Fast Multipole Method
The Fast Multipole Method (FMM) calculates the potentials and forces which arise in various scientific applications such as molecular dynamics and plasma physics. All these applications have in common that long-range interactions between huge numbers of particles have to be calculated. The FMM allows the efficient computation of the interactions by means of expansions of the potentials and forces into multipole moments. The main idea of the FMM is to group remote charges together such that a collection of distant charges can be treated as one single charge. The FMM is a computational scheme how to manipulate the multipole expansions to achieve linear scaling with regard to the number of particles.
FMM: hierarchical decomposition
Our FMM implementation is based on a new approach to minimize the computation time for a given system of point charges by optimization of the FMM-parameters. We have improved the accuracy of the FMM by a new approach to compute the Wigner rotation matrices numerically stable in particular for high multipole moments. An alternative approach to compute the gradient has been implemented. This method requires less than 1% of the total computation time. Thus the new FMM implementation is able to compute systems consisting of more than a billion point charges within hours on a single CPU.
FMM: near field interaction
Current activities include the parallelization of the FMM. The goal is a massively parallel version of the FMM to exploit today's computing resources. Another activity is the optimization of the FMM program for the IBM BlueGene/L system.
Features
-error control
-can treat open and 1D/2D/3D periodic systems
-Coulomb or linear cusp potential
Contact:
Dr. Holger Dachsel
last change 09.04.2009 |
Ivo Kabadshow | Print
The Fast Multipole Method (FMM) calculates the potentials and forces which arise in various scientific applications such as molecular dynamics and plasma physics. All these applications have in common that long-range interactions between huge numbers of particles have to be calculated. The FMM allows the efficient computation of the interactions by means of expansions of the potentials and forces into multipole moments. The main idea of the FMM is to group remote charges together such that a collection of distant charges can be treated as one single charge. The FMM is a computational scheme how to manipulate the multipole expansions to achieve linear scaling with regard to the number of particles.
FMM: hierarchical decomposition
Our FMM implementation is based on a new approach to minimize the computation time for a given system of point charges by optimization of the FMM-parameters. We have improved the accuracy of the FMM by a new approach to compute the Wigner rotation matrices numerically stable in particular for high multipole moments. An alternative approach to compute the gradient has been implemented. This method requires less than 1% of the total computation time. Thus the new FMM implementation is able to compute systems consisting of more than a billion point charges within hours on a single CPU.
FMM: near field interaction
Current activities include the parallelization of the FMM. The goal is a massively parallel version of the FMM to exploit today's computing resources. Another activity is the optimization of the FMM program for the IBM BlueGene/L system.
Features
-error control
-can treat open and 1D/2D/3D periodic systems
-Coulomb or linear cusp potential
Contact:
Dr. Holger Dachsellast change 09.04.2009 |
Ivo Kabadshow | Print