Related papers: A connected component-based method for efficiently…
We propose a hierarchical splitting approach to differential equations that provides a design principle for constructing splitting methods for $N$-split systems by iteratively applying splitting methods for two-split systems. We analyze the…
We present the results of gravitational direct $N$-body simulations using the Graphics Processing Unit (GPU) on a commercial NVIDIA GeForce 8800GTX designed for gaming computers. The force evaluation of the $N$-body problem is implemented…
We present a gravitational hierarchical N-body code that is designed to run efficiently on Graphics Processing Units (GPUs). All parts of the algorithm are executed on the GPU which eliminates the need for data transfer between the Central…
Time-symmetric integration schemes share with symplectic schemes the property that their energy errors show a much better behavior than is the case for generic integration schemes. Allowing adaptive time steps typically leads to a loss of…
Modeling of collisionless galactic systems is based on the N-body model, which requires large computational resources due to the long-range nature of gravitational forces. The most common method for calculating gravity is the TreeCode…
We propose a hybrid tree algorithm for reducing calculation and communication cost of collision-less N-body simulations. The concept of our algorithm is that we split interaction force into two parts: hard-force from neighbor particles and…
In this study, a variety of methods are tested and compared for the numerical solution of the Schr\"odinger equation for few-body systems with explicitely time-dependent Hamiltonians, with the aim to find the optimal one. The configuration…
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,…
We study the accumulation of errors in cosmological N-body algorithms that are caused by representing the continuous distribution of matter by massive particles, comparing the PPPM and Adaptive Multigrid codes. We use for this a new measure…
Many exoplanetary systems are multiplanet configurations whose long-term dynamics are governed by N-body gravitational interactions. Consequently, their detection signatures cannot be adequately described by Keplerian orbits. Accurately…
We describe source code level parallelization for the {\tt kira} direct gravitational $N$-body integrator, the workhorse of the {\tt starlab} production environment for simulating dense stellar systems. The parallelization strategy, called…
Hybrid computational architectures based on the joint power of Central Processing Units and Graphic Processing Units (GPUs) are becoming popular and powerful hardware tools for a wide range of simulations in biology, chemistry, engineering,…
We propose an efficient approach for time integration of Klein-Gordon equations with highly oscillatory in time input terms. The new methods are highly accurate in the entire range, from slowly varying up to highly oscillatory regimes. Our…
We present non-convex maximal dissipation principle (NMDP), a time integration scheme for articulated bodies with simultaneous contacts. Our scheme resolves contact forces via the maximal dissipation principle (MDP). Prior MDP solvers…
Many-body systems arising in condensed matter physics and quantum optics inevitably couple to the environment and need to be modelled as open quantum systems. While near-optimal algorithms have been developed for simulating many-body…
The gravitational N-body simulation in the Solar system was performed using different parallel approaches with the comparisons in the computational times and speed-up values being carried out under different model sizes and the number of…
We describe a parallel hybrid symplectic integrator for planetary system integration that runs on a graphics processing unit (GPU). The integrator identifies close approaches between particles and switches from symplectic to Hermite…
We present new splitting methods designed for the numerical integration of near-integrable Hamiltonian systems, and in particular for planetary N-body problems, when one is interested in very accurate results over a large time span. We…
Quantum-chemical fragmentation methods offer an efficient approach for the treatment of large proteins, in particular if local target quantities such as protein--ligand interaction energies, enzymatic reaction energies, or spectroscopic…
The two-dimensional n-body problem of classical mechanics is a non-integrable Hamiltonian system for n > 2. Traditional numerical integration algorithms, which are polynomials in the time step, typically lead to systematic drifts in the…