Related papers: Towards time symmetric N-body integration
The presence of corners in the computational domain, in general, reduces the regularity of solutions of parabolic problems and diminishes the convergence properties of the finite element approximation introducing a so-called "pollution…
Distributed nonconvex optimization problems underlie many applications in learning and autonomy, and such problems commonly face asynchrony in agents' computations and communications. When delays in these operations are bounded, they are…
Isolated many-body quantum systems quenched far from equilibrium can eventually equilibrate, but it is not yet clear how long they take to do so. To answer this question, we use exact numerical methods and analyze the entire evolution, from…
Cosmological large scale structure $N$-body simulations are computation-light, memory-heavy problems in supercomputing. The considerable amount of memory is usually dominated by an inefficient way of storing more than sufficient phase space…
Simulation of continuous time evolution requires time discretization on both classical and quantum computers. A finer time step improves simulation precision, but it inevitably leads to increased computational efforts. This is particularly…
We present a numerical method to simulate the time evolution, according to a Hamiltonian made of local interactions, of quantum spin chains and systems alike. The efficiency of the scheme depends on the amount of the entanglement involved…
Symplectic integrators are widely used for the study of planetary dynamics and other $N$-body problems. In a study of the outer Solar system, we demonstrate that individual symplectic integrations can yield biased errors in the semi-major…
An adpative integration technique for time advancement of particle motion in the context of coupled computational fluid dynamics (CFD) - discrete element method (DEM) simulations is presented in this work. CFD-DEM models provide an accurate…
A nonlinear adaptive procedure for optimising both the schemes in time and space is proposed in view of increasing the numerical efficiency and reducing the computational time. The method is based on a four-parameter family of schemes we…
We present an N-body computer code - aimed at studies of galactic dynamics - with a CPU-efficient algorithm for a continuous (i.e. time-dependent) stellar mass-loss. First, we summarize available data on stellar mass-loss and derive the…
The main problem is to understand and to find periodic symmetric orbits in the $n$-body problem, in the sense of finding methods to prove or compute their existence, and more importantly to describe their qualitative and quantitative…
Cosmological N-body simulations are done on massively parallel computers. This necessitates the use of simple time integrators, and, additionally, of mesh-grid approximations of the potentials. Recently, Adamek et al. (2015);…
Cosmological simulations require the use of a multiple time-stepping scheme. Without such a scheme, cosmological simulations would be impossible due to their high level of dynamic range; over eleven orders of magnitude in density. Such a…
I describe here the performances of a parallel treecode with individual particle timesteps. The code is based on the Barnes-Hut algorithm and runs cosmological N-body simulations on parallel machines with a distributed memory architecture…
The "gravitational million-body problem," to model the dynamical evolution of a self-gravitating, collisional N-body system with ~10^6 particles over many relaxation times, remains a major challenge in computational astrophysics.…
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…
A broken time-reversal symmetry, i.e. broken detailed balance, is central to non-equilibrium physics and is a prerequisite for life. However, it turns out to be quite challenging to unambiguously define and quantify time-reversal symmetry…
Immersed boundary methods have attracted substantial interest in the last decades due to their potential for computations involving complex geometries. Often these cannot be efficiently discretized using boundary-fitted finite elements.…
We construct an advanced model for interacting multiple stellar systems in which we compute all trajectories with a numerical N-body integrator, namely the Bulirsch--Stoer from the SWIFT package. We can then derive various observables:…
We present the multi-GPU realization of the StePS (Stereographically Projected Cosmological Simulations) algorithm with MPI-OpenMP-CUDA hybrid parallelization and nearly ideal scale-out to multiple compute nodes. Our new zoom-in…