CSIAM Transactions on Applied Mathematics
type: channel
description: The CSIAM Transactions on Applied Mathematics (CSIAM-AM) is the flagship journal of the Chinese Society for Industrial and Applied Mathematics. It publishes original research articles of high quality on a topic in applied mathematics or computational mathematics or scientific computing. Papers should address mathematically and computationally interesting and challenging problems. Manuscripts applying known methods to previously solved problems will not be accepted.
publisher: Global Science Press
language: en
publication name: CSIAM Transactions on Applied Mathematics
issn: 2708-0560
items: Thermodynamics of Freshwater Production via CuS-Infused Porous Membrane Solar Absorber in Seawater Desalination
items: Superconvergence Points of Several Polynomial and Nonpolynomial Hermite Spectral Interpolations
items: An Efficient Iterative Convolution-Thresholding Method for Image Inpainting
items: Assessment and Evaluation of Surface Water Quality and Human Health Risk in the Inkomati River Catchment Basin, South Africa
items: Double-Domain Driven Unet for Selective Segmentation of Medical Image
items: Bifurcation and Crossover Processes in the Dynamics of a Marburg Haemorrhagic Fever Model
items: Interface Laplace Learning: Learnable Interface Term Helps Semi-Supervised Learning
items: Error Estimates of Operator Splitting Spectral Method for Semiclassical Sub-Diffusive Gross-Pitaevskii Equation
items: A Mathematical Analysis for the Dynamics of Multiple Languages
items: pETNNs: Partial Evolutionary Tensor Neural Networks for Solving Time-Dependent Partial Differential Equations
items: Global Solvability in a Two-Species Keller-Segel-Navier-Stokes System with Sub-Logistic Source
items: A Sharp Uniform-in-Time Error Estimate for Stochastic Gradient Langevin Dynamics
items: An Efficient Iteration Based on Reduced Basis Method for Time-Dependent Problems with Random Inputs
items: Two Methods Addressing Variable-Exponent Fractional Initial and Boundary Value Problems and Abel Integral Equation
items: Convergent Finite Elements on Arbitrary Meshes, the WG Method
items: Benchmarking Density Functional Theory for Noble Metal Hydrides: A High-Fidelity PES and Vibrational Analysis of the ${\rm AgAuH}^−$ Anion
items: Construction and Analysis for Adams Explicit Discretization of High-Index Saddle Dynamics
items: Well-Posedness and Regularity Analyses for Nonlocal Nonautonomous System
items: Global-in-Time Energy Stability for a General Class of Stabilization Single-Step Schemes Applied to the Swift-Hohenberg Equation
items: New Finite Volume Element Schemes Based on a Two-Layer Dual Strategy
items: Highly Efficient Gauss’s Law-Preserving Spectral Algorithms for Maxwell’s Double-Curl Source and Eigenvalue Problems Based on Eigen-Decomposition
items: $\mathbf{H}$(${\rm curl}^2$) Conforming Element for Maxwell’s Transmission Eigenvalue Problem Using Fixed-Point Approach
items: Efficient Numerical Methods for Computing Stationary States of Spherical Landau-Brazovskii Model
items: A Hue-Preserving Color Image Restoration Model Using Saturation-Value Total Variation
items: Exploring Fractional-Order Nonlinear Dynamics in Biodiesel Production with Optimal Control
items: Optical Wave Turbulence: The Conformal Symmetry Transformations of Statistics of the Quantum Fluids of Light
items: A Numerical Algorithm with Linear Complexity for Multi-Marginal Optimal Transport with $L^1$ Cost
items: A Deep Learning Approach for Solving the Inverse Problem of the Wave Equation
items: Enhanced Expressive Power and Fast Training of Neural Networks by Random Projections
items: Multipliers Correction Methods for Optimization Problems over the Stiefel Manifold

