Article
Mathematics, Applied
Xiuxiu Lin, Yanping Chen, Yunqing Huang
Summary: In this article, we investigate the L-2-norm state constrained control problem with the first bi-harmonic equation. We derive the optimality conditions of the control problem and establish spectral discretization of the problem. A priori error analysis for control variable, state, and adjoint state variable is conducted based on the property of the projection operator. Furthermore, we propose an efficient projected gradient algorithm, and the numerical results verify the analytical results by demonstrating high order accuracy and fast convergence rate.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Energy & Fuels
Dalia Yousri, Ahmed Fathy, Hegazy Rezk
Summary: This paper introduces an improved metaheuristic approach of comprehensive learning marine predator algorithm (CLMPA) to identify optimal parameters of supercapacitor equivalent circuit. By utilizing the principle of comprehensive learning strategy, the proposed approach shares best experiences among all particles to avoid immature convergence.
JOURNAL OF ENERGY STORAGE
(2021)
Article
Computer Science, Artificial Intelligence
Jiang Min, Zhiqing Meng, Gengui Zhou, Rui Shen
Summary: This paper explores the use of a smoothing norm objective penalty function for two-cardinality sparse constrained optimization problems, demonstrating its good properties and convergence in solving such problems. The proposed algorithm is able to find a satisfactory approximate optimal solution in a numerical example.
Article
Mathematics, Applied
Gianluca Frasca-Caccia, Pranav Singh
Summary: In this paper, we present a procedure for identifying optimal methods in parametric families of numerical schemes for initial value problems in partial differential equations. The procedure maximizes accuracy by adaptively computing optimal parameters that minimize a defect-based estimate of the local error at each time step. We propose viable refinements to reduce computational overheads and maintain conservation properties of the original methods. Numerical tests demonstrate the improved efficiency of the new technique compared to existing methods.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Mathematics, Applied
Hengzhi Zhao, Jiwei Zhang, Jing Lu, Jiang Hu
Summary: In this study, the principle of contraction mapping is employed to establish the approximate controllability and existence of optimal control for a multi-delay stochastic fractional differential equation system with a control function featuring Poisson jumps, given the Hurst parameter in the range of 0 < H < 1/2. The validity of the theory is substantiated through the implementation of a pertinent example.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Benyamin Abdollahzadeh, Saeid Barshandeh, Hatef Javadi, Nicola Epicoco
Summary: This paper introduces an enhanced binary SMA for solving the 0-1 knapsack problem at different scales. By using multiple transfer functions and bitwise and Gaussian mutation operators, along with penalty function and repair algorithm to handle infeasible solutions, the superiority of the proposed method is demonstrated.
ENGINEERING WITH COMPUTERS
(2022)
Article
Mathematics, Applied
Gilbert Peralta
Summary: This paper analyzes the mixed and hybrid finite element discretizations for distributed optimal control problems governed by an elliptic equation. It also studies a cost functional that keeps track of both the state and its gradient. A priori error estimates and super-convergence properties for the continuous and discrete optimal states, adjoint states, and controls are given, and the approximating finite-dimensional systems are solved by adding penalization terms for the state and the associated Lagrange multipliers.
ADVANCES IN COMPUTATIONAL MATHEMATICS
(2022)
Article
Mathematics
Tobias Holck Colding, William P. Minicozzi
Summary: For any manifold with polynomial volume growth, the dimension of ancient caloric functions with polynomial growth is bounded by the degree of growth times the dimension of harmonic functions with the same growth. This leads to a sharp bound for the dimension of ancient caloric functions on spaces where Yau's 1974 conjecture about polynomial growth harmonic functions holds.
DUKE MATHEMATICAL JOURNAL
(2021)
Article
Mathematics, Applied
Qian Zhang, Yuzhu Han, Jian Wang
Summary: In this note, a critical bi-harmonic elliptic equation with logarithmic perturbation is investigated. The existence condition of weak solutions is relaxed compared to a recent study by Li et al. (2023), and the types of weak solutions are specified using Brezis-Lieb's lemma and Ekeland's variational principle.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Computer Science, Artificial Intelligence
Sasan Harifi
Summary: This paper proposes a binary version of the ancient-inspired algorithm for solving the 0-1 knapsack problem, and compares its performance with four popular metaheuristic algorithms. The results show that the proposed algorithm performs better.
Article
Environmental Sciences
Degen Wang, Tong Wang, Weichen Cui, Cheng Liu
Summary: This article proposes an efficient sparse recovery STAP algorithm for detecting moving targets in strong clutter backgrounds for airborne early warning radar systems. The algorithm improves performance by establishing a new optimization objective function and obtaining closed-form solutions through an alternating minimization algorithm. A restart strategy is also employed to adaptively update the support and reduce computational complexity.
