相关论文: 6th and 8th Order Hermite Integrator for N-body Si…

To efficiently implement many-particle quantum simulations on quantum computers we develop and present methods for inverting the Campbell-Baker-Hausdorff lemma to 3rd and 4th order in the commutator. That is, we reexpress exp{-i(H_1 + H_2 +…

Large-scale cosmological simulations are an indispensable tool for modern cosmology. To enable model-space exploration, fast and accurate predictions are critical. In this paper, we show that the performance of such simulations can be…

The derivation of combined prefactored compact schemes for first and second order derivatives is described here, relying on the Fourier analysis of the original prefactored compact schemes. By this approach, the order of accuracy of the…

The concept of effective order is a popular methodology in the deterministic literature for the construction of efficient and accurate integrators for differential equations over long times. The idea is to enhance the accuracy of a…

In this paper, we present a new hybrid algorithm for the time integration of collisional N-body systems. In this algorithm, gravitational force between two particles is divided into short-range and long-range terms, using a…

In the simulation of biological molecules, it is customary to impose constraints on the fastest degrees of freedom to increase the time step. The evaluation of the involved constraint forces must be performed in an efficient manner, for…

We propose a new framework of Hessian-free force-gradient integrators that do not require the analytical expression of the force-gradient term based on the Hessian of the potential. Due to that the new class of decomposition algorithms for…

We introduce a novel technique for constructing higher-order variational integrators for Hamiltonian systems of ODEs. In particular, we are concerned with generating globally smooth approximations to solutions of a Hamiltonian system. Our…

When training large models, such as neural networks, the full derivatives of order 2 and beyond are usually inaccessible, due to their computational cost. Therefore, among the second-order optimization methods, it is common to bypass the…

We discuss systematic extensions of the standard (St{\"o}rmer-Verlet) splitting method for differential equations of Hamiltonian mechanics, with relative accuracy of order $\tau^2$ for a timestep of length $\tau$, to higher orders in…

First-order fully implicit as well as implicit--explicit schemes for coupled elliptic-parabolic systems are discussed in [Ern and Meunier, ESAIM: M2AN, 2009] and [Altmann et al., Math.\ Comp., 2021], respectively. The extension of the…

High order discretization schemes play more important role in fractional operators than classical ones. This is because usually for classical derivatives the stencil for high order discretization schemes is wider than low order ones; but…

The equivalence between integral-chain differentiator and usual high-gain differentiator is given under suitable coordinate transformation. Integral-chain differentiator can restrain noises more thoroughly than usual high-gain linear…

Direct N-body simulations and symplectic integrators are effective tools to study the long-term evolution of planetary systems. The Wisdom-Holman (WH) integrator in particular has been used extensively in planetary dynamics as it allows for…

In this work, we develop a class of high-order multiderivative time integration methods that is able to preserve certain functionals discretely. Important ingredients are the recently developed Hermite-Birkhoff-Predictor-Corrector methods…

Variational integrators are momentum-preserving and symplectic numerical methods used to propagate the evolution of Hamiltonian systems. In this paper, we introduce a new class of variational integrators that achieve fourth-order…

Hamiltonian splitting methods are an established technique to derive stable and accurate integration schemes in molecular dynamics, in which additional accuracy can be gained using force gradients. For rigid bodies, a tradition exists in…

Many applications in computational physics that use numerical integrators based on splitting and composition can benefit from the development of optimized algorithms and from choosing the best ordering of terms. The cost in programming and…

We present a high-performance N-body code for self-gravitating collisional systems accelerated with the aid of a new SIMD instruction set extension of the x86 architecture: Advanced Vector eXtensions (AVX), an enhanced version of the…

We present initial results of the use of Force Gradient integrators for lattice field theories. These promise to give significant performance improvements, especially for light fermions and large lattices. Our results show that this is…