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Poisson Solvers

by streeter — last modified 2007-03-30 04:02

For self-gravitating system, a fast Poisson solver is necessary to obtain the gravitational potential. In ZEUS-MP v1.0, two Poisson solvers are available:

Fast Fourier Transform using FFTW algorithm developed by Matteo Frigo and Steven G. Johnson at MIT. The algorithm is parallelized using MPI. To activate the FFTW, "#define GRAV_FFT" must be enabled in the definition file (zeusmp.def). As limited by the existing FFTW algorithm, only periodic boundary condition can be handled using FFTW. Also, slab decomposition of the domain is required. This Poisson solver will serve as a fast algorithm for small problem size. Computing time for gravitational potential using FFTW is minimal compare to the other calculation in ZEUS-MP. Users need to ensure that the FFTW library is installed on their platform and modify the Makefile for appropriate path setting.
Multigrid Method using MGMPI algorithm developed by J. Bordner at UCSD. MGMPI is an MPI-based Fortran library for solving general three-dimensional second-order elliptic PDE's, including Poisson equation, on rectangular, cylindrical, or spherical domains. To activate MGMPI, "#define GRAV" must be enabled in the definition file. This algorithm can handle Periodic, dirichlet, and Neuman boundary conditions and 3D spatial domain decomposition is allowed. Therefore, this algorithm is suitable for more general problems when large amount of processors are available. However, in general, the computing time for MGMPI is comparable to the rest of ZEUS-MP computation.

Calculation of an isolated, self-gravitating gas sphere is performed using MGMPI. For Dirichlet boundary condition, the potential at the boundaries are calculated using multipole expansion up to the quadrupole term.

July 2008

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Poisson Solvers