Thermodynamics of Freshwater Production via CuS-Infused Porous Membrane Solar Absorber in Seawater Desalination
type: item
description: In our advanced modern world, ensuring the availability and access to freshwater resources remains a significant global challenge. Seawater desalination is viewed as one of the most promising solutions to address the increasing human demand for freshwater. This study theoretically examines the thermodynamics of a novel desalination system that integrates a copper sulfide (CuS) nanomaterial-porous membrane solar absorber for freshwater production. The governing partial differential equations for energy and mass balance in the model were derived from conservation laws and solved numerically using the method of lines. The impact of various parameters on steam temperature and freshwater production rate was analyzed in two scenarios: (i) under constant solar radiation flux in a controlled laboratory setting, and (ii) as a time-dependent function under typical daily solar radiation conditions. The pertinent results were presented graphically and discussed. It was found that the Nusselt number at the surface of the porous membrane solar absorber increases with the infusion of CuS nanomaterial. The desalination system reached a steady state with steam temperature, and the rate of freshwater production improved as the volume fraction of CuS nanomaterial in the porous membrane solar absorber increased. Additionally, an increase in steam generation and condensation Biot numbers further boosted the freshwater production rate.
subject: Articles
  topic: section
subject: Seawater desalination
  topic: keywords
subject: freshwater production
  topic: keywords
subject: selective porous solar absorber
  topic: keywords
subject: copper sulfide nanomaterial
  topic: keywords
subject: thermodynamics analysis
  topic: keywords
creator: A. E. Makinde
creator: O. D. Makinde
creator: M. Maaza
creator: T. Mokrani
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2025-12-08
publication date: 2025-12-08
doi: 10.4208/csiam-am.SO-2025-0011

Superconvergence Points of Several Polynomial and Nonpolynomial Hermite Spectral Interpolations
type: item
description: In this paper, we analyze the superconvergence properties for spectral interpolations by Hermite polynomials and mapped Hermite functions. At the superconvergence points, the $(N−k)$-th term in the Hermite spectral interpolation remainder for the $(k+1)$-th derivatives vanish. To solve multi-point weakly singular nonlocal problems, we previously introduced mapped Hermite functions (MHFs), which are constructed by applying a mapping to the Hermite polynomials. We prove that the superconvergence points of the spectral interpolations based on MHFs for the $(k+1)$-th derivatives are the zero points of the $(N−k)$-th term. Additionally, due to the rapid growth of the logarithmic function at the endpoints 0 and 1, we further propose generalized mapped Hermite functions (GMHFs). We develop basic approximation theory for these new orthogonal functions and prove the projection error and interpolation error in the $L^2$-weighted space using the pseudo-derivative. We demonstrate that the superconvergence points of the spectral interpolations based on both MHFs and GMHFs for the $(k+1)$-th derivative are the zero points of the $(N−k)$-th term. Numerical experiments confirm our theoretical results.
subject: Articles
  topic: section
creator: Min Wang
creator: Zhimin Zhang
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2025-12-04
publication date: 2025-12-04
doi: 10.4208/csiam-am.SO-2024-0046

An Efficient Iterative Convolution-Thresholding Method for Image Inpainting
type: item
description: Variational methods have been developed for image inpainting, which involve minimizing an objective functional consisting of the regularization term and the fidelity term. The fidelity term controls the consistency of the restored region with the original image, while the regularization term smooths the boundary of the region. In this paper, we develop an efficient iterative convolution-thresholding method to solve variational approach-based image inpainting problems. In the proposed method, the region is represented by its indicator function, and the regularization term is approximated by the heat kernel convolution with the indicator function. Based on this approximation, we derive an efficient iterative method to update the indicator function only within the damaged region by alternating the convolution and thresholding steps, relying on a relaxation and linearization procedure. Extensive numerical experiments demonstrate the simplicity and efficiency of the proposed method.
subject: Articles
  topic: section
subject: Iterative convolution-thresholding method
  topic: keywords
subject: heat kernel
  topic: keywords
subject: image inpainting
  topic: keywords
creator: Caixia Nan
creator: Zhonghua Qiao
creator: Dong Wang
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2025-12-04
publication date: 2025-12-04
doi: 10.4208/csiam-am.SO-2024-0044

