Related papers: Perturbation-theory informed integrators for cosmo…
Many Material Point Method implementations favor explicit time integration. However large time steps are often desirable for special reasons - for example, for partitioned coupling with another large-step solver, or for imposing…
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…
Upcoming Large Scale Structure surveys aim to achieve an unprecedented level of precision in measuring galaxy clustering. However, accurately modeling these statistics may require theoretical templates that go beyond second-order…
When simulating molecular systems using deterministic equations of motion (e.g., Newtonian dynamics), such equations are generally numerically integrated according to a well-developed set of algorithms that share commonly agreed-upon…
The most effective use of data from current and upcoming large scale structure~(LSS) and CMB observations requires the ability to predict the clustering of LSS with very high precision. The Effective Field Theory of Large Scale Structure…
We implement an adaptation of the COLA approach, a hybrid scheme that combines Lagrangian perturbation theory with an N-body approach, to model non-linear collapse in chameleon and symmetron modified gravity models. Gravitational screening…
This is the first in a series of papers devoted to fully general-relativistic $N$-body simulations applied to late-time cosmology. The purpose of this paper is to present the combination of a numerical relativity scheme, discretization…
Lagrangian particle methods based on detailed atomic and molecular models are powerful computational tools for studying the dynamics of microscale and nanoscale systems. However, the maximum time step is limited by the smallest oscillation…
Context. Due to our increasing knowledge on the Galactic and stellar neighborhood of the Solar System, modern long-period comet motion studies have to take into account both stellar perturbations and the overall Galactic potential. Aims.…
Semi-analytical methods, based on Eulerian perturbation theory, are a promising tool to follow the time evolution of cosmological perturbations at small redshifts and at mildly nonlinear scales. All these schemes are based on two…
We change a previous time-stepping algorithm for solving a multi-scale Vlasov-Poisson system within a Particle-In-Cell method, in order to do accurate long time simulations. As an exponential integrator, the new scheme allows to use large…
We explore the Lagrangian perturbation theory (LPT) at 1-loop order with Gaussian initial conditions. We present an expansion method to approximately compute the power spectrum in LPT. Our approximate solution has good convergence in the…
Geometric numerical integration has recently been exploited to design symplectic accelerated optimization algorithms by simulating the Lagrangian and Hamiltonian systems from the variational framework introduced in Wibisono et al. In this…
Stiff hyperbolic balance laws exhibit large spectral gaps, especially if the relaxation term significantly varies in space. Using examples from rarefied gases and the general form of the underlying balance law model, we perform a detailed…
Cosmic-ray acceleration processes in astrophysical plasmas are often investigated with fully-kinetic or hybrid kinetic numerical simulations, which enable us to describe a detailed microphysics of particle energization mechanisms. Tracing…
Numerical integration methods are central to the study of self-gravitating systems, particularly those comprised of many bodies or otherwise beyond the reach of analytical methods. Predictor-corrector schemes, both multi-step methods and…
We present a new implicit asymptotic preserving time integration scheme for charged-particle orbit computation in arbitrary electromagnetic fields. The scheme is built on the Crank-Nicolson integrator and continues to recover full-orbit…
The integration time step is a critical determinant of performance in molecular dynamics simulations, governing the trade-off between speed and fidelity. Although 2 fs remains the standard in atomistic biomolecular simulations, the push for…
The numerical simulation of multiphase flows involving dispersed components with large scale disparities, such as the collisions between millimeter-sized bubbles and micron-sized mineral particles in flotation, poses a significant…
Universal Machine Learning Interactomic Potentials (MLIPs) enable accelerated simulations for materials discovery. However, current research efforts fail to impactfully utilize MLIPs due to: 1. Overreliance on Density Functional Theory…