications
VECPAR'02 Proceedings of the 5th international conference on High performance computing for computational science
Journal of Computational Physics
A Parallel Geometric Multigrid Method for Finite Elements on Octree Meshes
SIAM Journal on Scientific Computing
Algorithms and data structures for massively parallel generic adaptive finite element codes
ACM Transactions on Mathematical Software (TOMS)
Journal of Computational Physics
Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
Massively parallel finite element programming
EuroMPI'10 Proceedings of the 17th European MPI users' group meeting conference on Recent advances in the message passing interface
Fast high-dimensional approximation with sparse occupancy trees
Journal of Computational and Applied Mathematics
Using hybrid parallelism to improve memory use in the Uintah framework
Proceedings of the 2011 TeraGrid Conference: Extreme Digital Discovery
Algorithms and data structures for massively parallel generic adaptive finite element codes
ACM Transactions on Mathematical Software (TOMS)
Towards adaptive kinetic-fluid simulations of weakly ionized plasmas
Journal of Computational Physics
Poster: parallel octree-based meshing for finite element computations
Proceedings of the 2011 companion on High Performance Computing Networking, Storage and Analysis Companion
A highly scalable matrix-free multigrid solver for μFE analysis based on a pointer-less octree
LSSC'11 Proceedings of the 8th international conference on Large-Scale Scientific Computing
Extreme-scale UQ for Bayesian inverse problems governed by PDEs
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Parallel geometric-algebraic multigrid on unstructured forests of octrees
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Journal of Scientific Computing
PRACE DECI (distributed european computing initiative) minisymposium
PARA'12 Proceedings of the 11th international conference on Applied Parallel and Scientific Computing
Enzo-P / Cello: scalable adaptive mesh refinement for astrophysics and cosmology
Proceedings of the Extreme Scaling Workshop
SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
A framework for hybrid parallel flow simulations with a trillion cells in complex geometries
SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Cluster optimization and parallelization of simulations with dynamically adaptive grids
Euro-Par'13 Proceedings of the 19th international conference on Parallel Processing
Advances in Engineering Software
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We present scalable algorithms for parallel adaptive mesh refinement and coarsening (AMR), partitioning, and 2:1 balancing on computational domains composed of multiple connected two-dimensional quadtrees or three-dimensional octrees, referred to as a forest of octrees. By distributing the union of octants from all octrees in parallel, we combine the high scalability proven previously for adaptive single-octree algorithms with the geometric flexibility that can be achieved by arbitrarily connected hexahedral macromeshes, in which each macroelement is the root of an adapted octree. A key concept of our approach is an encoding scheme of the interoctree connectivity that permits arbitrary relative orientations between octrees. Based on this encoding we develop interoctree transformations of octants. These form the basis for high-level parallel octree algorithms, which are designed to interact with an application code such as a numerical solver for partial differential equations. We have implemented and tested these algorithms in the p4est software library. We demonstrate the parallel scalability of p4est on its own and in combination with two geophysics codes. Using p4est we generate and adapt multioctree meshes with up to $5.13\times10^{11}$ octants on as many as 220,320 CPU cores and execute the 2:1 balance algorithm in less than 10 seconds per million octants per process.