Assessment and Evaluation of Surface Water Quality and Human Health Risk in the Inkomati River Catchment Basin, South Africa
type: item
description: Multivariate statistical methods, dimensionality reduction, clustering techniques, water quality indices (WQIs) of the Canadian Council of Ministers of the Environment (CCME), comprehensive pollution index (CPI), and human health risk assessment indices for carcinogenic risk of heavy metals, using the hazard index (HI), are utilized in this work to assess the surface water quality of the Inkomati catchment. Six physicochemical parameters – ${\rm EC},$ pH, ${\rm SO_4},$ Fe, Mn, and Cu were measured monthly from January 2015 to June 2019 from two sites Crocodile and Sabie rivers. The outcomes were compared to standard regulatory guidelines values. Recommended parameter values from US-EPA and peer-reviewed literature were used for the HI. The findings indicated that the river water was turbid and suffered from EC, specifically distressed due to trace metals. The US-WQI range (103.15-431.38) showed that the water quality level of the catchment was in the poor category but excellent during the winter. Water quality improved from marginal to good, according to the CCME-WQI scores, whereas the CPI scores (2.359-8.459) showed that the catchment’s water quality was in a very poor condition. The US-WQI suggested that the overall quality of the basin has declined in both the upper and lower portions. The hazard quotient through ingestion exposure did not exceed the threshold limit of 1 for children. This implies there is no potential carcinogenic health risk from trace elements via ingestion of drinking water for children. However, cancer risk for children was computed in relation to Cu, Fe, Mn, and levels. It did not exceed the carcinogenic threshold limit of $10^{-4}$ for both sites.
subject: Articles
  topic: section
subject: Inkomati catchment
  topic: keywords
subject: river water quality
  topic: keywords
subject: water quality indices
  topic: keywords
subject: robust statistical techniques
  topic: keywords
subject: health risk assessment
  topic: keywords
creator: Ernestine Atangana
creator: Rodrigue G. Batogna
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2025-12-04
publication date: 2025-12-04
doi: 10.4208/csiam-am.SO-2024-0060

Double-Domain Driven Unet for Selective Segmentation of Medical Image
type: item
description: Selective segmentation has been a notable increase in interest in the use of interactive deep learning-based methods. However, developing an efficient and accurate segmentation method for medical applications remains a formidable challenge, primarily due to the inherent complexity and diversity of medical image structures. To address these challenges, we introduce a novel deep learning approach, termed the double-domain driven Unet method (DDUM), designed for the selective segmentation of medical images. Our approach utilizes a threshold geodesic distance in conjunction with the original images as input to construct a parallel Unet architecture that captures information from both the image domain and the geodesic distance domain. To further enhance the accuracy and efficacy of the segmentation process, we employ soft threshold dynamics as a replacement for the sigmoid activation function in the final layer. The efficacy of our proposed DDUM is substantiated through extensive experiments conducted on multiple medical image datasets. In particular, the DDUM method exhibits exceptional performance in terms of both segmentation accuracy and robustness.
subject: Articles
  topic: section
subject: Image segmentation
  topic: keywords
subject: regions of interest
  topic: keywords
subject: threshold geodesic distance
  topic: keywords
subject: double-domain driven Unet method
  topic: keywords
subject: soft threshold dynamics
  topic: keywords
creator: Zhi-Feng Pang
creator: Lin Yang
creator: Mingxiang Wu
creator: Ziyu Niu
creator: Raymond Chan
creator: Xue-Cheng Tai
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2025-12-04
publication date: 2025-12-04
doi: 10.4208/csiam-am.SO-2024-0043

Bifurcation and Crossover Processes in the Dynamics of a Marburg Haemorrhagic Fever Model
type: item
description: Just like Ebola disease, Marburg virus disease (MVD) remains a constant threat to people’s lives, not only in Africa, but also in other parts of the globe. Recorded past outbreaks have occurred in Europe, the Americas, and of course Africa, especially in places where inhabitants come into contact with wild animal products or live alongside wild animals such as apes, monkeys, and fruit bats on a daily basis. Therefore, studying the dynamics of the Marburg virus and conducting some epidemiological assessments remain relevant and important for preventing future outbreaks. In this paper, we analyze a Marburg epidemic model with nonlinear transmission. The well-posedness result is established, along with conditions for boundedness and dissipativity. Then, we intensively analyze the stability of the model’s equilibria. The bifurcation dynamics indicate the existence of both transcritical bifurcation (exchange of stability between the endemic equilibrium (EE) and the disease-free equilibrium (DFE)) and backward bifurcation, where the classical epidemiological condition for MVD to die out $(\mathcal{R}_0 < 1)$ is no longer sufficient, but remains necessary. Lastly, some numerical simulations show the convergence of trajectories to both the EE and the DFE. Some adequate preventive measures are provided.
subject: Articles
  topic: section
subject: Marburg hemorrhagic fever model
  topic: keywords
subject: numerical solvability
  topic: keywords
subject: filovirus
  topic: keywords
subject: nonlinear incidence
  topic: keywords
subject: bifurcation
  topic: keywords
subject: crossover
  topic: keywords
subject: stability
  topic: keywords
creator: EF. Doungmo Goufo
creator: I. Tchangou Toudjeu
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2025-12-01
publication date: 2025-12-01
doi: 10.4208/csiam-am.SO-2025-0014

