167 citations · 494 across the 32 of their papers we have counts for
32 papers
Low regularity integrators for semilinear parabolic equations with maximum bound principles
Cao-Kha Doan, Thi-Thao-Phuong Hoang, Lili Ju +1
This paper is concerned with conditionally structure-preserving, low regularity time integration methods for a class of semilinear parabolic equations of Allen-Cahn type. Important…
A linear second-order maximum bound principle-preserving BDF scheme for the Allen-Cahn equation with a general mobility
Dianming Hou, Lili Ju, Zhonghua Qiao
In this paper, we propose and analyze a linear second-order numerical method for solving the Allen-Cahn equation with a general mobility. The proposed fully-discrete scheme is care…
Efficient Exponential Integrator Finite Element Method for Semilinear Parabolic Equations
Jianguo Huang, Lili Ju, Yuejin Xu
In this paper, we propose an efficient exponential integrator finite element method for solving a class of semilinear parabolic equations in rectangular domains. The proposed metho…
A Multifidelity Monte Carlo Method for Realistic Computational Budgets
Anthony Gruber, Max Gunzburger, Lili Ju +1
A method for the multifidelity Monte Carlo (MFMC) estimation of statistical quantities is proposed which is applicable to computational budgets of any size. Based on a sequence of…
Energetically Consistent Model Reduction for Metriplectic Systems
Anthony Gruber, Max Gunzburger, Lili Ju +1
The metriplectic formalism is useful for describing complete dynamical systems which conserve energy and produce entropy. This creates challenges for model reduction, as the elimin…
Stabilized exponential-SAV schemes preserving energy dissipation law and maximum bound principle for the Allen-Cahn type equations
Lili Ju, Xiao Li, Zhonghua Qiao
It is well-known that the Allen-Cahn equation not only satisfies the energy dissipation law but also possesses the maximum bound principle (MBP) in the sense that the absolute valu…
Generalized SAV-exponential integrator schemes for Allen-Cahn type gradient flows
Lili Ju, Xiao Li, Zhonghua Qiao
The energy dissipation law and the maximum bound principle (MBP) are two important physical features of the well-known Allen-Cahn equation. While some commonly-used first-order tim…
Level set learning with pseudo-reversible neural networks for nonlinear dimension reduction in function approximation
Yuankai Teng, Zhu Wang, Lili Ju +2
Due to the curse of dimensionality and the limitation on training data, approximating high-dimensional functions is a very challenging task even for powerful deep neural networks.…
A Comparison of Neural Network Architectures for Data-Driven Reduced-Order Modeling
Anthony Gruber, Max Gunzburger, Lili Ju +1
The popularity of deep convolutional autoencoders (CAEs) has engendered new and effective reduced-order models (ROMs) for the simulation of large-scale dynamical systems. Despite t…
Unconditionally stable exponential time differencing schemes for the mass-conserving Allen-Cahn equation with nonlocal and local effects
Kun Jiang, Lili Ju, Jingwei Li +1
It is well known that the classic Allen-Cahn equation satisfies the maximum bound principle (MBP), that is, the absolute value of its solution is uniformly bounded for all time by…
Parallel Exponential Time Differencing Methods for Geophysical Flow Simulations
Rihui Lan, Wei Leng, Zhu Wang +2
Two ocean models are considered for geophysical flow simulations: the multi-layer shallow water equations and the multi-layer primitive equations. For the former, we investigate th…
High-Order Multirate Explicit Time-Stepping Schemes for the Baroclinic-Barotropic Split Dynamics in Primitive Equations
Rihui Lan, Lili Ju, Zhu Wang +2
In order to treat the multiple time scales of ocean dynamics in an efficient manner, the baroclinic-barotropic splitting technique has been widely used for solving the primitive eq…
Learning Green's Functions of Linear Reaction-Diffusion Equations with Application to Fast Numerical Solver
Yuankai Teng, Xiaoping Zhang, Zhu Wang +1
Partial differential equations are often used to model various physical phenomena, such as heat diffusion, wave propagation, fluid dynamics, elasticity, electrodynamics and image p…
DANNet: A One-Stage Domain Adaptation Network for Unsupervised Nighttime Semantic Segmentation
Xinyi Wu, Zhenyao Wu, Hao Guo +2
Semantic segmentation of nighttime images plays an equally important role as that of daytime images in autonomous driving, but the former is much more challenging due to poor illum…
Stabilized integrating factor Runge-Kutta method and unconditional preservation of maximum bound principle
Jingwei Li, Xiao Li, Lili Ju +1
Maximum bound principle (MBP) is an important property for a large class of semilinear parabolic equations, in the sense that the time-dependent solution of the equation with appro…
Nonlinear Level Set Learning for Function Approximation on Sparse Data with Applications to Parametric Differential Equations
Anthony Gruber, Max Gunzburger, Lili Ju +2
A dimension reduction method based on the "Nonlinear Level set Learning" (NLL) approach is presented for the pointwise prediction of functions which have been sparsely sampled. Lev…
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…
Maximum bound principles for a class of semilinear parabolic equations and exponential time differencing schemes
Qiang Du, Lili Ju, Xiao Li +1
The ubiquity of semilinear parabolic equations has been illustrated in their numerous applications ranging from physics, biology, to materials and social sciences. In this paper, w…
Trace Transfer-based Diagonal Sweeping Domain Decomposition Method for the Helmholtz Equation: Algorithms and Convergence Analysis
Wei Leng, Lili Ju
By utilizing the perfectly matched layer (PML) and source transfer techniques, the diagonal sweeping domain decomposition method (DDM) was recently developed for solving the high-f…
A diagonal sweeping domain decomposition method with source transfer for the Helmholtz equation
Wei Leng, Lili Ju
In this paper, we propose and test a novel diagonal sweeping domain decomposition method (DDM) with source transfer for solving the high-frequency Helmholtz equation in $\mathbb{R}…
Conservative numerical schemes with optimal dispersive wave relations -- Part II. Numerical evaluations
Qingshan Chen, Lili Ju, Roger Temam
A new energy and enstrophy conserving scheme is evaluated using a suite of test cases over the global spherical domain or bounded domains. The evaluation is organized around a set…
Conservative numerical schemes with optimal dispersive wave relations -- Part I. Derivations and analyses
Qingshan Chen, Lili Ju, Roger Temam
An energy-conserving and an energy-and-enstrophy conserving numerical schemes are derived, by approximating the Hamiltonian formulation, based on the Poisson brackets and the vorti…
High Order Explicit Local Time-Stepping Methods For Hyperbolic Conservation Laws
Thi-Thao-Phuong Hoang, Lili Ju, Wei Leng +1
In this paper we present and analyze a general framework for constructing high order explicit local time stepping (LTS) methods for hyperbolic conservation laws. In particular, we…
Maximum principle preserving exponential time differencing schemes for the nonlocal Allen-Cahn equation
Qiang Du, Lili Ju, Xiao Li +1
The nonlocal Allen-Cahn (NAC) equation is a generalization of the classic Allen-Cahn equation by replacing the Laplacian with a parameterized nonlocal diffusion operator, and satis…