Article
Mathematics, Applied
Lingde Su, Jian Huang, V. I. Vasil'ev, Ao Li, A. M. Kardashevsky
Summary: An effective numerical method is proposed in this paper for solving the inverse problem of a time fractional parabolic equation. The method is shown to be efficient and stable in solving the inverse problem, even with noisy measurements, through numerical experiments.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Guang Lin, Zecheng Zhang, Zhidong Zhang
Summary: This paper investigates the inverse source problem in the parabolic equation with a semi-discrete unknown source. The authors theoretically prove that the flux data from any nonempty open subset of the boundary can uniquely determine the semi-discrete source. For numerical reconstruction, they propose a Bayesian sequential prediction approach and conduct numerical examples to estimate the space-time-dependent source state. The results demonstrate the accuracy and efficiency of the inversion.
Article
Mathematics, Applied
Qin Zhou, Binjie Li
Summary: This paper analyzes the discretization of a Neumann boundary control problem with a stochastic parabolic equation, where an additive noise occurs in the Neumann boundary condition. The convergence is established for general filtration, and the convergence rate O(tau(1/4-epsilon)+h(1/2-epsilon)) is derived for the natural filtration of the Q-Wiener process.
SCIENCE CHINA-MATHEMATICS
(2023)
Article
Mathematics, Applied
Binjie Li, Qin Zhou
Summary: This paper analyzes the discretization of an optimal control problem of a stochastic parabolic equation driven by multiplicative noise. The state equation is discretized using the Continuous Piecewise Linear Element method in space and the Backward Euler scheme in time, with a rigorously derived convergence rate of O(tau(1/2) + h(2)).
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Computer Science, Artificial Intelligence
S. D. Agashe, B. K. Lande, Vanita Jain, Gopal Chaudhary, Fadi Al-turjman
Summary: This paper proposes a new method for computing the optimal control, which steers the initial state of a system to a specified or unspecified point in the state space by minimizing a given performance index. The classical Calculus of Variations and the modern approach of variation in control that leads to Pontriagin's principle are compared. By deriving the maximum principle of Pontriagin using the classical Calculus of Variations modified with brief perturbation, an expression for the change in the value of performance index is obtained. Three examples are provided to demonstrate the feasibility of the derived methods.
Article
Mathematics
Yilihamujiang Yimamu, Zuicha Deng
Summary: Based on the theoretical framework of the Black-Scholes model, this study investigates the convergence of the inverse volatility problem in degenerate parabolic equations. By introducing variable substitutions, the problem is transformed into an inverse principal coefficient problem in a bounded area, allowing the recovery of an unknown volatility and the resolution of deficiencies caused by artificial truncation. Using the optimal control framework, the problem is transformed into an optimization problem, and the existence and convergence of the optimal solution are mathematically proven.
Article
Mathematics
Ebru Ozbilge, Fatma Kanca, Emre Ozbilge
Summary: This article discusses the inverse problem of time fractional parabolic partial differential equations with nonlocal boundary conditions. It uses Dirichlet-measured output data to identify the unknown coefficients and constructs a finite difference scheme for numerical approximation. Examples and numerical experiments, such as man-made noise, are provided to demonstrate the stability and efficiency of this numerical method.
Article
Physics, Multidisciplinary
Zui-Cha Deng, Liu Yang
Summary: This work focuses on solving the inverse problem of identifying the refractive index in terrain parabolic equations. The problem has important applications in various applied scientific fields. The study proposes an optimal control framework to transform the recognition problem into an optimization problem and deduces the existence and necessary condition of the minimizer for the cost functional. The paper also introduces a gradient descent iterative scheme to solve the numerical solution of the inverse problem and demonstrates its validity through numerical examples.
