On the structure of parallelism in a highly concurrent PDE solver
Journal of Parallel and Distributed Computing
A fast algorithm for particle simulations
Journal of Computational Physics
Solving problems on concurrent processors. Vol. 1: General techniques and regular problems
Solving problems on concurrent processors. Vol. 1: General techniques and regular problems
Multilevel matrix multiplication and fast solution of integral equations
Journal of Computational Physics
Normalized convergence rates for the PSMG method
SIAM Journal on Scientific and Statistical Computing
Astrophysical N-body simulations using hierarchical tree data structures
Proceedings of the 1992 ACM/IEEE conference on Supercomputing
Journal of Parallel and Distributed Computing
SIAM Journal on Scientific Computing
Journal of Computational Physics
Parallelism in multigrid methods: how much is too much?
International Journal of Parallel Programming
The full domain partition approach to distributing adaptive grids
Proceedings of international centre for mathematical sciences on Grid adaptation in computational PDES : theory and applications: theory and applications
Parallel transient dynamics simulations
Journal of Parallel and Distributed Computing - Special issue on irregular problems in supercomputing applications
An adaptive multigrid technique for evaluating long-range forces in biomolecular simulations
Applied Mathematics and Computation
NAMD2: greater scalability for parallel molecular dynamics
Journal of Computational Physics - Special issue on computational molecular biophysics
Parallel multigrid in an adaptive PDE solver based on hashing and space-filling curves
Parallel Computing - Special issue on parallelization techniques for numerical modelling
Improving Error Bounds for Multipole-Based Treecodes
SIAM Journal on Scientific Computing
Semicoarsening Multigrid on Distributed Memory Machines
SIAM Journal on Scientific Computing
Compression of particle data from hierarchical approximate methods
ACM Transactions on Mathematical Software (TOMS)
Computing in Science and Engineering
A portable distributed implementation of the parallel multipole tree algorithm
HPDC '95 Proceedings of the 4th IEEE International Symposium on High Performance Distributed Computing
ProtoMol, an object-oriented framework for prototyping novel algorithms for molecular dynamics
ACM Transactions on Mathematical Software (TOMS)
Journal of Parallel and Distributed Computing
Molecular Dynamics Simulations on High-Performance Reconfigurable Computing Systems
ACM Transactions on Reconfigurable Technology and Systems (TRETS)
Preparing scientific application software for exascale computing
PARA'12 Proceedings of the 11th international conference on Applied Parallel and Scientific Computing
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An @Q(n) parallel multigrid summation method (MG) for the N-body problem is presented. The method was originally devised for vacuum boundary conditions. Here, it is extended to periodic boundary conditions and implemented in parallel using force decomposition and MPI. MG is based on a hierarchical decomposition of computational kernels on multiple grids. For low accuracy calculations, appropriate for molecular dynamics, a sequential implementation is as fast or faster than particle mesh Ewald (PME). Our parallel implementation is more scalable than PME. The method can be combined with multiple time stepping integrators to produce a powerful simulation protocol for simulation of biological molecules and other materials. The parallel implementation is tested on both a Linux cluster with Myrinet interconnect and a shared memory computer. It is available as open-source at http://protomol.sourceforge.net. An auxiliary tool allows the automatic selection of optimal parameters for MG, and is available at http://mdsimaid.cse.nd.edu.