相关论文: Fast and reliable symplectic integration for plane…

We report 90 new observations of three post common envelope binaries at primary eclipse spanning between December 2018 to February 2022. We combine recent primary eclipse timing observations with previously published values to search for…

We construct a symplectic, globally defined, minimal-coordinate, equivariant integrator on products of 2-spheres. Examples of corresponding Hamiltonian systems, called spin systems, include the reduced free rigid body, the motion of point…

We study supermassive black hole (SMBH) binary eccentricity of equal-mass galaxy mergers in $N$-body simulations with the KETJU code, which combines the GAGDET-4 fast multipole gravity solver with accurate regularised integration and…

The time-dependent restricted $(n+1)$-body problem concerns the study of a massless body (satellite) under the influence of the gravitational field generated by $n$ primary bodies following a periodic solution of the $n$-body problem. We…

The kinetic term of the $N$-body Hamiltonian system defined on the surface of the sphere is non-separable. As a result, standard explicit symplectic integrators are inapplicable. We exploit an underlying hierarchy in the structure of the…

The reproducibility of experiments is one of the main principles of the scientific method. However, numerical N-body experiments, especially those of planetary systems, are currently not reproducible. In the most optimistic scenario, they…

In order to perform numerical studies of long-term stability in nonlinear Hamiltonian systems, one needs a numerical integration algorithm which is symplectic. Further, this algorithm should be fast and accurate. In this paper, we propose…

This paper presents in detail our fast semistochastic heat-bath configuration interaction (SHCI) method for solving the many-body Schrodinger equation. We identify and eliminate computational bottlenecks in both the variational and…

In a Keplerian system, a large number of bodies orbit a central mass. Accretion disks, protoplanetary disks, asteroid belts, and planetary rings are examples. Simulations of these systems require algorithms that are computationally…

Hamiltonian systems such as the gravitational N-body problem have time-reversal symmetry. However, all numerical N-body integration schemes, including symplectic ones, respect this property only approximately. In this paper, we present the…

Finite element methods for electromagnetic problems modeled by Maxwell-type equations are highly sensitive to the conformity of approximation spaces, and non-conforming methods may cause loss of convergence. This fact leads to an essential…

The singularities that arise in elliptic boundary value problems are treated locally by a singular function boundary integral method. This method extracts the leading singular coefficients from a series expansion that describes the local…

We provide an iterative solution approach for the indefinite Helmholtz equation discretised using finite elements, based upon a Hermitian Skew-Hermitian Splitting (HSS) iteration applied to the shifted operator, and prove that the iteration…

We propose a family of integrators, Flow-Composed Implicit Runge-Kutta (FCIRK) methods, for perturbations of nonlinear ordinary differential equations, consisting of the composition of flows of the unperturbed part alternated with one step…

In this work we revisit the problem of the dynamical stability of hierarchical triple systems with applications to circumbinary planetary orbits. We carry out more than 3 10^8 numerical simulations of planets between the size of Mercury and…

Symplectic integrators evolve dynamical systems according to modified Hamiltonians whose error terms are also well-defined Hamiltonians. The error of the algorithm is the sum of each error Hamiltonian's perturbation on the exact solution.…

We construct a new global, fully analytic, approximate spacetime which accurately describes the dynamics of non-precessing, spinning black hole binaries during the inspiral phase of the relativistic merger process. This approximate solution…

We present a novel, computationally efficient approach to accelerate quantum optimal control calculations of large multi-qubit systems used in a variety of quantum computing applications. By leveraging the intrinsic symmetry of finite…

Direct $N$-body simulations of a large number of particles, especially in the study of planetesimal dynamics and planet formation, have been computationally challenging even with modern machines. This work presents the combination of fully…

Many exoplanets are discovered in binary star systems in internal or in circumbinary orbits. Whether the planet can be habitable or not depends on the possibility to maintain liquid water on its surface, and therefore on the luminosity of…