Related papers: An O(N) Method for Rapidly Computing Periodic Pote…
Simulating long-range interacting systems is a challenging task due to its computational complexity that the computational effort for each local update is of order $\cal{O}$$(N)$, where $N$ is the size of system. Recently, a technique,…
Recently the rank-structured tensor approach suggested a progress in the numerical treatment of the long-range electrostatic potentials in many-particle systems and the respective interaction energy and forces [39,40,2]. In this paper, we…
The most critical limitation to the wide-scale use of classical molecular dynamics for alloy design is the availability of suitable interatomic potentials. In this work, we demonstrate a simple procedure to generate a library of accurate…
This work presents an alternative methodology for computing potentials matrix elements within the Lagrange-mesh method in momentum space. The proposed approach extends the range of treatable potentials to include previously inaccessible…
A combination of the variable-constant and complex coordinate rotation methods is used to solve the two-body Schr\"odinger equation. The latter is replaced by a system of linear first-order differential equations, which enables one to…
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 a fast adaptive method for the evaluation of heat potentials, which plays a key role in the integral equation approach for the solution of the heat equation, especially in a non-stationary domain. The algorithm utilizes a…
The extended Hubbard model on a two-dimensional lattice captures key physical phenomena, but is challenging to simulate due to the presence of long-range interactions. In this work, we present an efficient quantum algorithm for simulating…
Motivated by the factorization inherent in the original fast multipole method and the improved fast Gauss transform we introduce a factorable form of attention that operates efficiently in high dimensions. This approach reduces the…
In the Bin Packing problem one is given $n$ items with weights $w_1,\ldots,w_n$ and $m$ bins with capacities $c_1,\ldots,c_m$. The goal is to find a partition of the items into sets $S_1,\ldots,S_m$ such that $w(S_j) \leq c_j$ for every bin…
Modal crosstalk is a fundamental limitation for orbital angular momentum (OAM)-based spatial-division multiplexing. Here, we introduce Annular Channel Eigenmodes (ACEs) - rigorously derived as the optimal band-limited solution for…
We improve the running times of $O(1)$-approximation algorithms for the set cover problem in geometric settings, specifically, covering points by disks in the plane, or covering points by halfspaces in three dimensions. In the unweighted…
Coupled-mode systems are used in physical literature to simplify the nonlinear Maxwell and Gross-Pitaevskii equations with a small periodic potential and to approximate localized solutions called gap solitons by analytical expressions…
Discrete-velocity approximations represent a popular way for computing the Boltzmann collision operator. The direct numerical evaluation of such methods involve a prohibitive cost, typically $O(N^{2d+1})$ where $d$ is the dimension of the…
The well-known Cornell quark-antiquark potential in momentum space contains singularities both in its one-gluon-exchange (OGE) and linear confining parts, which prevents a direct use of the convenient Nystr\"om method to solve the…
In boundary element methods (BEM) in $\mathbb{R}^3$, matrix elements and right hand sides are typically computed via analytical or numerical quadrature of the layer potential multiplied by some function over line, triangle and tetrahedral…
In this paper, we introduce a higher-order multiscale method for time-dependent problems with highly oscillatory coefficients. Building on the localized orthogonal decomposition (LOD) framework, we construct enriched correction operators to…
We develop a meta-algorithm that, given a polynomial (in one or more variables), and a prime p, produces a fast (logarithmic time) algorithm that takes a positive integer n and outputs the number of times each residue class modulo p appears…
We consider the problem of structured canonical polyadic decomposition. If the size of the problem is very big, then stochastic gradient approaches are viable alternatives to classical methods, such as Alternating Optimization and…
A new order-N method for calculating the electronic structure of general (non-tight-binding) potentials is presented. The method uses a combination of the ``purification''-based approaches used by Li, Nunes and Vanderbilt, and Daw, and a…