Achieving high sustained performance in an unstructured mesh CFD application
SC '99 Proceedings of the 1999 ACM/IEEE conference on Supercomputing
Performance modeling and tuning of an unstructured mesh CFD application
Proceedings of the 2000 ACM/IEEE conference on Supercomputing
Multigrid
Special Bilinear Quadrilateral Elements For Locally Refined Finite Element Grids
SIAM Journal on Scientific Computing
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
SuperLU_DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems
ACM Transactions on Mathematical Software (TOMS)
Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries
Journal of Computational Physics
Proceedings of the 2004 ACM/IEEE conference on Supercomputing
SCALLOP: A Highly Scalable Parallel Poisson Solver in Three Dimensions
Proceedings of the 2003 ACM/IEEE conference on Supercomputing
High Resolution Forward And Inverse Earthquake Modeling on Terascale Computers
Proceedings of the 2003 ACM/IEEE conference on Supercomputing
Improving the computational intensity of unstructured mesh applications
Proceedings of the 19th annual international 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
High Resolution Aerospace Applications using the NASA Columbia Supercomputer
SC '05 Proceedings of the 2005 ACM/IEEE conference on Supercomputing
An Introduction to Algebraic Multigrid
Computing in Science and Engineering
A Cache-Aware Algorithm for PDEs on Hierarchical Data Structures Based on Space-Filling Curves
SIAM Journal on Scientific Computing
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
A parallel adaptive cartesian PDE solver using space–filling curves
Euro-Par'06 Proceedings of the 12th international conference on Parallel Processing
A massively parallel adaptive fast-multipole method on heterogeneous architectures
Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis
Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
Petascale Direct Numerical Simulation of Blood Flow on 200K Cores and Heterogeneous Architectures
Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
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
Peano—A Traversal and Storage Scheme for Octree-Like Adaptive Cartesian Multiscale Grids
SIAM Journal on Scientific Computing
A Second Order Discretization of Maxwell's Equations in the Quasi-Static Regime on OcTree 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
Efficient asynchronous executions of AMR computations and visualization on a GPU system
Journal of Parallel and Distributed Computing
Hi-index | 0.00 |
In this article, we present Dendro, a suite of parallel algorithms for the discretization and solution of partial differential equations (PDEs) involving second-order elliptic operators. Dendro uses trilinear finite element discretizations constructed using octrees. Dendro, comprises four main modules: a bottom-up octree generation and 2:1 balancing module, a meshing module, a geometric multiplicative multigrid module, and a module for adaptive mesh refinement (AMR). Here, we focus on the multigrid and AMR modules. The key features of Dendro are coarsening/refinement, inter-octree transfers of scalar and vector fields, and parallel partition of multilevel octree forests. We describe a bottom-up algorithm for constructing the coarser multigrid levels. The input is an arbitrary 2:1 balanced octree-based mesh, representing the fine level mesh. The output is a set of octrees and meshes that are used in the multigrid sweeps. Also, we describe matrix-free implementations for the discretized PDE operators and the intergrid transfer operations. We present results on up to 4096 CPUs on the Cray XT3 ("BigBen"), the Intel 64 system ("Abe"), and the Sun Constellation Linux cluster ("Ranger").