相关论文: Yet another fast multipole method without multipol…
The pseudoparticle approach is a numerical technique to compute path integrals without discretizing spacetime. The basic idea is to integrate over those field configurations, which can be represented by a sum of a fixed number of localized…
It is well known that, using fast algorithms for polynomial multiplication and division, evaluation of a polynomial $F \in \mathbb{C}[x]$ of degree $n$ at $n$ complex-valued points can be done with $\tilde{O}(n)$ exact field operations in…
A new scheme is presented for imposing periodic boundary conditions on unit cells with arbitrary source distributions. We restrict our attention here to the Poisson, modified Helmholtz, Stokes and modified Stokes equations. The approach…
We develop an efficient and high order panel method with applications in airfoil design. Through the use of analytic work and careful considerations near singularities our approach is quadrature-free. The resulting method is examined with…
We give a quantum algorithm for evaluating a class of boolean formulas (such as NAND trees and 3-majority trees) on a restricted set of inputs. Due to the structure of the allowed inputs, our algorithm can evaluate a depth $n$ tree using…
In theories with supersymmetry, we can calculate a special partition function, known as the superconformal index. In particular, for a gauge group of $\mathrm{U}(N)$ and particles belonging to the adjoint representation, there is a fast…
The Fast Multipole Method (FMM) provides a highly efficient computational tool for solving constant coefficient partial differential equations (e.g. the Poisson equation) on infinite domains. The solution to such an equation is given as the…
The notion of well-separated sets is crucial in fast multipole methods as the main idea is to approximate the interaction between such sets via cluster expansions. We revisit the one-parameter multipole acceptance criterion in a general…
Here we describe an approach for simulating electronic structure on quantum computers with significantly lower asymptotic complexity than prior work. The approach uses a real-space first-quantised representation of the molecular Hamiltonian…
Electromagnetic particle-in-cell (PIC) codes are widely used to perform computer simulations of a variety of physical systems, including fusion plasmas, astrophysical plasmas, plasma wakefield particle accelerators, and secondary photon…
The singularities of the electromagnetic field are derived to include all the point-like multipoles representing an electric charge and current distribution. We show that for higher orders, it is more efficient to have fields represented in…
A new approximation method for inverting the Poisson's equation is presented for a continuously distributed and finite-sized source in an unbound domain. The advantage of this image multipole method arises from its ability to place the…
We demonstrate a new, hybrid symbolic-numerical method for the automatic synthesis of all families of translation operators required for the execution of the Fast Multipole Method (FMM). Our method is applicable in any dimensionality and to…
The Fast Multipole Method (FMM) offers an acceleration for pairwise interaction calculation, known as $N$-body problems, from $\mathcal{O}(N^2)$ to $\mathcal{O}(N)$ with $N$ particles. This has brought dramatic increase in the capability of…
Ab initio pseudopotentials are a linchpin of modern molecular and condensed matter electronic structure calculations. In this work, we employ multi-objective optimization to maximize pseudopotential softness while maintaining high accuracy…
The evaluation of long-range potentials in periodic, many-body systems arises as a necessary step in the numerical modeling of a multitude of interesting physical problems. Direct evaluation of these potentials requires O(N^2) operations…
We describe recent progress in developing practical ab initio methods for which the computer effort is proportional to the number of atoms: linear scaling or O(N) methods. It is shown that the locality property of the density matrix gives a…
Self-consistent multi-particle simulation plays an important role in studying beam-beam effects and space charge effects in high-intensity beams. The Poisson equation has to be solved at each time-step based on the particle density…
Real-world point sets tend to be clustered, so using a machine word for each point is wasteful. In this paper we first show how a compact representation of quadtrees using $\Oh{1}$ bits per node can break this bound on clustered point sets,…
We introduce our new binary tree code for neighbour search and gravitational force calculations in an N-particle system. The tree is built in a "top-down" fashion by "recursive coordinate bisection" where on each tree level we split the…