Related papers: A New Time-Symmetric Block Time-Step Algorithm for…
Quantum walks are expected to serve important modelling and algorithmic applications in many areas of science and mathematics. Although quantum walks have been successfully implemented physically in recent times, no major efforts have been…
We present a high-fidelity realization of the cosmological $N$-body simulation from the Schneider et al. (2016) code comparison project. The simulation was performed with our Abacus $N$-body code, which offers high force accuracy, high…
We describe an algorithm for long-term planetary orbit integrations, including the dominant post-Newtonian effects, that employs individual timesteps for each planet. The algorithm is symplectic and exhibits short-term errors that are…
A version of the time-parallel algorithm parareal is analyzed and applied to stochastic models in chemical kinetics. A fast predictor at the macroscopic scale (evaluated in serial) is available in the form of the usual reaction rate…
Symmetry is a unifying concept in physics. In quantum information and beyond, it is known that quantum states possessing symmetry are not useful for certain information-processing tasks. For example, states that commute with a Hamiltonian…
Quantum dynamics can be simulated on a quantum computer by exponentiating elementary terms from the Hamiltonian in a sequential manner. However, such an implementation of Trotter steps has gate complexity depending on the total Hamiltonian…
Simulation is an efficient tool in the design and control of power electronic systems. However, quick and accurate simulation of them is still challenging, especially when the system contains a large number of switches and state variables.…
In many systems, the time scales of the microscopic dynamics and macroscopic dynamics of interest are separated by many orders of magnitude. Examples abound, for instance nucleation, protein folding, and chemical reactions. For these…
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…
Stencil computations consume a major part of runtime in many scientific simulation codes. As prototypes for this class of algorithms we consider the iterative Jacobi and Gauss-Seidel smoothers and aim at highly efficient parallel…
We present a new numerical algorithm for the solution of coupled collisional and collisionless systems, based on the block structured adaptive mesh and time refinement strategy (AMR). We describe the issues associated with the…
Time-reversal symmetry arises naturally as a structural property in many dynamical systems of interest. While the importance of hard-wiring symmetry is increasingly recognized in machine learning, to date this has eluded time-reversibility.…
An improved implementation of an N-body code for simulating collisionless cosmological dynamics is presented. TPM (Tree-Particle-Mesh) combines the PM method on large scales with a tree code to handle particle-particle interactions at small…
A minimal requirement for simulating multi-scale systems is to reproduce the statistical behavior of the slow variables. In particular, a good numerical method should accurately aproximate the probability density function of the…
We describe a new algorithm for the integration of self-gravitating fluid systems using SPH method. We split the Hamiltonian of a self-gravitating fluid system to the gravitational potential and others (kinetic and internal energies) and…
We present a parallel time-stepping method for fluid-structure interactions. The interaction between the incompressible Navier-Stokes equations and a hyperelastic solid is formulated in a fully monolithic framework. Discretization in space…
We consider settings for which one needs to perform multiple flow simulations based on the Navier-Stokes equations, each having different values for the physical parameters and/or different initial condition data, boundary conditions data,…
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…
We propose a variational symplectic numerical method for the time integration of dynamical systems issued from the least action principle. We assume a quadratic internal interpolation of the state and we approximate the action in a small…
In this work, we present a symplectic integration scheme to numerically compute space debris motion. Such an integrator is particularly suitable to obtain reliable trajectories of objects lying on high orbits, especially geostationary ones.…