Related papers: Leapfrog time-stepping for Hermite methods

In order to treat the multiple time scales of ocean dynamics in an efficient manner, the baroclinic-barotropic splitting technique has been widely used for solving the primitive equations for ocean modeling. Based on the framework of strong…

Learning time-evolving objects such as multivariate time series and dynamic networks requires the development of novel knowledge representation mechanisms and neural network architectures, which allow for capturing implicit time-dependent…

First-order stochastic methods are the state-of-the-art in large-scale machine learning optimization owing to efficient per-iteration complexity. Second-order methods, while able to provide faster convergence, have been much less explored…

We propose a multi-moment method for one-dimensional hyperbolic equations with smooth coefficient and piecewise constant coefficient. The method is entirely based on the backward characteristic method and uses the solution and its…

The aim of this paper is to investigate the response of this system/scheme in terms of stability in presence of explicitly treated residual terms, as it inevitably occurs in the reality of NWP. This sudy is restricted to the impact of…

This work is focused on constructing space-time covariance functions through a hierarchical mixture approach that can serve as building blocks for capturing complex dependency structures. This hierarchical mixture approach provides a…

We demonstrate how steepest descent arguments and singularity analysis from analytic combinatorics allow for an accurate description of the behavior of linear numerical schemes -- including the notorious leap-frog scheme -- in presence of…

In this paper we present and analyze a general framework for constructing high order explicit local time stepping (LTS) methods for hyperbolic conservation laws. In particular, we consider the model problem discretized by Runge-Kutta…

In this paper, we address the full discretization of Friedrichs' systems with a two-field structure, such as Maxwell's equations or the acoustic wave equation in div-grad form, cf. [14]. We focus on a discontinuous Galerkin space…

A mass-preserving two-step Lagrange-Galerkin scheme of second order in time for convection-diffusion problems is presented, and convergence with optimal error estimates is proved in the framework of $L^2$-theory. The introduced scheme…

We construct a high-order adaptive time stepping scheme for vesicle suspensions with viscosity contrast. The high-order accuracy is achieved using a spectral deferred correction (SDC) method, and adaptivity is achieved by estimating the…

A high-order space-time flux reconstruction (FR) method has been developed to solve conservation laws on moving domains. In the space-time framework, the moving domain simulation is similar to that on a stationary domain, except that the…

Hybrid Monte Carlo simulations that implement the fermion action using multiple terms are commonly used. By the nature of their formulation they involve multiple integration time scales in the evolution of the system through simulation…

When dealing with stiff conservation laws, explicit time integration forces to employ very small time steps, due to the restrictive CFL stability condition. Implicit methods offer an alternative, yielding the possibility to choose the time…

A new class of Hermite methods for solving nonlinear conservation laws is presented. While preserving the high order spatial accuracy for smooth solutions in the existing Hermite methods, the new methods come with better stability…

A third-order moving mesh cell-centered scheme without the remapping of physical variables is developed for the numerical solution of one-dimensional elastic-plastic flows with the Mie-Gr\"{u}neisen equation of state, the Wilkins…

We derive a posteriori error estimates for the the scalar wave equation discretized in space by continuous finite elements and in time by the explicit leapfrog scheme. Our analysis combines the idea of invoking extra time-regularity for the…

We analyze composition methods with complex coefficients exhibiting the so-called ``symmetry-conjugate'' pattern in their distribution. In particular, we study their behavior with respect to preservation of qualitative properties when…

We explore the construction of new symplectic numerical integration schemes to be used in Hamiltonian Monte Carlo and study their efficiency. Two integration schemes from Blanes et al. (2014), and a new scheme based on optimal acceptance…

Progressive Hedging is a popular decomposition algorithm for solving multi-stage stochastic optimization problems. A computational bottleneck of this algorithm is that all scenario subproblems have to be solved at each iteration. In this…