293 citations · 634 across the 48 of their papers we have counts for
48 papers
Exponential Low-Regularity Parareal Algorithms for Nonlinear Schrödinger Equations
Qingle Lin, Zhi Zhou
The parareal algorithm is one of the most widely studied parallel-in-time methods for the numerical approximation of time-dependent problems. For non-diffusive equations, however,…
Linear Convergence of Parareal Algorithm for Semilinear Parabolic Equations
Guanglian Li, Qingle Lin, Shu-lin Wu +1
Long-time simulations of evolution equations present substantial computational challenges due to the inherently sequential nature of conventional time-stepping schemes. The pararea…
Dual Variational Neural Network for the -Laplace Problem
Tianhao Hu, Guanglian Li, Fengru Wang +2
The reliable and accurate numerical approximation of the -Laplacian is particularly challenging in the extreme regimes and , where the operator becomes ei…
Convergence analysis of a parareal algorithm with multistep fine propagator
Georgios Akrivis, Qingle Lin, Zhi Zhou
The parareal algorithm is a powerful parallel-in-time integration method that accelerates the numerical solution of evolution equations by iteratively combining a fine propagator a…
Optimized Two-Step Coarse Propagators in Parareal Algorithms
Guanglian Li, Qingle Lin, Kai Zhang +1
In this work, we propose a novel framework for accelerating the parareal algorithm, in which the coarse propagator is formulated as a two-step method and optimized with respect to…
Regularity Analysis and High-Order Time Stepping Scheme for Quasilinear Subdiffusion
Bangti Jin, Qimeng Quan, Barbara Wohlmuth +1
In this work, we investigate a quasilinear subdiffusion model which involves a fractional derivative of order in time and a nonlinear diffusion coefficient. First, usi…
Numerical Recovery of the Diffusion Coefficient in Diffusion Equations from Terminal Measurement
Bangti Jin, Xiliang Lu, Qimeng Quan +1
In this work, we investigate a numerical procedure for recovering a space-dependent diffusion coefficient in a (sub)diffusion model from the given terminal data, and provide a rigo…
Inverse Coefficient Problem for One-Dimensional Subdiffusion with Data on Disjoint Sets in Time
Siyu Cen, Bangti Jin, Yavar Kian +3
In this work we investigate an inverse coefficient problem for the one-dimensional subdiffusion model, which involves a Caputo fractional derivative in time. The inverse problem is…
Numerical Recovery of a Time-Dependent Potential in Subdiffusion
Bangti Jin, Kwancheol Shin, Zhi Zhou
In this work we investigate an inverse problem of recovering a time-dependent potential in a semilinear subdiffusion model from an integral measurement of the solution over the dom…
Optimizing Coarse Propagators in Parareal Algorithms
Bangti Jin, Qingle Lin, Zhi Zhou
The parareal algorithm represents an important class of parallel-in-time algorithms for solving evolution equations and has been widely applied in practice. To achieve effective sp…
Numerical Reconstruction of Diffusion and Potential Coefficients from Two Observations: Decoupled Recovery and Error Estimates
Siyu Cen, Zhi Zhou
The focus of this paper is on the concurrent reconstruction of both the diffusion and potential coefficients present in an elliptic/parabolic equation, utilizing two internal measu…
Solving Poisson Problems in Polygonal Domains with Singularity Enriched Physics Informed Neural Networks
Tianhao Hu, Bangti Jin, Zhi Zhou
Physics-Informed Neural Networks (PINNs) are a powerful class of numerical solvers for partial differential equations, employing deep neural networks with successful applications a…
Solving Elliptic Optimal Control Problems via Neural Networks and Optimality System
Yongcheng Dai, Bangti Jin, Ramesh Sau +1
In this work, we investigate a neural network based solver for optimal control problems (without / with box constraint) for linear and semilinear second-order elliptic problems. It…
High-order splitting finite element methods for the subdiffusion equation with limited smoothing property
Buyang Li, Zongze Yang, Zhi Zhou
In contrast with the diffusion equation which smoothens the initial data to for (away from the corners/edges of the domain), the subdiffusion equation only exhibit…
Recovery of Multiple Parameters in Subdiffusion from One Lateral Boundary Measurement
Siyu Cen, Bangti Jin, Yikan Liu +1
This work is concerned with numerically recovering multiple parameters simultaneously in the subdiffusion model from one single lateral measurement on a part of the boundary, while…
Electrical Impedance Tomography with Deep Calderón Method
Siyu Cen, Bangti Jin, Kwancheol Shin +1
Electrical impedance tomography (EIT) is a noninvasive medical imaging modality utilizing the current-density/voltage data measured on the surface of the subject. Calderón's method…
Conductivity Imaging from Internal Measurements with Mixed Least-Squares Deep Neural Networks
Bangti Jin, Xiyao Li, Qimeng Quan +1
In this work we develop a novel approach using deep neural networks to reconstruct the conductivity distribution in elliptic problems from one measurement of the solution over the…
Hybrid Neural-Network FEM Approximation of Diffusion Coefficient in Elliptic and Parabolic Problems
Siyu Cen, Bangti Jin, Qimeng Quan +1
In this work we investigate the numerical identification of the diffusion coefficient in elliptic and parabolic problems using neural networks. The numerical scheme is based on the…
Solving Elliptic Problems with Singular Sources using Singularity Splitting Deep Ritz Method
Tianhao Hu, Bangti Jin, Zhi Zhou
In this work, we develop an efficient solver based on neural networks for second-order elliptic equations with variable coefficients and singular sources. This class of problems co…
Stability and numerical analysis of backward problem for subdiffusion with time-dependent coefficients
Zhengqi Zhang, Zhi Zhou
Our aim is to study the backward problem, i.e. recover the initial data from the terminal observation, of the subdiffusion with time dependent coefficients. First of all, by using…
Modified BDF2 schemes for subdiffusion models with a singular source term
Minghua Chen, Jiankang Shi, Zhi Zhou
The aim of this paper is to study the time stepping scheme for approximately solving the subdiffusion equation with a weakly singular source term. In this case, many popular time s…
Convergence Rate Analysis of Galerkin Approximation of Inverse Potential Problem
Bangti Jin, Xiliang Lu, Qimeng Quan +1
In this work we analyze the inverse problem of recovering the space-dependent potential coefficient in an elliptic / parabolic problem from distributed observation. We establish no…
Nonlocal diffusion models with consistent local and fractional limits
Qiang Du, Xiaochuan Tian, Zhi Zhou
For some spatially nonlocal diffusion models with a finite range of nonlocal interactions measured by a positive parameter , we review their formulation defined on a bounded dom…
Recovery of a Space-Time Dependent Diffusion Coefficient in Subdiffusion: Stability, Approximation and Error Analysis
Bangti Jin, Zhi Zhou
In this work, we study an inverse problem of recovering a space-time dependent diffusion coefficient in the subdiffusion model from the distributed observation, where the mathemati…