Journal of Parallel and Distributed Computing - Special issue on dynamic load balancing
Parallel multigrid in an adaptive PDE solver based on hashing and space-filling curves
Parallel Computing - Special issue on parallelization techniques for numerical modelling
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
Journal of Computational Physics
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
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
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Computing with Hp-Adaptive Finite Elements, Vol. 2: Frontiers Three Dimensional Elliptic and Maxwell Problems with Applications
Nodal discontinuous Galerkin methods on graphics processors
Journal of Computational Physics
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
p4est: Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees
SIAM Journal on Scientific Computing
Journal of Computational Physics
Algorithms and data structures for massively parallel generic adaptive finite element codes
ACM Transactions on Mathematical Software (TOMS)
Peta-scale phase-field simulation for dendritic solidification on the TSUBAME 2.0 supercomputer
Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis
Peano—A Traversal and Storage Scheme for Octree-Like Adaptive Cartesian Multiscale Grids
SIAM Journal on 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
High throughput software for direct numerical simulations of compressible two-phase flows
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Hierarchical task mapping of cell-based AMR cosmology simulations
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Discontinuous Galerkin unsteady discrete adjoint method for real-time efficient tsunami simulations
Journal of Computational Physics
High quality real-time image-to-mesh conversion for finite element simulations
Proceedings of the 27th international ACM conference on International conference on supercomputing
Efficient asynchronous executions of AMR computations and visualization on a GPU system
Journal of Parallel and Distributed Computing
High quality real-time Image-to-Mesh conversion for finite element simulations
Journal of Parallel and Distributed Computing
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Many problems are characterized by dynamics occurring on a wide range of length and time scales. One approach to overcoming the tyranny of scales is adaptive mesh refinement/coarsening (AMR), which dynamically adapts the mesh to resolve features of interest. However, the benefits of AMR are difficult to achieve in practice, particularly on the petascale computers that are essential for difficult problems. Due to the complex dynamic data structures and frequent load balancing, scaling dynamic AMR to hundreds of thousands of cores has long been considered a challenge. Another difficulty is extending parallel AMR techniques to high-order-accurate, complex-geometry-respecting methods that are favored for many classes of problems. Here we present new parallel algorithms for parallel dynamic AMR on forest-ofoctrees geometries with arbitrary-order continuous and discontinuous finite/spectral element discretizations. The implementations of these algorithms exhibit excellent weak and strong scaling to over 224,000 Cray XT5 cores for multiscale geophysics problems.