A method of local corrections for computing the velocity field due to a distribution of vortex blobs
Journal of Computational Physics
A fast algorithm for particle simulations
Journal of Computational Physics
A domain decomposition algorithm using a hierarchical basis
SIAM Journal on Scientific and Statistical Computing
A fast vortex method for computing 2D viscous flow
Journal of Computational Physics
Fast potential theory. II: Layer potentials and discrete sums
Journal of Computational Physics
A fast adaptive vortex method in three dimensions
Journal of Computational Physics
Numerical methods for engineers
Numerical methods for engineers
A direct adaptive Poisson solver of arbitrary order accuracy
Journal of Computational Physics
Software infrastructure for non-uniform scientific computations on parallel processors
ACM SIGAPP Applied Computing Review
Efficient run-time support for irregular block-structured applications
Journal of Parallel and Distributed Computing - Special issue on irregular problems in supercomputing applications
Run-time partitioning of scientific continuum calculations running on multiprocessors
Run-time partitioning of scientific continuum calculations running on multiprocessors
A finite-difference domain decomposition method using local corrections for the solution of poisson's equation
SCALLOP: A Highly Scalable Parallel Poisson Solver in Three Dimensions
Proceedings of the 2003 ACM/IEEE conference on Supercomputing
An unsplit, cell-centered Godunov method for ideal MHD
Journal of Computational Physics
Adaptive Mesh Refinement for Multiscale Nonequilibrium Physics
Computing in Science and Engineering
Productivity and performance using partitioned global address space languages
Proceedings of the 2007 international workshop on Parallel symbolic computation
Parallel Languages and Compilers: Perspective From the Titanium Experience
International Journal of High Performance Computing Applications
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.46 |
We present a domain decomposition method for computing finite difference solutions to the Poisson equation with infinite domain boundary conditions. Our method is a finite difference analogue of Anderson's Method of Local Corrections. The solution is computed in three steps. First, fine-grid solutions are computed in parallel using infinite domain boundary conditions on each subdomain. Second, information is transferred globally through a coarse-grid representation of the charge, and a global coarse-grid solution is found. Third, a fine-grid solution is computed on each subdomain using boundary conditions set with the global coarse solution, corrected locally with fine-grid information from nearby subdomains. There are three important features of our algorithm. First, our method requires only a single iteration between the local fine-grid solutions and the global coarse representation. Second, the error introduced by the domain decomposition is small relative to the solution error obtained in a single-grid calculation. Third, the computed solution is second-order accurate and only weakly dependent on the coarse-grid spacing and the number of subdomains. As a result of these features, we are able to compute accurate solutions in parallel with a much smaller ratio of communication to computation than more traditional domain decomposition methods. We present results to verify the overall accuracy, confirm the small communication costs, and demonstrate the parallel scalability of the method.