102 citations · 190 across the 17 of their papers we have counts for
13 papers · 1 filter
Long time -stability of fast L2-1 method on general nonuniform meshes for subdiffusion equations
Chaoyu Quan, Xu Wu, Jiang Yang
In this work, the global-in-time -stability of a fast L2-1 method on general nonuniform meshes is studied for subdiffusion equations, where the convolution kernel in the C…
Priori Error Estimate of Deep Mixed Residual Method for Elliptic PDEs
Lingfeng Li, Xue-cheng Tai, Jiang Yang +1
In this work, we derive a priori error estimate of the mixed residual method when solving some elliptic PDEs. Our work is the first theoretical study of this method. We prove that…
Energy plus maximum bound preserving Runge-Kutta methods for the Allen-Cahn equation
Zhaohui Fu, Tao Tang, Jiang Yang
It is difficult to design high order numerical schemes which could preserve both the maximum bound property (MBP) and energy dissipation law for certain phase field equations. Stro…
Energy diminishing implicit-explicit Runge--Kutta methods for gradient flows
Zhaohui Fu, Tao Tang, Jiang Yang
This study focuses on the development and analysis of a group of high-order implicit-explicit (IMEX) Runge--Kutta (RK) methods that are suitable for discretizing gradient flows wit…
A decreasing upper bound of energy for time-fractional phase-field equations
Chaoyu Quan, Tao Tang, Boyi Wang +1
In this article, we study the energy dissipation property of time-fractional Allen-Cahn equation. We propose a decreasing upper bound of energy that decreases with respect to time…
Robust Convergence of Parareal Algorithms with Arbitrarily High-order Fine Propagators
Jiang Yang, Zhaoming Yuan, Zhi Zhou
The aim of this paper is to analyze the robust convergence of a class of parareal algorithms for solving parabolic problems. The coarse propagator is fixed to the backward Euler me…
A provably efficient monotonic-decreasing algorithm for shape optimization in Stokes flows by phase-field approaches
Futuan Li, Jiang Yang
In this work, we study shape optimization problems in the Stokes flows. By phase-field approaches, the resulted total objective function consists of the dissipation energy of the f…
A Local Deep Learning Method for Solving High Order Partial Differential Equations
Quanhui Zhu, Jiang Yang
At present, deep learning based methods are being employed to resolve the computational challenges of high-dimensional partial differential equations (PDEs). But the computation of…
Arbitrarily High-order Maximum Bound Preserving Schemes with Cut-off Postprocessing for Allen-Cahn Equations
Jiang Yang, Zhaoming Yuan, Zhi Zhou
We develop and analyze a class of maximum bound preserving schemes for approximately solving Allen--Cahn equations. We apply a th-order single-step scheme in time (where the non…
Maximum bound principle preserving integrating factor Runge-Kutta methods for semilinear parabolic equations
Lili Ju, Xiao Li, Zhonghua Qiao +1
A large class of semilinear parabolic equations satisfy the maximum bound principle (MBP) in the sense that the time-dependent solution preserves for any time a uniform pointwise b…
Arbitrarily high-order exponential cut-off methods for preserving maximum principle of parabolic equations
Buyang Li, Jiang Yang, Zhi Zhou
A new class of high-order maximum principle preserving numerical methods is proposed for solving parabolic equations, with application to the semilinear Allen--Cahn equation. The p…
Numerical Energy Dissipation for Time-Fractional Phase-Field Equations
Chaoyu Quan, Tao Tang, Jiang Yang
The numerical integration of phase-field equations is a delicate task which needs to recover at the discrete level intrinsic properties of the solution such as energy dissipation a…
Time-Fractional Allen-Cahn Equations: Analysis and Numerical Methods
Qiang Du, Jiang Yang, Zhi Zhou
In this work, we consider a time-fractional Allen-Cahn equation, where the conventional first order time derivative is replaced by a Caputo fractional derivative with order $α\in(0…