Related papers: A fast multipole method for stellar dynamics
We propose a new theoretical method for the calculation of the interaction energy between macromolecular systems at large distances. The method provides a linear scaling of the computing time with the system size and is considered as an…
The use of integral equation methods for the efficient numerical solution of PDE boundary value problems requires two main tools: quadrature rules for the evaluation of layer potential integral operators with singular kernels, and fast…
Approximate full mass matrix methods for the material point method, known as FMPM(k) of order k, can improve the calculation of grid velocities from grid momentum. It can be implemented in any MPM code by inserting a new calculation task…
The determination of potentials of mean force for solute insertion in a membrane by means of all-atom molecular dynamics simulations is often hampered by sampling issues. A multiscale approach to conformational sampling was recently…
The kernel-independent fast multipole method (KIFMM) proposed in [1] is of almost linear complexity. In the original KIFMM the time-consuming M2L translations are accelerated by FFT. However, when more equivalent points are used to achieve…
We present $\texttt{Abacus}$, a fast and accurate cosmological $N$-body code based on a new method for calculating the gravitational potential from a static multipole mesh. The method analytically separates the near- and far-field forces,…
Series expansions have been a cornerstone of applied mathematics and engineering for centuries. In this paper, we revisit the Taylor series expansion from a modern Machine Learning perspective. Specifically, we introduce the Fast Continuous…
We present a computational algorithm for computing short range forces between particles. The algorithm has two distinguishing features. First, it is optimized for multi-processor computers, and will use as many processors as are available.…
This paper reports large-scale direct numerical simulations of homogeneous-isotropic fluid turbulence, achieving sustained performance of 1.08 petaflop/s on gpu hardware using single precision. The simulations use a vortex particle method…
Yen et al. (2012) advanced a direct approach for the calculation of self-gravitational force to second order accuracy based on uniform grid discretization. This method improves the accuracy of N-body calculation by using exact integration…
The Feynman integral is one of the most accurate methods for calculating density operator dynamics in open quantum systems. However, the number of time steps that can realistically be used is always limited, therefore one often obtains an…
The standard particle-in-cell algorithm suffers from grid heating. There exists a gridless alternative which bypasses the deposition step and calculates each Fourier mode of the charge density directly from the particle positions. We show…
We propose a Fast Fourier Transform based Periodic Interpolation Method (FFT-PIM), a flexible and computationally efficient approach for computing the scalar potential given by a superposition sum in a unit cell of an infinitely periodic…
Optical force responses underpin nanophotonic actuator design, which requires a large number of force simulations to optimize structures. Commonly used computation methods, such as the finite-difference time-domain (FDTD) method, are…
Monte Carlo (MC) simulation is commonly considered to be the most accurate dose calculation method in radiotherapy. However, its efficiency still requires improvement for many routine clinical applications. In this paper, we present our…
We present a new method, in the following called MMM2D, to accurately calculate the electrostatic energy and forces on charges being distributed in a two dimensional periodic array of finite thickness. It is not based on an Ewald summation…
The present work attempts to integrate the independent efforts in the fast N-body community to create the fastest N-body library for many-core and heterogenous architectures. Focus is placed on low accuracy optimizations, in response to the…
We introduce the Fast Free Memory method (FFM), a new fast method for the numerical evaluation of convolution products. Inheriting from the Fast Multipole Method, the FFM is a descent-only and kernel-independent algorithm. We give the…
A novel Material Point Method (MPM) is introduced for addressing frictional contact problems. In contrast to the standard multi-velocity field approach, this method employs a penalty method to evaluate contact forces at the discretised…
In the molecular dynamics calculations for the free energy of ions and ionic molecules, we often encounter wet charged molecular systems where electrical neutrality condition is broken. This causes a problem in the evaluation of…