Three-dimensional Fast Multipole Method Research Articles

A large scale molecular dynamics simulation code using the fast multipole algorithm (FMD): performance and application

We present the performance of the fast classical molecular dynamics (MD) code, fast molecular dynamics (FMD), designed for efficient, object-oriented, and scalable large scale simulations, and summarize its application to a liquid crystalline cluster. FMD uses an implementation of the three-dimensional fast multipole method, developed in our group. The fast multipole method offers an efficient way (order O( N)) to handle long range electrostatic interactions, thus, enabling more realistic simulations of large molecular systems. Performance testing was carried out on IBM SP2, SGI Origin 2000, and CRAY T3E massively parallel systems using the MPI massage passing library. The electrostatic forces were tested on models of up to 100,000 randomly placed charges, and on protein and liquid crystalline molecular systems of over 99,000 atoms. Tests on the stability of the method are presented, along with comparisons with direct calculations, the namd2 code, and the physical multipole-based cell-multipole method.

A methodology towards automatic implementation of N-body algorithms

We propose a methodology aimed at automating the software development of fast discrete transforms for N-body problems. The methodology starts with a representation of the transform matrix in compact form. Then, two translation phases are applied. One translates matrix notation to an intermediate form. The other translates the intermediate form to compilable code for a target computing environment. The generated target code employs a library of pre-defined and optimized routines. We apply our methodology systematically to implement the three-dimensional fast multipole method. We demonstrate the efficiency of our code in a molecular dynamics simulation.

Concise, efficient three-dimensional fast multipole method for micromagnetics

This paper presents derivation of the three-dimensional (3-D) fast multipole method for use in calculating magnetostatic fields. Many other derivations use complex, inefficient, and awkward function normalizations. In this derivation, tensor functions and an operator are defined that greatly simplify the theory and implementation of the algorithm. This paper provides proof of O(N) scaling, implementation, and parallelization tips, performance results, and an error analysis.

A Matrix Version of the Fast Multipole Method

We present a matrix interpretation of the three-dimensional fast multipole method (FMM). The FMM is for efficient computation of gravitational/electrostatic potentials and fields. It has found various applications and inspired the design of many efficient algorithms. The one-dimensional FMM is well interpreted in terms of matrix computations. The three-dimensional matrix version reveals the underlying matrix structures and computational techniques used in FMM. It also provides a unified view of algorithm variants as well as existing and emerging implementations of the FMM.

Large Scale Molecular Dynamics Simulations of a Liquid Crystalline Droplet with Fast Multipole Implementations

AbstractThe Fast Multipole Method (FMM) offers an efficient way (order O(N)) to handle long range electrostatic interactions, thus enabling more realistic molecular dynamics simulations of large molecular systems. The performance of the fast molecular dynamics (FMD) code, a parallel MD code being developed in our group, using the three-dimensional fast multipole method, shows a good speedup. The application to the full atomic-scale molecular dynamics simulation of a liquid crystalline droplet of 4-n-pentyl-4'-cyanobiphenyl (5CB) molecules, of size 35,872 atoms, shows strong surface effects on various orientational order parameters.