Related papers: Symplectic integrators with adaptive time steps
Domain decomposition based time integrators allow the usage of parallel and distributed hardware, making them well-suited for the temporal discretization of parabolic systems, in general, and degenerate parabolic problems, in particular.…
We show that adaptive time stepping in particle accelerator simulation is an enhancement for certain problems. The new algorithm has been implemented in the OPAL (Object Oriented Parallel Accelerator Library) framework, and is compared to…
Recent applications (e.g. active gels and self-assembly of elastic sheets) motivate the need to efficiently simulate the dynamics of thin elastic sheets. We present semi-implicit time stepping algorithms to improve the time step constraints…
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…
Time-reversible symplectic methods, which are precisely compatible with Liouville's phase-volume-conservation theorem, are often recommended for computational simulations of Hamiltonian mechanics. Lack of energy drift is an apparent…
Symplectic integrator plays a pivotal role in the long-term tracking of charged particles within accelerators. To get symplectic maps in accurate simulation of single-particle trajectories, two key components are addressed: precise…
Time integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators are desirable for their stability properties, significantly relaxing…
A drift-kick-drift (DKD) type leapfrog symplectic integrator applied for a time-transformed separable Hamiltonian (or time-transformed symplectic integrator; TSI) has been known to conserve the Kepler orbit exactly. We find that for an…
This paper is devoted to the numerical symplectic approximation of the charged-particle dynamics (CPD) with arbitrary electromagnetic fields. By utilizing continuous-stage methods and exponential integrators, a general class of symplectic…
Within this paper, we introduce and analyze a novel time stepping scheme for linear poroelasticity. In each time frame, we iteratively solve the flow and mechanics equations with an additional damping step for the pressure variable.…
A new approach is developed to integrate numerically the equations of motion for systems of interacting rigid polyatomic molecules. With the aid of a leapfrog framework, we directly involve principal angular velocities into the integration,…
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…
We study a recent timestep adaptation technique for hyperbolic conservation laws. The key tool is a space-time splitting of adjoint error representations for target functionals due to S\"uli and Hartmann. It provides an efficient choice of…
Recently, continuous-time dynamical systems have proved useful in providing conceptual and quantitative insights into gradient-based optimization, widely used in modern machine learning and statistics. An important question that arises in…
A new family of methods involving complex coefficients for the numerical integration of differential equations is presented and analyzed. They are constructed as linear combinations of symmetric-conjugate compositions obtained from a basic…
We present a new time-stepping algorithm for nonlinear PDEs that exhibit scale separation in time. Our scheme combines asymptotic techniques (which are inexpensive but can have insufficient accuracy) with parallel-in-time methods (which,…
In a recent work of Wu, Wang, Sun and Liu, a second-order explicit symplectic integrator was proposed for the integrable Kerr spacetime geometry. It is still suited for simulating the nonintegrable dynamics of charged particles moving…
In view of the existing limitations of sequential computing, parallelization has emerged as an alternative in order to improve the speedup of numerical simulations. In the framework of evolutionary problems, space-time parallel methods…
We study the time evolution for the quantum harmonic oscillator subjected to a sudden change of frequency. It is based on an approximate analytic solution to the time dependent Ermakov equation for a step function. This approach allows for…
We present a variational integrator based on the Lobatto quadrature for the time integration of dynamical systems issued from the least action principle. This numerical method uses a cubic interpolation of the states and the action is…