52 citations · 371 across the 64 of their papers we have counts for
68 papers
Pressure Monotonicity for a Rotation-Based Biot Discretization with Circumcentric Mass Lumping
Huipeng Gu, Mingchao Cai, Jingzhi Li
We establish cellwise pressure monotonicity for a mixed finite element discretization of the rotation-based Biot system. The spatial discretization is based on compatible discrete…
Iterative Decoupling Methods for a Total-Pressure Formulation of Quasi-Static Electroporoelasticity
Huipeng Gu, Mingchao Cai, Jingzhi Li
Quasi-static electroporoelasticity couples Maxwell's equations with Biot's poroelasticity through electrokinetic coupling between the electric field and the pressure gradient. By i…
A Unified Model for Thermo- and Multiple-Network Poroelasticity with a Global-in-Time Iterative Decoupling Scheme
Huipeng Gu, Mingchao Cai, Jingzhi Li +1
This paper introduces a unified model for thermo-poroelasticity and multiple-network poroelasticity, reformulated into a total-pressure-based system. We first establish the well-po…
Global Convergence and Uniqueness for an Inverse Problem Posed by Gelfand
Michael V. Klibanov, Jingzhi Li, Tian Niu +1
The first globally convergent numerical method is developed for a coefficient inverse problem (CIP) for the d, wave equation with the unknown potential in the most ch…
Convexification Numerical Method for Imaging of Moving Targets
Michael V. Klibanov, Jingzhi Li, Vladimir G. Romanov +1
The problem of imaging of a moving target is formulated as a Coefficient Inverse Problem for a hyperbolic equation with its coefficient depending on all three spatial variables and…
POD-based reduced order modeling of global-in-time iterative decoupled algorithms for Biot's consolidation model
Huipeng Gu, Francesco Ballarin, Mingchao Cai +1
This paper focuses on the efficient numerical algorithms of a three-field Biot's consolidation model. The approach begins with the introduction of innovative monolithic and global-…
Some semi-decoupled algorithms with optimal convergence for a four-field linear thermo-poroelastic model
Ziliang Li, Mingchao Cai, Jingzhi Li +1
We propose three semi-decoupled algorithms for efficiently solving a four-field thermoporoelastic model. The first two algorithms adopt a sequential strategy: at the initial time s…
FaceInsight: A Multimodal Large Language Model for Face Perception
Jingzhi Li, Changjiang Luo, Ruoyu Chen +4
Recent advances in multimodal large language models (MLLMs) have demonstrated strong capabilities in understanding general visual content. However, these general-domain MLLMs perfo…
Convexification With the Viscocity Term for Electrical Impedance Tomography
Michael V. Klibanov, Jingzhi Li, Zhipeng Yang
A version of the globally convergent convexification numerical method is constructed for the problem of Electrical Impedance Tomography in the 2D case. An important element of this…
An Efficient Iterative Decoupling Method for Thermo-Poroelasticity Based on a Four-Field Formulation
Mingchao Cai, Jingzhi Li, Ziliang Li +1
This paper studies the thermo-poroelasticity model. By introducing an intermediate variable, we transform the original three-field model into a four-field model. Building upon this…
Parameter-Robust Preconditioners for A Four-Field Thermo-Poroelasticity Model
Mingchao Cai, Miroslav Kuchta, Jingzhi Li +2
We study a thermo-poroelasticity model which describes the interaction between the deformation of an elastic porous material and fluid flow under non-isothermal conditions. The mod…
Shape Taylor expansion for wave scattering problems
Gang Bao, Haoran Ma, Jun Lai +1
The Taylor expansion of wave fields with respect to shape parameters has a wide range of applications in wave scattering problems, including inverse scattering, optimal design, and…
Crank-Nicolson-type iterative decoupled algorithms for Biot's consolidation model using total pressure
Huipeng Gu, Mingchao Cai, Jingzhi Li
In this work, we develop Crank-Nicolson-type iterative decoupled algorithms for a three-field formulation of Biot's consolidation model using total pressure. We begin by constructi…
Convexification for the 3D Problem of Travel Time Tomography
Michael V. Klibanov, Jingzhi Li, Vladimir G. Romanov +1
The travel time tomography problem is a coefficient inverse problem for the eikonal equation. This problem has well known applications in seismic. The eikonal equation is considere…
Convexification for a Coefficient Inverse Problem for a System of Two Coupled Nonlinear Parabolic Equations
Michael V. Klibanov, Jingzhi Li, Zhipeng Yang
A system of two coupled nonlinear parabolic partial differential equations with two opposite directions of time is considered. In fact, this is the so-called "Mean Field Games Syst…
Spatiotemporal Monitoring of Epidemics via Solution of a Coefficient Inverse Problem
Michael V. Klibanov, Jingzhi Li, Zhipeng Yang
Let S,I and R be susceptible, infected and recovered populations in a city affected by an epidemic. The SIR model of Lee, Liu, Tembine, Li and Osher, \emph{SIAM J. Appl. Math.},~81…
Hölder Stability Estimate for a Retrospective Problem of Mean Field Games With a Non-Quadratic Hamiltonian
Michael V. Klibanov, Mikhail Y. Kokurin, Jingzhi Li
Hölder stability estimate and uniqueness are proven for a retrospective problem of Mean Field Games with a non-quadratic Hamiltonian. The previous result was only for the quadratic…
Convexification for a Coefficient Inverse Problem of Mean Field Games
Michael V. Klibanov, Jingzhi Li, Zhipeng Yang
The globally convergent convexification numerical method is constructed for a Coefficient Inverse Problem for the Mean Field Games System. A coefficient characterizing the global i…
An Iteratively Decoupled Algorithm for Multiple-Network Poroelastic Model with Applications in Brain Edema Simulations
Mingchao Cai, Meng Lei, Jingzhi Li +2
In this work, we present an iteratively decoupled algorithm for solving the quasi-static multiple-network poroelastic model. Our approach employs a total-pressure-based formulation…
Convexification Numerical Method for the Retrospective Problem of Mean Field Games
Michael V. Klibanov, Jingzhi Li, Zhipeng Yang
The convexification numerical method with the rigorously established global convergence property is constructed for a problem for the Mean Field Games System of the second order. T…
An Inverse Problem With the Final Overdetermination for the Mean Field Games System
Michael V. Klibanov, Jingzhi Li, Hongyu Liu
The mean field games (MFG) theory has broad application in mathematical modeling of social phenomena. The Mean Field Games System (MFGS) is the key to the MFG theory. This is a sys…
Hölder Stability and Uniqueness for The Mean Field Games System via Carleman Estimates
Michael V. Klibanov, Jingzhi Li, Hongyu Liu
We are concerned with the mathematical study of the Mean Field Games system (MFGS). In the conventional setup, the MFGS is a system of two coupled nonlinear parabolic PDEs of the s…
Convexification for the Viscocity Solution for a Coefficient Inverse Problem for the Radiative Transfer Equation
Michael V. Klibanov, Jingzhi Li, Zhipeng Yang
A Coefficient Inverse Problem for the radiative transport equation is considered. The globally convergent numerical method, the so-called convexification, is developed. For the fir…
On The Mean Field Games System With the Lateral Cauchy Data via Carleman Estimates
Michael V. Klibanov, Jingzhi Li, Hongyu Liu
The second order Mean Field Games system (MFGS) in a bounded domain with the lateral Cauchy data is considered. This means that both Dirichlet and Neumann boundary data for the sol…