Premium
A fast‐adaptive composite grid algorithm for solving the free‐space Poisson problem on the cell broadband engine
Author(s) -
Ritter Daniel,
Stürmer Markus,
Rüde Ulrich
Publication year - 2010
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.703
Subject(s) - grid , discretization , computer science , poisson's equation , algorithm , code (set theory) , parallel computing , mathematical optimization , set (abstract data type) , mathematics , computational science , mathematical analysis , geometry , programming language
Abstract Fast solvers for Poisson's equation with boundary conditions at infinity are an important building block for molecular dynamics. One issue that arises when this equation is solved numerically is the infinite size of the domain. This prevents a direct solution so that other concepts have to be considered. Within this paper a method is discussed that employs hierarchically coarsened grids to overcome this problem. Special attention has to be paid to the discretization at the grid interfaces. A finite volume approach is used for the same. The resulting set of linear equations is solved using a fast‐adaptive composite grid algorithm. Emphasis is put on the implementation of the method on the STI cell broadband engine, a modern multi core processor, that is powerful in floating point operations and memory bandwidth. Code optimization techniques are applied as well as parallelization of the code to get maximum performance on this processor. For validation of the performance test runs are executed and the runtime is analyzed in detail. Copyright © 2010 John Wiley & Sons, Ltd.