Article
Mathematics, Applied
Yajing Gu, Yuanguo Zhu
Summary: This paper investigates a new type of optimal control problem involving a parabolic uncertain partial differential equation, where the objective function adopts an expected value criterion. The fundamental idea of Haar wavelet transformation is to approximate the proposed problem with arbitrary accuracy by converting it into an uncertain optimal control problem due to the infinitely increasing dimensions of Haar basis. The relative convergence theorem is proven, and an application to an optimal control problem with an uncertain heat equation is presented to demonstrate the effectiveness of the proposed method.
Article
Mathematics, Applied
Liuping Huang, Hai Zhao, Tongjun Sun
Summary: This paper investigates an iterative proper orthogonal decomposition (POD) method for a parabolic optimal control problem. The finite element method is constructed, with piecewise linear continuous functions used for space discretization and the backward Euler method used for time discretization. The POD method is then applied as a model order reduction method to reduce computation. Different POD basis functions for the state and co-state variables are established through an iterative procedure, using finite element solutions at certain time instances as snapshots. A priori error estimates are derived for the state, co-state, and control variables. Numerical experiments are provided to support the theoretical results.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2023)
Article
Automation & Control Systems
Rahel Bruegger, Helmut Harbrecht, Johannes Tausch
Summary: This article discusses the solution to a time-dependent shape identification problem, focusing on detecting an inclusion by minimizing the mismatch of the Neumann data. The time-dependent shape optimization problem is solved using a gradient-based optimization method, with numerical results validating the approach.
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
(2021)
Article
Mathematical & Computational Biology
Mario Lefebvre
Summary: This article investigates a two-dimensional diffusion process and finds a control method to minimize the expected cost. It also obtains explicit solutions to the value function in specific cases and boundary conditions, using the method of similarity solutions for a non-linear second-order partial differential equation.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2023)
Article
Mathematics, Applied
Tiantian Zhang, Wenwen Xu, Xindong Li, Yan Wang
Summary: This paper investigates the application of the semi-discrete multipoint flux mixed finite element method for parabolic optimal control problems, approximating the state and control variables to solve the problem. The advantage lies in decoupling the state and adjoint state variables, obtaining convergence orders and error estimates.
Article
Mathematics, Applied
M. Tadi
Summary: This article presents a computational method for the inverse problem of the Helmholtz equation, aiming to recover subsurface material properties based on boundary data. The major improvement of this method is that it eliminates the need for linearizing the working equations, making it simple and efficient. Using just one set of data is sufficient to obtain a good approximation of the unknown material property, while additional data sets can further improve the quality of the recovered function.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Mathematics
Constanza S. Fernandez De la Vega, Richard Moore, Mariana Ines Prieto, Diego Rial
Summary: In this study, we investigate an optimal internal control problem for the cubic nonlinear Schrodinger equation on the line. We establish the well-posedness of the problem and prove the existence of an optimal control. Additionally, we present first order optimality conditions and numerical simulations.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Engineering, Multidisciplinary
Xiao-Bo Rao, Yu-Xin Wang, Kun Qian, Zui-Cha Deng, Liu Yang
APPLIED MATHEMATICAL MODELLING
(2015)
Article
Mathematics, Applied
Zui-Cha Deng, Y. C. Hon, V. Isakov
Article
Mathematics, Applied
Liu Yang, Zui-Cha Deng
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2016)
Article
Mathematics, Applied
Liu Yang, Zui-Cha Deng
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2017)
Article
Engineering, Multidisciplinary
Liu Yang, Jian-Ning Yu, Guan-Wei Luo, Zui-Cha Deng
APPLIED MATHEMATICAL MODELLING
(2013)
Article
Mathematics, Applied
Zui-Cha Deng, Liu Yang, Jian-Ning Yu, Guan-Wei Luo
APPLIED MATHEMATICS AND COMPUTATION
(2013)
Article
Mathematics
Zuicha Deng, Liu Yang
CHINESE ANNALS OF MATHEMATICS SERIES B
(2014)
Article
