Related papers: A Hierarchical O(N) Force Calculation Algorithm
An efficient low-order scaling method is presented for large-scale electronic structure calculations based on the density functional theory using localized basis functions, which directly computes selected elements of the density matrix by…
In this paper we report on a high-order fast method to numerically calculate wakefield forces in an electron beam given a wake function model. This method is based on a Newton-Cotes quadrature rule for integral approximation and an FFT…
We develop data structures for dynamic closest pair problems with arbitrary distance functions, that do not necessarily come from any geometric structure on the objects. Based on a technique previously used by the author for Euclidean…
We present an efficient method to mix well converged ab initio forces with simpler and faster ones in molecular dynamics. While the cheap forces are evaluated every time step, the converged ones correct the trajectory only every n time…
We present an implementation of the hierarchical tree algorithm on the individual timestep algorithm (the Hermite scheme) for collisional $N$-body simulations, running on GRAPE-9 system, a special-purpose hardware accelerator for…
We present a new algorithm to rapidly compute the two-point (2PCF), three-point (3PCF) and n-point (n-PCF) correlation functions in roughly O(N log N) time for N particles, instead of O(N^n) as required by brute force approaches. The…
We developed a new direct-tree hybrid N-body algorithm for fully self-consistent N-body simulations of star clusters in their parent galaxies. In such simulations, star clusters need high accuracy, while galaxies need a fast scheme because…
A theory is presented for a novel recursion method for O(N) ab initio tight-binding calculations. A long-standing problem of generalizing the recursion method to a non-orthogonal basis, which is a crucial step to make the recursion method…
We describe a new parallel N-body code for cosmological simulations. The code is based on a work- and data sharing scheme, and is implemented within the Cray Research Corporation's CRAFT programming environment. Different data distribution…
An improved implementation of an N-body code for simulating collisionless cosmological dynamics is presented. TPM (Tree-Particle-Mesh) combines the PM method on large scales with a tree code to handle particle-particle interactions at small…
We present time-space trade-offs for computing the Euclidean minimum spanning tree of a set $S$ of $n$ point-sites in the plane. More precisely, we assume that $S$ resides in a random-access memory that can only be read. The edges of the…
The plasma force on grains of specified charge and height in a collisional DC plasma sheath are calculated using the multidimensional particle in cell code COPTIC. The background ion velocity distribution functions for the unperturbed…
The multiplication of matrices is an important arithmetic operation in computational mathematics. In the context of hierarchical matrices, this operation can be realized by the multiplication of structured block-wise low-rank matrices,…
There have been several algorithms designed to optimise matrix multiplication. From schoolbook method with complexity $O(n^3)$ to advanced tensor-based tools with time complexity $O(n^{2.3728639})$ (lowest possible bound achieved), a lot of…
Template matching is widely used for many applications in image and signal processing and usually is time-critical. Traditional methods usually focus on how to reduce the search locations by coarse-to-fine strategy or full search combined…
Three-nucleon (3N) forces are an indispensable ingredient for accurate few-body and many-body nuclear structure and reaction theory calculations. While the direct implementation of chiral 3N forces can be technically very challenging, a…
Linear-scaling electronic-structure techniques, also called O(N) techniques, rely heavily on the multiplication of sparse matrices, where the sparsity arises from spatial cut-offs. In order to treat very large systems, the calculations must…
The three-nucleon (NNN) interaction derived within the chiral effective field theory at the next-to-next-to-leading order (N2LO) is regulated with a function depending on the magnitude of the momentum transfer. The regulated NNN interaction…
Ab initio calculations have achieved remarkable success in nuclear structure studies. Numerous works highlight the pivotal role of three-body forces in nuclear ab initio calculations. Concurrently, efforts have been made to replicate these…
Given a set $P$ of $n$ points that are moving in the plane, we consider the problem of computing a spanning tree for these moving points that does not change its combinatorial structure during the point movement. The objective is to…