Related papers: Multi-Point Hermite Methods for the N-Body Problem

We study analytically and experimentally certain symplectic and time-reversible N-body integrators which employ a Kepler solver for each pair-wise interaction, including the method of Hernandez & Bertschinger (2015). Owing to the Kepler…

High accuracy energies of low-lying excited states, in molecular systems, have been determined by means of a procedure which combines the G-particle-hole Hypervirial (GHV) equation method [Alcoba et al. Int. J. Quantum Chem. 109:3178…

Numerical integration and emulation are fundamental topics across scientific fields. We propose novel adaptive quadrature schemes based on an active learning procedure. We consider an interpolative approach for building a surrogate…

In this paper, we consider an efficient iterative approach to the solution of the discrete Helmholtz equation with Dirichlet, Neumann and Sommerfeld-like boundary conditions based on a compact sixth order approximation scheme and…

Vector extrapolation methods are widely used in large-scale simulation studies, and numerous extrapolation-based acceleration techniques have been developed to enhance the convergence of linear and nonlinear fixed-point iterative methods.…

We present a new time integrator for articulated body dynamics. We formulate the governing equations of the dynamics using only the position variables and recast the position-based articulated dynamics as an optimization problem. Our…

In a Keplerian system, a large number of bodies orbit a central mass. Accretion disks, protoplanetary disks, asteroid belts, and planetary rings are examples. Simulations of these systems require algorithms that are computationally…

This paper considers the approximation of partial differential equations with a point collocation framework based on high-order local maximum-entropy schemes (HOLMES). In this approach, smooth basis functions are computed through an…

We introduce a family of piecewise-exponential functions that have the Hermite interpolation property. Our design is motivated by the search for an effective scheme for the joint interpolation of points and associated tangents on a curve…

This article considers Hamiltonian mechanical systems with potential functions admitting jump discontinuities. The focus is on accurate and efficient numerical approximations of their solutions, which will be defined via the laws of…

To efficiently implement many-qubit gates for use in quantum simulations on quantum computers we develop and present methods reexpressing exp[-i (H_1 + H_2 + ...) \Delta t] as a product of factors exp[-i H_1 \Delta t], exp[-i H_2 \Delta t],…

We apply the semi-discrete method, c.f. \emph{N. Halidias and I.S. Stamatiou (2016), On the numerical solution of some non-linear stochastic differential equations using the semi-discrete method, Computational Methods in Applied…

We introduce FastPM, a highly-scalable approximated particle mesh N-body solver, which implements the particle mesh (PM) scheme enforcing correct linear displacement (1LPT) evolution via modified kick and drift factors. Employing a…

A single-step high-order implicit time integration scheme with controllable numerical dissipation at high frequencies is presented for the transient analysis of structural dynamic problems. The amount of numerical dissipation is controlled…

We consider a new splitting based on the Sherman-Morrison-Woodbury formula, which is particularly effective with iterative methods for the numerical solution of large linear systems. These systems involve matrices that are perturbations of…

We present a new multigrid method called neural multigrid which is based on joining multigrid ideas with concepts from neural nets. The main idea is to use the Greenbaum criterion as a cost functional for the neural net. The algorithm is…

Composite convex optimization models arise in several applications, and are especially prevalent in inverse problems with a sparsity inducing norm and in general convex optimization with simple constraints. The most widely used algorithms…

Multipoint secant and interpolation methods are effective tools for solving systems of nonlinear equations. They use quasi-Newton updates for approximating the Jacobian matrix. Owing to their ability to more completely utilize the…

Hermite interpolation property is desired in applied and computational mathematics. Hermite and vector subdivision schemes are of interest in CAGD for generating subdivision curves and in computational mathematics for building Hermite…

In a companion paper (hep-th/0512317), we have presented an approximation scheme to solve the Non Perturbative Renormalization Group equations that allows the calculation of the $n$-point functions for arbitrary values of the external…