Thermodynamics
Liu Yang, Jian-Ning Yu, Guan-Wei Luo, Zui-Cha Deng
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2012)
Article
Engineering, Multidisciplinary
Zui-Cha Deng, Kun Qian, Xiao-Bo Rao, Liu Yang, Guan-Wei Luo
INVERSE PROBLEMS IN SCIENCE AND ENGINEERING
(2015)
Article
Mathematics, Applied
Zui-Cha Deng, Liu Yang
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2011)
Article
Mathematics, Applied
Zui-Cha Deng, Liu Yang, Jian-Ning Yu, Guan-Wei Luo
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2010)
Article
Mathematics, Applied
Zui-Cha Deng, Liu Yang, Nan Chen
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2011)
Article
Operations Research & Management Science
Zui-Cha Deng, Y. -C. Hon, Liu Yang
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2014)
Article
Mathematics
Zui-Cha Deng, Liu Yang
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY
(2019)
Article
Mathematics, Applied
Liu Yang, Zui-Cha Deng, Yiu-Chung Hon
DYNAMIC SYSTEMS AND APPLICATIONS
(2016)
Article
Engineering, Multidisciplinary
A. A. Aganin, A. I. Davletshin
Summary: A mathematical model of interaction of weakly non-spherical gas bubbles in liquid is proposed in this paper. The model equations are more accurate and compact compared to existing analogs. Five problems are considered for validation, and the results show good agreement with experimental data and numerical solutions. The model is also used to analyze the behavior of bubbles in different clusters, providing meaningful insights.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Hao Wu, Jie Sun, Wen Peng, Lei Jin, Dianhua Zhang
Summary: This study establishes an analytical model for the coupling of temperature, deformation, and residual stress to explore the mechanism of residual stress formation in hot-rolled strip and how to control it. The accuracy of the model is verified by comparing it with a finite element model, and a method to calculate the critical exit crown ratio to maintain strip flatness is proposed.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Shengwen Tu, Naoki Morita, Tsutomu Fukui, Kazuki Shibanuma
Summary: This study aimed to extend the finite element method to cope with elastic-plastic problems by introducing the s-version FEM. The s-version FEM, which overlays a set of local mesh with fine element size on the conventional FE mesh, simplifies domain discretisation and provides accurate numerical predictions. Previous applications of the s-version FEM were limited to elastic problems, lacking instructions for stress update in plasticity. This study presents detailed instructions and formulations for addressing plasticity problems with the s-version FEM and analyzes a stress concentration problem with linear/nonlinear material properties.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Bo Fan, Zhongmin Wang
Summary: A 3D rotating hyperelastic composite REF model was proposed to analyze the influence of tread structure and rotating angular speed on the vibration characteristics of radial tire. Nonlinear dynamic differential equations and modal equations were established to study the effects of internal pressure, tread pressure sharing ratio, belt structure, and rotating angular speed on the vibration characteristics.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
X. W. Chen, Z. Q. Yue, Wendal Victor Yue
Summary: This paper examines the axisymmetric problem of a flat mixed-mode annular crack near and parallel to an arbitrarily graded interface in functionally graded materials (FGMs). The crack is modeled as plane circular dislocation loop and an efficient solution for dislocation in FGMs is used to calculate the stress field at the crack plane. The analytical solutions of the stress intensity factors are obtained and numerical study is conducted to investigate the fracture mechanics of annular crack in FGMs.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Xumin Guo, Jianfei Gu, Hui Li, Kaihua Sun, Xin Wang, Bingjie Zhang, Rangwei Zhang, Dongwu Gao, Junzhe Lin, Bo Wang, Zhong Luo, Wei Sun, Hui Ma
Summary: In this study, a novel approach combining the transfer matrix method and lumped parameter method is proposed to analyze the vibration response of aero-engine pipelines under base harmonic and random excitations. The characteristics of the pipelines are investigated through simulation and experiments, validating the effectiveness of the proposed method.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Xiangyu Sha, Aizhong Lu, Ning Zhang
