Asymptotic error expansion and richardson extrapolation for linear fine elements
Numerische Mathematik
Journal of Computational Physics
Computing
Implicit extrapolation methods for multilevel finite element computations
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Multilevel k-way partitioning scheme for irregular graphs
Journal of Parallel and Distributed Computing
Implicit Extrapolation Methods for Variable Coefficient Problems
SIAM Journal on Scientific Computing
A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
Journal of Computational Physics
A Supernodal Approach to Sparse Partial Pivoting
SIAM Journal on Matrix Analysis and Applications
A multigrid tutorial: second edition
A multigrid tutorial: second edition
Multigrid
Making sparse Gaussian elimination scalable by static pivoting
SC '98 Proceedings of the 1998 ACM/IEEE conference on Supercomputing
BoomerAMG: a parallel algebraic multigrid solver and preconditioner
Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
hypre: A Library of High Performance Preconditioners
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
A node-centered local refinement algorithm for Poisson's equation in complex geometries
Journal of Computational Physics
Proceedings of the 2004 ACM/IEEE conference on Supercomputing
A Massively Parallel Multigrid Method for Finite Elements
Computing in Science and Engineering
Low-constant parallel algorithms for finite element simulations using linear octrees
Proceedings of the 2007 ACM/IEEE conference on Supercomputing
Hierarchical hybrid grids: achieving TERAFLOP performance on large scale finite element simulations
International Journal of Parallel, Emergent and Distributed Systems
Dendro: parallel algorithms for multigrid and AMR methods on 2:1 balanced octrees
Proceedings of the 2008 ACM/IEEE conference on Supercomputing
Co-processor acceleration of an unmodified parallel solid mechanics code with FEASTGPU
International Journal of Computational Science and Engineering
Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
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
Parallel geometric-algebraic multigrid on unstructured forests of octrees
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
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The hierarchical hybrid Grids (HHG) framework attempts to remove limitations on the size of problem that can be solved using a finite element discretization of a partial differential equation (PDE) by using a process of regular refinement, of an unstructured input grid, to generate a nested hierarchy of patch-wise structured grids that is suitable for use with geometric multigrid. The regularity of the resulting grids may be exploited in such a way that it is no longer necessary to explicitly assemble the global discretization matrix. In particular, given an appropriate input grid, the discretization matrix may be defined implicitly using stencils that are constant for each structured patch. This drastically reduces the amonnt of memory required for the discretization, thus allowing for a much larger problem to be solved. Here we present a brief description of the HHG framework: detailing the principles that led to solving a finite element system with 1.7 x 10^10 unknowns, on an SGI Altix supercomputer, using 1024 nodes, with an overall performance of 0.96 TFLOP/s, on a logically unstructured grid, using geometric mmiltigrid as a solver.