Computer Methods in Applied Mechanics and Engineering - Special edition on the 20th Anniversary
Journal of Parallel and Distributed Computing - Special issue on dynamic load balancing
Plate tectonics and convection in the earth's mantle: Toward a numerical simulation
Computing in Science and Engineering
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Proceedings of the 2000 ACM/IEEE conference on Supercomputing
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ICS '03 Proceedings of the 17th annual international conference on Supercomputing
Scalable Parallel Octree Meshing for TeraScale Applications
SC '05 Proceedings of the 2005 ACM/IEEE conference on Supercomputing
High Resolution Aerospace Applications using the NASA Columbia Supercomputer
SC '05 Proceedings of the 2005 ACM/IEEE conference on Supercomputing
Reducing Complexity in Parallel Algebraic Multigrid Preconditioners
SIAM Journal on Matrix Analysis and Applications
libMesh: a C++ library for parallel adaptive mesh refinement/coarsening simulations
Engineering with Computers
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Journal of Computational Physics
deal.II—A general-purpose object-oriented finite element library
ACM Transactions on Mathematical Software (TOMS)
Bottom-Up Construction and 2:1 Balance Refinement of Linear Octrees in Parallel
SIAM Journal on Scientific Computing
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
Parallel symmetric sparse matrix-vector product on scalar multi-core CPUs
Parallel Computing
Journal of Computational Physics
Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
PerfExpert: An Easy-to-Use Performance Diagnosis Tool for HPC Applications
Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
Algorithms and data structures for massively parallel generic adaptive finite element codes
ACM Transactions on Mathematical Software (TOMS)
p4est: Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees
SIAM Journal on Scientific Computing
Peano—A Traversal and Storage Scheme for Octree-Like Adaptive Cartesian Multiscale Grids
SIAM Journal on Scientific Computing
Parallel geometric-algebraic multigrid on unstructured forests of octrees
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
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
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Mantle convection is the principal control on the thermal and geological evolution of the Earth. Mantle convection modeling involves solution of the mass, momentum, and energy equations for a viscous, creeping, incompressible non-Newtonian fluid at high Rayleigh and Peclet numbers. Our goal is to conduct global mantle convection simulations that can resolve faulted plate boundaries, down to 1 km scales. However, uniform resolution at these scales would result in meshes with a trillion elements, which would elude even sustained petaflops supercomputers. Thus parallel adaptive mesh refinement and coarsening (AMR) is essential. We present RHEA, a new generation mantle convection code designed to scale to hundreds of thousands of cores. RHEA is built on ALPS, a parallel octree-based adaptive mesh finite element library that provides new distributed data structures and parallel algorithms for dynamic coarsening, refinement, rebalancing, and repartitioning of the mesh. ALPS currently supports low order continuous Lagrange elements, and arbitrary order discontinuous Galerkin spectral elements, on octree meshes. A forest-of-octrees implementation permits nearly arbitrary geometries to be accommodated. Using TACC's 579 teraflops Ranger supercomputer, we demonstrate excellent weak and strong scalability of parallel AMR on up to 62,464 cores for problems with up to 12.4 billion elements. With RHEA'S adaptive capabilities, we have been able to reduce the number of elements by over three orders of magnitude, thus enabling us to simulate large-scale mantle convection with finest local resolution of 1.5 km.