Article
Chemistry, Multidisciplinary
Ahmed S. Abbas, Ragab A. El-Sehiemy, Adel Abou El-Ela, Eman Salah Ali, Karar Mahmoud, Matti Lehtonen, Mohamed M. F. Darwish
Summary: This paper proposes a harmonic mitigation method based on the Water Cycle Algorithm to address the harmonic distortion issues caused by inverter-based distributed generation units in distribution systems. The effectiveness of the proposed planning model is demonstrated on the IEEE 69-bus distribution system, showing significant reductions in harmonic distortion.
APPLIED SCIENCES-BASEL
(2021)
Article
Mathematics
Manu Centeno-Telleria, Ekaitz Zulueta, Unai Fernandez-Gamiz, Daniel Teso-Fz-Betono, Adrian Teso-Fz-Betono
Summary: This paper presents a methodology for tuning optimal parameters in the differential evolution algorithm using an artificial neural network. Experimental results on 24 test problems reveal three distinct cases for optimal parameter tuning, and a comparison with other tuning rules is conducted for performance validation.
Article
Computer Science, Artificial Intelligence
Xiang Wu, Jinxing Lin, Kanjian Zhang, Ming Cheng
Summary: This paper proposes a solution to the optimal control problem of switched dynamical systems with control input and system state constraints. By introducing integer constraints, the switching conditions are transformed into continuous-time inequality constraints, and then the original optimal control problem is approximated by using relaxation methods, control vector parameterization techniques, and time-scaling transformations.
APPLIED SOFT COMPUTING
(2022)
Article
Engineering, Electrical & Electronic
Zeeshan Akhtar, Amrit Singh Bedi, Srujan Teja Thomdapu, Ketan Rajawat
Summary: This work introduces the first SBFW algorithm to solve stochastic bi-level optimization problems in a projection-free manner. It also proposes the SCFW algorithm for stochastic compositional optimization problems. Extensive numerical tests demonstrate the usefulness and flexibility of SBFW and SCFW algorithms.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2022)
Article
Computer Science, Interdisciplinary Applications
Hui Guo, Xinyuan Liu, Yang Yang
JOURNAL OF COMPUTATIONAL PHYSICS
(2020)
Article
Computer Science, Interdisciplinary Applications
Ziyao Xu, Yang Yang
JOURNAL OF COMPUTATIONAL PHYSICS
(2020)
Article
Mathematics, Applied
Hui Guo, Rui Jia, Lulu Tian, Yang Yang
Summary: This paper applies two fully-discrete LDG methods to compressible wormhole propagation, proving stability and error estimates, introduces a new auxiliary variable and special time integration for porosity to obtain stability of the fully-discrete LDG methods, and demonstrates optimal error estimates for pressure, velocity, porosity, and concentration under weak temporal-spatial conditions.
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
(2021)
Article
Water Resources
Hui Guo, Wenjing Feng, Ziyao Xu, Yang Yang
Summary: This study improves the traditional discrete fracture model to be applicable on non-conforming meshes, and combines the interior penalty discontinuous Galerkin and enriched Galerkin methods to handle the pressure equation, ensuring local mass conservation. Numerical experiments in porous media demonstrate the effectiveness of the proposed methods.
ADVANCES IN WATER RESOURCES
(2021)
Article
Computer Science, Interdisciplinary Applications
Xiaofeng Cai, Jing-Mei Qiu, Yang Yang
Summary: The paper introduces a new method called ELDG, which incorporates a modified adjoint problem and integration of PDE over a space-time region partitioned by time-dependent linear functions. By introducing a new flux term to account for errors in characteristics approximation, the ELDG method combines the advantages of SL DG and classical Eulerian RK DG methods. The use of linear functions for characteristics approximation in the EL DG framework simplifies shapes of upstream cells and reduces time step constraints.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Ruize Yang, Yang Yang, Yulong Xing
Summary: In this paper, a family of second and third order temporal integration methods for stiff ordinary differential equations is proposed, combining traditional Runge-Kutta and exponential Runge-Kutta methods to preserve sign and steady-state properties. These methods are applied with well-balanced discontinuous Galerkin spatial discretization to solve nonlinear shallow water equations with friction terms. The fully discrete schemes are demonstrated to satisfy well-balanced, positivity-preserving, and sign-preserving properties simultaneously, showing good numerical results on various test cases.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Water Resources
Guosheng Fu, Yang Yang
Summary: We propose a hybrid-mixed finite element method for a novel hybrid-dimensional model of single-phase Darcy flow in fractured porous media. Our method distinguishes between conductive and blocking fractures and uses a combination of classical interface model and recent Dirac-delta function approach to handle them. The use of Dirac-delta function approach allows for nonconforming meshes with respect to the blocking fractures. Our numerical scheme produces locally conservative velocity approximations and leads to a symmetric positive definite linear system involving pressure degrees of freedom on the mesh skeleton only.
