102 citations · 190 across the 17 of their papers we have counts for
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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…
Asymptotic Analysis on the Sharp Interface Limit of the Time-Fractional Cahn--Hilliard Equation
Tao Tang, Boyi Wang, Jiang Yang
In this paper, we aim to study the motions of interfaces and coarsening rates governed by the time-fractional Cahn--Hilliard equation (TFCHE). It is observed by many numerical expe…
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…
Generalization Error Analysis of Neural networks with Gradient Based Regularization
Lingfeng Li, Xue-Cheng Tai, Jiang Yang
We study gradient-based regularization methods for neural networks. We mainly focus on two regularization methods: the total variation and the Tikhonov regularization. Applying the…
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…