An Infinite Domain 3D Poisson Solver Based on the Barnes-Hut Algorithm
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
We present a domain decomposition method for the solution of the 3D Poisson equation with infinite domain boundary conditions. The method is based on an application of the Barnes-Hut tree particle scheme adapted to gridded data. Long range interactions are computed using the first two terms in the Cartesian multipole expansion of Green’s function convoluted with the charge while short range computations are performed using Hockney’s domain doubling algorithm. A standard domain decomposition strategy requires O(N2) applications of Hockney’s algorithm, where N is the number of subdomains that intersect that charge support, while in the present approach only O(Nlog2N) such computations suffice. The discretization scheme employed is a sixth order Mehrstellen approximation of the 3D Laplace opera tor. The method exhibits satisfactory accuracy at a substantially reduced computational cost compared to the full domain decomposition Hockney’s algorithm.
- Research Organization:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- DOE Contract Number:
- AC52-07NA27344; AC02-05CH11231
- OSTI ID:
- 1959567
- Report Number(s):
- LLNL-TR-844547; 1067802
- Country of Publication:
- United States
- Language:
- English
Similar Records
A 6th Order Mehrstellen Finite Volume Discretization of Poisson's Equation in Three Dimensions
A sixth order Mehrstellen scheme with an application to the Method of Local Corrections for the 3D Poisson equation