Jingzhi Li

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 $n -$ d, $n \geq 2$ 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…

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…

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…

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…

math.NA2023★ 1 cited

Locating multiple magnetized anomalies by geomagnetic monitoring

Rongliang Chen, Youjun Deng, Yang Gao +2

The presence of magnetized anomalies in the shell of the Earth interrupts its geomagnetic field. We consider the inverse problem of identifying the anomalies by monitoring the vari…

Convexification Numerical Method for a Coefficient Inverse Problem for the Riemannian Radiative Transfer Equation

Michael V. Klibanov, Jingzhi Li, Loc H. Nguyen +2

The first globally convergent numerical method for a Coefficient Inverse Problem (CIP) for the Riemannian Radiative Transfer Equation (RRTE) is constructed. This is a version of th…

A priori error estimates of two fully discrete coupled schemes for Biot's consolidation model

Huipeng Gu, Mingchao Cai, Jingzhi Li +1

This paper concentrates on a priori error estimates of two fully discrete coupled schemes for Biot's consolidation model based on the three-field formulation introduced by Oyarzua…

Numerical Solution of the 3-D Travel Time Tomography Problem

Michael V. Klibanova Jingzhi Li, Wenlong Zhang

The first numerical solution of the 3-D travel time tomography problem is presented. The globally convergent convexification numerical method is applied.