A massively parallel adaptive finite element method with dynamic load balancing
Proceedings of the 1993 ACM/IEEE conference on Supercomputing
Fast iterative solution of stabilised Stokes systems part II: using general block preconditioners
SIAM Journal on Numerical Analysis
A posteriori error estimation and adaptive mesh-refinement techniques
ICCAM'92 Proceedings of the fifth international conference on Computational and applied mathematics
On a Data Structure for Adaptive Finite Element Mesh Refinements
ACM Transactions on Mathematical Software (TOMS)
Design of object oriented finite element code
Advances in Engineering Software
The C++ Programming Language, Third Edition
The C++ Programming Language, Third Edition
Computational Partial Differential Equations: Numerical Methods and Diffpack Programming
Computational Partial Differential Equations: Numerical Methods and Diffpack Programming
Pursuing scalability for hypre's conceptual interfaces
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
An overview of the Trilinos project
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Scalable Parallel Octree Meshing for TeraScale Applications
SC '05 Proceedings of the 2005 ACM/IEEE conference on Supercomputing
libMesh: a C++ library for parallel adaptive mesh refinement/coarsening simulations
Engineering with Computers
Performance counters and development of SPEC CPU2006
ACM SIGARCH Computer Architecture News
deal.II—A general-purpose object-oriented finite element library
ACM Transactions on Mathematical Software (TOMS)
Arbitrary-level hanging nodes and automatic adaptivity in the hp-FEM
Mathematics and Computers in Simulation
Toward interoperable mesh, geometry and field components for PDE simulation development
Engineering with Computers
Bottom-Up Construction and 2:1 Balance Refinement of Linear Octrees in Parallel
SIAM Journal on Scientific Computing
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
Intel threading building blocks
Intel threading building blocks
Data structures and requirements for hp finite element software
ACM Transactions on Mathematical Software (TOMS)
Mesh algorithms for PDE with Sieve I: Mesh distribution
Scientific Programming
Efficient representation of computational meshes
International Journal of Computational Science and Engineering
DOLFIN: Automated finite element computing
ACM Transactions on Mathematical Software (TOMS)
A strongly conservative finite element method for the coupling of Stokes and Darcy flow
Journal of Computational Physics
An Interoperable, Data-Structure-Neutral Component for Mesh Query and Manipulation
ACM Transactions on Mathematical Software (TOMS)
Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
p4est: Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees
SIAM Journal on Scientific Computing
p4est: Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees
SIAM Journal on Scientific Computing
Numerical and computational efficiency of solvers for two-phase problems
Computers & Mathematics with Applications
PRACE DECI (distributed european computing initiative) minisymposium
PARA'12 Proceedings of the 11th international conference on Applied Parallel and Scientific Computing
Advances in Engineering Software
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Today's largest supercomputers have 100,000s of processor cores and offer the potential to solve partial differential equations discretized by billions of unknowns. However, the complexity of scaling to such large machines and problem sizes has so far prevented the emergence of generic software libraries that support such computations, although these would lower the threshold of entry and enable many more applications to benefit from large-scale computing. We are concerned with providing this functionality for mesh-adaptive finite element computations. We assume the existence of an “oracle” that implements the generation and modification of an adaptive mesh distributed across many processors, and that responds to queries about its structure. Based on querying the oracle, we develop scalable algorithms and data structures for generic finite element methods. Specifically, we consider the parallel distribution of mesh data, global enumeration of degrees of freedom, constraints, and postprocessing. Our algorithms remove the bottlenecks that typically limit large-scale adaptive finite element analyses. We demonstrate scalability of complete finite element workflows on up to 16,384 processors. An implementation of the proposed algorithms, based on the open source software p4est as mesh oracle, is provided under an open source license through the widely used deal.II finite element software library.