ADVANCES IN WATER RESOURCES
(2022)
Article
Mathematics, Applied
Lulu Tian, Hui Guo, Rui Jia, Yang Yang
Summary: This paper investigates the application of local discontinuous Galerkin methods to compressible wormhole propagation with a Darcy-Forchheimer model. By addressing various theoretical challenges, stability and error estimates of the scheme are proven, followed by numerical experiments to verify the results.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Wenjing Feng, Hui Guo, Yue Kang, Yang Yang
Summary: In this paper, we introduce a novel SIPEC time marching method for the coupled system of two-component compressible miscible displacements. By incorporating a correction stage in each time step, we achieve second-order accuracy while maintaining bound preservation for the concentration equation.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Jie Du, Yang Yang
Summary: This paper presents high-order bound-preserving discontinuous Galerkin (DG) methods for multicomponent chemically reacting flows. The proposed methods address the challenges of positivity preservation, ensuring the mass fractions sum up to 1, and handling stiff sources. The numerical experiments demonstrate the effectiveness of the proposed schemes.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Hui Guo, Xueting Liang, Yang Yang
Summary: In this paper, numerical algorithms are investigated to capture the blow-up time for a class of convection-diffusion equations with blow-up solutions. The positivity-preserving technique is used to enforce stability and the L1-stability and L2-norm of numerical approximations are utilized to detect the blow-up phenomenon. Two methods for defining the numerical blow-up time are proposed and their convergence to the exact time is proven.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Ziyao Xu, Zhaoqin Huang, Yang Yang
Summary: In this paper, a novel discrete fracture model is proposed for flow simulation of fractured porous media with flow blocking barriers on non-conforming meshes. The traditional Darcy's law is modified into a hybrid-dimensional Darcy's law to represent the fractures and barriers using Dirac-delta functions in the permeability tensor and resistance tensor, respectively. The model accurately accounts for the influence of highly conductive fractures and blocking barriers on non-conforming meshes, and the local discontinuous Galerkin method is employed to handle the pressure/flux discontinuity.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Wenjing Feng, Hui Guo, Lulu Tian, Yang Yang
Summary: In this paper, we propose a sign-preserving second-order IMplicit Pressure Explicit Concentration (IMPEC) time method for generalized coupled non-Darcy flow and transport problems in petroleum engineering. The method utilizes interior penalty discontinuous Galerkin (IPDG) methods for spatial discretization and a bound-preserving technique to ensure physically relevant numerical approximations. The proposed method is different from previous algorithms as it linearizes the velocity equation and introduces a direct solver to solve for velocity, resulting in first-order accurate solutions and reduced computational cost.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Water Resources
Guosheng Fu, Yang Yang
Summary: We propose a new hybridizable discontinuous Galerkin (HDG) method on unfitted meshes for single-phase Darcy flow in a fractured porous medium. Our numerical scheme uses a Dirac-6 function approach for fractures, allowing for unfitted meshes with respect to the fractures. The scheme is simple and locally mass conservative.
ADVANCES IN WATER RESOURCES
(2023)
Article
Mathematics, Applied
Jie Du, Eric Chung, Yang Yang
Summary: This paper studies the classical Allen-Cahn equations and investigates the maximum-principle-preserving (MPP) techniques. It discusses the application of the local discontinuous Galerkin (LDG) method and the use of conservative modified exponential Runge-Kutta methods. Numerical experiments are used to demonstrate the effectiveness of the MPP LDG scheme.
COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics, Applied
Manh Tuan Hoang, Matthias Ehrhardt
Summary: In this paper, a simple approach for solving stiff problems is proposed. Through nonlinear approximation and rigorous mathematical analysis, a class of explicit second-order one-step methods with L-stability and second-order convergence are constructed. The proposed methods generalize and improve existing nonstandard explicit integration schemes, and can be extended to higher-order explicit one-step methods.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Jian Liu, Zengqin Zhao
Summary: In this article, we investigate p(x)-biharmonic equations involving Leray-Lions type operators and Hardy potentials. Some new theorems regarding the existence of generalized solutions are reestablished for such equations when the Leray-Lions type operator and the nonlinearity satisfy suitable hypotheses in variable exponent Lebesgue spaces.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Chengcheng Cheng, Rong Yuan
Summary: This paper investigates the spreading dynamics of a nonlocal diffusion KPP model with free boundaries in time almost periodic media. By applying the novel positive time almost periodic function and satisfying the threshold condition for the kernel function, the unique asymptotic spreading speed of the free boundary problem is accurately expressed.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Xia Wang, Xin Meng, Libin Rong
Summary: In this study, a multiscale model incorporating the modes of infection and types of immune responses of HCV is developed. The basic and immune reproduction numbers are derived and five equilibria are identified. The global asymptotic stability of the equilibria is established using Lyapunov functions, highlighting the significant impact of the reproduction numbers on the overall stability of the model.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Junpu Li, Lan Zhang, Shouyu Cai, Na Li
Summary: This research proposes a regularized singular boundary method for quickly calculating the singularity of the special Green's function at origin. By utilizing the special Green's function and the origin intensity factor technique, an explicit intensity factor suitable for three-dimensional ocean dynamics is derived. The method does not involve singular integrals, resulting in improved computational efficiency and accuracy.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Ying Dong, Shuai Zhang, Yichen Zhang
Summary: This paper investigates a 2D chemotaxis-consumption system with rotation and no-flux-Dirichlet boundary conditions. It proves that under certain conditions on the rotation angle, the corresponding initial-boundary value problem has a classical solution that blows up at a finite time.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Shuhan Yao, Qi Hong, Yuezheng Gong
Summary: In this article, an extended quadratic auxiliary variable method is introduced for a droplet liquid film model. The method shows good numerical solvability and accuracy.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Tong Wang, Binxiang Dai
Summary: This paper investigates the spreading speed and traveling wave of an impulsive reaction-diffusion model with non-monotone birth function and age structure, which models the evolution of annually synchronized emergence of adult population with maturation. The result extends the work recently established in Bai, Lou, and Zhao (J. Nonlinear Sci. 2022). Numerical simulations are conducted to illustrate the findings.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Dinghao Zhu, Xiaodong Zhu
Summary: This paper constructs the soliton solutions of the KdV equation with non-zero background using the Riemann-Hilbert approach. The irregular Riemann-Hilbert problem is first constructed by direct and inverse scattering transform, and then regularized by introducing a novel transformation. The residue theorem is applied to derive the multi-soliton solutions at the simple poles of the Riemann-Hilbert problem. In particular, the interaction dynamics of the two-soliton solution are illustrated by considering their evolutions at different time.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Danhua He, Liguang Xu
Summary: This paper investigates the stability of conformable fractional delay differential systems with impulses. By establishing a conformable fractional Halanay inequality, the paper provides sufficient criteria for the conformable exponential stability of the systems.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Fei Sun, Xiaoli Li, Hongxing Rui
Summary: This paper presents a high-order numerical scheme for solving the compressible wormhole propagation problem. The scheme utilizes the fourth-order implicit Runge-Kutta method and the block-centered finite difference method, along with high-order interpolation technique and cut-off approach to achieve high-order and bound-preserving.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Zhijie Du, Huoyuan Duan
Summary: This study analyzes a direct discretization method for computing the eigenvalues of the Maxwell eigenproblem. It utilizes a specific finite element space and the classical variational formulation, and proves the convergence of the obtained finite element solutions.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Hongliang Li, Pingbing Ming
Summary: This paper proposes an asymptotic-preserving finite element method for solving a fourth order singular perturbation problem, which preserves the asymptotic transition of the underlying partial differential equation. The NZT element is analyzed as a representative, and a linear convergence rate is proved for the solution with sharp boundary layer. Numerical examples in two and three dimensions are consistent with the theoretical prediction.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Shuyang Xue, Yongli Song
Summary: This paper investigates the spatiotemporal dynamics of the memory-based diffusion equation driven by memory delay and nonlocal interaction. The nonlocal interaction, characterized by the given Green function, leads to inhomogeneous steady states with any modes. The joint effect of nonlocal interaction and memory delay can result in spatially inhomogeneous Hopf bifurcation and Turing-Hopf bifurcation.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Baoquan Zhou, Ningzhong Shi
Summary: This paper develops a stochastic SEIS epidemic model perturbed by Black-Karasinski process and investigates the impact of random fluctuations on disease outbreak. The results show that random fluctuations facilitate disease outbreak, and a sufficient condition for disease persistence is established.
APPLIED MATHEMATICS LETTERS
(2024)
