Related papers: Provably Stable Full-Spectrum Dispersion Relation …
This article presents the formulation and steady-state analysis of the distributed estimation algorithms based on the diffusion cooperation scheme in the presence of errors due to the unreliable data transfer among nodes. In particular, we…
We are concerned with fully-discrete schemes for the numerical approximation of diffusive-dispersive hyperbolic conservation laws with a discontinuous flux function in one-space dimension. More precisely, we show the convergence of…
Let $P$ be a set of points in $\mathbb{R}^d$, where each point $p\in P$ has an associated transmission range $\rho(p)$. The range assignment $\rho$ induces a directed communication graph $\mathcal{G}_{\rho}(P)$ on $P$, which contains an…
We develop an asymptotic preserving scheme for the gray radiative transfer equation. Two asymptotic regimes are considered: one is a diffusive regime described by a nonlinear diffusion equation for the material temperature; the other is a…
The main contribution of this work is to construct and analyze stable and high order schemes to efficiently solve the two-dimensional time Caputo-Fabrizio fractional diffusion equation. Based on a third-order finite difference method in…
Splitting methods constitute a widely used class of numerical integrators for ordinary and partial differential equations, particularly well suited to problems that can be decomposed into simpler subproblems. High-order splitting schemes…
We address the propagation into an unstable state of a localised disturbance in a forward-backward diffusion pseudo-parabolic equation. Three asymptotic regimes are distinguished as t tends to infinity, the first being a regime ahead of the…
We introduced and analyzed robust recovery-based a posteriori error estimators for various lower order finite element approximations to interface problems in [9, 10], where the recoveries of the flux and/or gradient are implicit (i.e.,…
Fractional differential equations (FDEs) are an extension of the theory of fractional calculus. However, due to the difficulty in finding analytical solutions, there have not been extensive applications of FDEs until recent decades. With…
We present an in-depth analysis regarding the error resistance and optimization of our all-optical Bell measurement and ultrafast long-distance quantum communication scheme proposed in [arXiv:1503.06777]. In order to promote our previous…
In order to improve the application maturity of high-order difference schemes, the free-stream preservation property, whose importance has been widely recognized in recent years, has been developed into a focus of study.. In past…
In this paper, we propose a high order residual distribution conservative finite difference scheme for solving steady state conservation laws. A new type of WENO (weighted essentially non-oscillatory) termed as WENO-ZQ integration is used…
We discuss the stability theory and numerical analysis of the Helmholtz equation with variable and possibly non-smooth or oscillatory coefficients. Using the unique continuation principle and the Fredholm alternative, we first give an…
Inspired by recent developments in the theory of stability results in the context of certain wave type phenomena, we discuss abstract damped hyperbolic type equations given in a block operator matrix form with regards to asymptotic…
We study some maximum principle preserving and energy stable schemes for the Allen-Cahn-Ohta-Kawasaki model with fixed volume constraint. With the inclusion of a nonlinear term in the Ohta-Kawasaki free energy functional, we show that the…
Synchronizations of processing elements (PEs) in massively parallel simulations, which arise due to communication or load imbalances between PEs, significantly affect the scalability of scientific applications. We have recently proposed a…
It is well-known that reliable and efficient domain truncation is crucial to accurate numerical solution of most wave propagation problems. The perfectly matched layer (PML) is a method which, when stable, can provide a domain truncation…
The finite-difference time-domain (FDTD) algorithm is a popular numerical method for solving electromagnetic problems. FDTD simulations can suffer from instability due to the explicit nature of the method. Stability enforcement can be…
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…
We develop structure-preserving numerical methods for the Serre-Green-Naghdi equations, a model for weakly dispersive free-surface waves. We consider both the classical form, requiring the inversion of a non-linear elliptic operator, and a…