Related papers: Multi-Point Hermite Methods for the N-Body Problem
Hypergraph matching has recently become a popular approach for solving correspondence problems in computer vision as it allows to integrate higher-order geometric information. Hypergraph matching can be formulated as a third-order…
In this paper, we propose and analyze a fast two-point gradient algorithm for solving nonlinear ill-posed problems, which is based on the sequential subspace optimization method. A complete convergence analysis is provided under the…
This study proposes a high-order multi-scale method tailored for time-dependent nonlinear thermo-electro-mechanical coupling problems of composite structures with highly spatial heterogeneity, which incorporate temperature-dependent…
Modelling the cosmic large-scale structure can be done through numerical N-body simulations or by using perturbation theory. Here, we present an N-body approach that effectively implements a multi-step forward model based on Lagrangian…
New implicit and implicit-explicit time-stepping methods for the wave equation in second-order form are described with application to two and three-dimensional problems discretized on overset grids. The implicit schemes are single step,…
Symplectic integration methods based on operator splitting are well established in many branches of science. For Hamiltonian systems which split in more than two parts, symplectic methods of higher order have been studied in detail only for…
The automation of ab initio simulations is essential in view of performing high-throughput (HT) computational screenings oriented to the discovery of novel materials with desired physical properties. In this work, we propose algorithms and…
It is well known that multigrid methods are optimally efficient for solution of elliptic equations (O(N)), which means that effort is proportional to the number of points at which the solution is evaluated). Thus this is an ideal method to…
We propose an efficient method for active particle selection, working with Hermite Individual Time Steps (HITS) scheme in direct N-body simulation code $\varphi$GRAPE. For a simulation with $N$ particles, this method can reduce the…
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…
Recently, Krukier et al. [Generalized skew-Hermitian triangular splitting iteration methods for saddle-point linear systems, Numer. Linear Algebra Appl. 21 (2014) 152-170] proposed an efficient generalized skew-Hermitian triangular…
In this paper, we propose two methods for multivariate Hermite interpolation of manifold-valued functions. On the one hand, we approach the problem via computing suitable weighted Riemannian barycenters. To satisfy the conditions for…
This paper proposes several explicit and implicit multistep frequency response optimized integrators considering first or second order derivative. A prediction-based method aiming at accelerating a novel power system transient simulation…
We present new almost time-reversible integrators for solution of planetary systems consisting of "planets" and a dominant mass ("star"). The algorithms can be considered adaptive generalizations of the Wisdom--Holman method, in which all…
This paper constructs adaptive sparse grid collocation method onto arbitrary order piecewise polynomial space. The sparse grid method is a popular technique for high dimensional problems, and the associated collocation method has been well…
We investigate a hybrid numerical algorithm aimed at the large-scale cosmological N-body simulation for the on-going and the future high precious sky surveys. It makes use of a truncated Fast Multiple Method (FMM) for short-range gravity,…
We introduce a class of fourth order symplectic algorithms that are ideal for doing long time integration of gravitational few-body problems. These algorithms have only positive time steps, but require computing the force gradient in…
Astrophysical research in recent decades has made significant progress thanks to the availability of various $N$-body simulation techniques. With the rapid development of high-performance computing technologies, modern simulations have been…
Astrophysical Challenges which demand the solution of the one million (or more) gravitating body problem are briefly discussed for the fields of cosmology, galactic nuclei and globular star clusters. Results from the classical three-body…
The Hermite methods of Goodrich, Hagstrom, and Lorenz (2006) use Hermite interpolation to construct high order numerical methods for hyperbolic initial value problems. The structure of the method has several favorable features for parallel…