Summary: This paper investigates the stress and displacement of a layered soil with a fractional-order viscoelastic model under time-varying loads. The correctness of the solutions is validated using numerical methods and comparison with existing literature. The research findings are of significant importance for exploring soil behavior and its engineering applications under time-varying loads.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Thuy Dong Dang, Thi Kieu My Do, Minh Duc Vu, Ngoc Ly Le, Tho Hung Vu, Hoai Nam Vu
Summary: This paper investigates the nonlinear torsional buckling of corrugated core sandwich toroidal shell segments with functionally graded graphene-reinforced composite (FG-GRC) laminated coatings in temperature change using the Ritz energy method. The results show the significant beneficial effects of FG-GRC laminated coatings and corrugated core on the nonlinear buckling responses of structures.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Zhihao Zhai, Chengbiao Cai, Qinglai Zhang, Shengyang Zhu
Summary: This paper investigates the effect of localized cracks induced by environmental factors on the dynamic performance and service life of ballastless track in high-speed railways. A mathematical approach for forced vibrations of Mindlin plates with a side crack is derived and implemented into a train-track coupled dynamic system. The accuracy of this approach is verified by comparing with simulation and experimental results, and the dynamic behavior of the side crack under different conditions is analyzed.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
James Vidler, Andrei Kotousov, Ching-Tai Ng
Summary: The far-field methodology, developed by J.C. Maxwell, is utilized to estimate the effective third order elastic constants of composite media containing random distribution of spherical particles. The results agree with previous studies and can be applied to homogenization problems in other fields.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Kim Q. Tran, Tien-Dat Hoang, Jaehong Lee, H. Nguyen-Xuan
Summary: This study presents novel frameworks for graphene platelets reinforced functionally graded triply periodic minimal surface (GPLR-FG-TPMS) plates and investigates their performance through static and free vibration analyses. The results show that the mass density framework has potential for comparing different porous cores and provides a low weight and high stiffness-to-weight ratio. Primitive plates exhibit superior performance among thick plates.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Bence Hauck, Andras Szekrenyes
Summary: This study explores several methods for computing the J-integral in laminated composite plate structures with delamination. It introduces two special types of plate finite elements and a numerical algorithm. The study presents compact formulations for calculating the J-integral and applies matrix multiplication to take advantage of plate transition elements. The models and algorithms are applied to case studies and compared with analytical and previously used finite element solutions.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Wu Ce Xing, Jiaxing Wang, Yan Qing Wang
Summary: This paper proposes an effective mathematical model for bolted flange joints to study their vibration characteristics. By modeling the flange and bolted joints, governing equations are derived. Experimental studies confirm that the model can accurately predict the vibration characteristics of multiple-plate structures.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Pingchao Yu, Li Hou, Ke Jiang, Zihan Jiang, Xuanjun Tao
Summary: This paper investigates the imbalance problem in rotating machinery and finds that mass imbalance can induce lateral-torsional coupling vibration. By developing a model and conducting detailed analysis, it is discovered that mass imbalance leads to nonlinear time-varying characteristics and there is no steady-state torsional vibration in small unbalanced rotors. Under largely unbalanced conditions, both resonant and unstable behavior can be observed, and increasing lateral damping can suppress instability and reduce lateral amplitude in the resonance region.
APPLIED MATHEMATICAL MODELLING
(2024)
Article
Engineering, Multidisciplinary
Yong Cao, Ziwen Guo, Yilin Qu
Summary: This paper investigates the mechanically induced electric potential and charge redistribution in a piezoelectric semiconductor cylindrical shell. The results show that doping levels can affect the electric potentials and mechanical displacements, and alter the peak position of the zeroth-order electric potential. The doping level also has an inhibiting effect on the first natural frequency. These findings are crucial for optimizing the design and performance of cylindrical shell-shaped sensors and energy harvesters.
APPLIED MATHEMATICAL MODELLING
(2024)
