Related papers: A high-order, conservative integrator with local t…
This study proposes an extension of the high-order compact gas-kinetic scheme (CGKS) to compressible flow simulation in an arbitrary Lagrangian-Eulerian (ALE) formulation in unstructured mesh. The ALE method is achieved by subdividing…
We analyze a variable-step extension of a family of arbitrarily high-order exponential time differencing multistep (ETD-MS) schemes recently developed by the authors. We prove that the schemes are unconditionally stable in the sense that a…
We introduce a hybrid method to couple continuous Galerkin finite element methods and high-order finite difference methods in a nonconforming multiblock fashion. The aim is to optimize computational efficiency when complex geometries are…
This study presents an efficient, accurate, effective and unconditionally stable time stepping scheme for the Darcy-Brinkman equations in double-diffusive convection. The stabilization within the proposed method uses the idea of stabilizing…
This paper presents a robust and efficient very high-order scheme for compressible flow simulation, addressing critical limitations of existing high-order methods. The proposed scheme combines the compact gas-kinetic scheme (CGKS) with an…
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…
This paper addresses the design and analysis of a multivariable gradient-based stochastic extremum-seeking control method for multi-input systems with arbitrary input delays. The approach accommodates systems with distinct time delays…
A novel probabilistic numerical method for quantifying the uncertainty induced by the time integration of ordinary differential equations (ODEs) is introduced. Departing from the classical strategy to randomize ODE solvers by adding a…
Prior to the recent development of symplectic integrators, the time-stepping operator $\e^{h(A+B)}$ was routinely decomposed into a sum of products of $\e^{h A}$ and $\e^{hB}$ in the study of hyperbolic partial differential equations. In…
By combining a standard symmetric, symplectic integrator with a new step size controller, we provide an integration scheme that is symmetric, reversible and conserves the values of the constants of motion. This new scheme is appropriate for…
Among the family of fourth-order time integration schemes, the two-stage Gauss--Legendre method, which is an implicit Runge--Kutta method based on collocation, is the only superconvergent. The computational cost of this implicit scheme for…
We present two types of meta-algorithm that can greatly improve the accuracy of existing algorithms for integrating the equations of motion of dynamical systems. The first meta-algorithm takes an integrator that is time-symmetric only for…
We present a novel methodology for constructing arbitrarily high-order structure-preserving methods tailored for damped Hamiltonian systems. This method combines the idea of exponential integrator and energy-preserving collocation methods,…
Structure-preserving linearly implicit exponential integrators are constructed for Hamiltonian partial differential equations with linear constant damping. Linearly implicit integrators are derived by polarizing the polynomial terms of the…
Exponential integrators are time stepping schemes which exactly solve the linear part of a semilinear ODE system. This class of schemes requires the approxima- tion of a matrix exponential in every step, and one successful modern method is…
Stochastic nonlinear dynamical systems can undergo rapid transitions relative to the change in their forcing, for example due to the occurrence of multiple equilibrium solutions for a specific interval of parameters. In this paper, we…
In this paper, we construct high order energy dissipative and conservative local discontinuous Galerkin methods for the Fornberg-Whitham type equations. We give the proofs for the dissipation and conservation for related conservative…
We present a second-order ensemble method based on a blended three-step backward differentiation formula (BDF) timestepping scheme to compute an ensemble of Navier-Stokes equations. Compared with the only existing second-order ensemble…
Exponential integrators are a well-known class of time integration methods that have been the subject of many studies and developments in the past two decades. Surprisingly, there have been limited efforts to analyze their stability and…
Hamiltonian Monte Carlo is a prominent Markov Chain Monte Carlo algorithm, which employs symplectic integrators to sample from high dimensional target distributions in many applications, such as statistical mechanics, Bayesian statistics…