相关论文: Hybrid Explicit-Implicit Predictor-Corrector Expon…

ADER (Arbitrary DERivative in space and time) methods for the time-evolution of hyperbolic conservation laws have recently generated a fair bit of interest. The ADER time update can be carried out in a single step, which is desirable in…

A single-step high-order implicit time integration scheme for the solution of transient and wave propagation problems is presented. It is constructed from the Pad\'e expansions of the matrix exponential solution of a system of first-order…

Time delays are ubiquitous in industry and nature, and they significantly affect both transient dynamics and stability properties. Consequently, it is often necessary to identify and account for the delays when, e.g., designing a…

Empirical mode decomposition (EMD) has developed into a prominent tool for adaptive, scale-based signal analysis in various fields like robotics, security and biomedical engineering. Since the dramatic increase in amount of data puts…

Parabolic optimal control problems with control constraints are generally challenging, from either theoretical analysis or algorithmic design perspectives. Conceptually, the well-known alternating direction method of multipliers (ADMM) can…

This paper develops methods for numerically solving stochastic delay-differential equations (SDDEs) with multiple fixed delays that do not align with a uniform time mesh. We focus on numerical schemes of strong convergence orders $1/2$ and…

In this paper we extend the polynomial time integration framework to include exponential integration for both partitioned and unpartitioned initial value problems. We then demonstrate the utility of the exponential polynomial framework by…

This work aims to extend the residual distribution (RD) framework to stiff relaxation problems. The RD is a class of schemes which is used to solve hyperbolic system of partial differential equations. Up to our knowledge, it was used only…

The applicability of the Parareal parallel-in-time integration scheme for the solution of a linear, two-dimensional hyperbolic acoustic-advection system, which is often used as a test case for integration schemes for numerical weather…

In this work, we provide a deep investigation of a family of arbitrary high order numerical methods for hyperbolic partial differential equations (PDEs), with particular emphasis on very high order versions, i.e., with order higher than 5.…

The nonequilibrium Green's function (NEGF) formalism is a powerful tool to study the nonequilibrium dynamics of correlated lattice systems, but its applicability to realistic system sizes and long timescales is limited by unfavorable memory…

Fully implicit Runge-Kutta (IRK) methods have many desirable accuracy and stability properties as time integration schemes, but high-order IRK methods are not commonly used in practice with large-scale numerical PDEs because of the…

Neural network-based solvers for partial differential equations (PDEs) have attracted considerable attention, yet they often face challenges in accuracy and computational efficiency. In this work, we focus on time-dependent PDEs and observe…

This paper is concerned about the implicit-explicit (IMEX) methods for a class of dissipative wave systems with time-varying velocity feedbacks and nonlinear potential energies, equipped with different boundary conditions. Firstly, we…

In this study, we propose a class of total variation diminishing (TVD) schemes for solving pseudo-monotone variational inequality arises in elasto-hydrodynamic lubrication point contact problem. A limiter based stable hybrid line splittings…

This thesis examines the empirical mode decomposition (EMD), a method for decomposing multicomponent signals, from a modern, both theoretical and practical, perspective. The motivation is to further formalize the concept and develop new…

Off-policy learning allows us to learn about possible policies of behavior from experience generated by a different behavior policy. Temporal difference (TD) learning algorithms can become unstable when combined with function approximation…

In this paper, we propose a new algorithm for the estimation of multiple time delays (TDs). Since a TD is a fundamental spatial cue for sensor array signal processing techniques, many methods for estimating it have been studied. Most of…

In [13], an Inexact variant of Stochastic Dual Dynamic Programming (SDDP) called ISDDP was introduced which uses approximate (instead of exact with SDDP) primal dual solutions of the problems solved in the forward and backward passes of the…

The implementation of the discrete adjoint method for exponential time differencing (ETD) schemes is considered. This is important for parameter estimation problems that are constrained by stiff time-dependent PDEs when the discretized PDE…