Interface Laplace Learning: Learnable Interface Term Helps Semi-Supervised Learning
type: item
description: We introduce a novel framework, called Interface Laplace Learning, for graph-based semi-supervised learning. Motivated by the observation that an interface should exist between different classes where the function value is non-smooth, we propose a Laplace learning model that incorporates an interface term. This model challenges the long-standing assumption that functions are smooth at all unlabeled points. In the proposed approach, we add an interface term to the Laplace learning model at the interface positions. We provide a practical algorithm to approximate the interface positions using k-hop neighborhood indices, and to learn the interface term from labeled data without artificial design. Our method is efficient and effective, and we present extensive experiments demonstrating that Interface Laplace Learning achieves better performance than other recent semi-supervised learning approaches at extremely low label rates on the MNIST, FashionMNIST, and CIFAR-10 datasets.
subject: Articles
  topic: section
subject: Graph-based semi-supervised learning
  topic: keywords
subject: Laplace learning
  topic: keywords
subject: interface
  topic: keywords
subject: nonlocal model
  topic: keywords
creator: Tangjun Wang
creator: Chenglong Bao
creator: Zuoqiang Shi
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2025-12-01
publication date: 2025-12-01
doi: 10.4208/csiam-am.SO-2024-0064

Error Estimates of Operator Splitting Spectral Method for Semiclassical Sub-Diffusive Gross-Pitaevskii Equation
type: item
description: Nonlinear Gross-Pitaevskii-type models are frequently seen in the fields of Bose-Einstein condensation and quantum mechanics. We derive error estimates for the Lie-Trotter operator splitting spectral method for semiclassical sub-diffusive Gross-Pitaevskii equation in the unbounded domain or with the periodic boundary condition. After establishing a priori estimates for the analytic solution in fractional Sobolev space, the local error estimates for the Lie-Trotter splitting operator method are derived. The related estimates for the Lie commutator of nonlocal linear operator and nonlinear operator play key roles in deriving the local error estimates. We then obtain the global error bounds for the fully discrete scheme based on the space approximation with mapped Chebyshev spectral-Galerkin methods in the case of the unbounded domain and with Fourier spectral methods in the case of the periodic boundary condition. Especially, their convergence orders with respect to the small (scaled) Planck constant $ε$ are obtained for the first time under the framework of Wentzel-Kramers-Brillouin analysis. Numerical experiments verify and complement our theoretical results.
subject: Articles
  topic: section
subject: Lie-Trotter operator splitting
  topic: keywords
subject: sub-diffusive Gross-Pitaevskii equation
  topic: keywords
subject: semiclassical regime
  topic: keywords
subject: error estimates
  topic: keywords
subject: mapped Chebyshev spectral-Galerkin methods
  topic: keywords
subject: Fourier spectral methods
  topic: keywords
creator: Wansheng Wang
creator: Yi Huang
creator: Yanming Zhang
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2025-11-25
publication date: 2025-11-25
doi: 10.4208/csiam-am.SO-2024-0047

A Mathematical Analysis for the Dynamics of Multiple Languages
type: item
description: In many regions of the world, languages coexist in daily life, but often one tongue increases its use at the expense of another. In the present paper, we build a large compartmental system of differential equations that meets the situation of two “prestigious” tongues and many local languages, whose use is reduced by social interaction. The focus is on the preferred language in social relationships for communicating, rather than mere knowledge. We aim at stating and proving theorems on the qualitative behavior of the system. Numerical simulations illustrate the results, giving rise to distinct dynamics.
subject: Articles
  topic: section
subject: Language competition
  topic: keywords
subject: mathematical model
  topic: keywords
subject: dynamical system
  topic: keywords
subject: simulation.
  topic: keywords
subject: 34A34
  topic: subjects
subject: 37M05
  topic: subjects
subject: 91D10
  topic: subjects
creator: Iván Area
creator: Marc Jornet
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-30
publication date: 2025-09-30
starting page: 842
ending page: 861
doi: 10.4208/csiam-am.SO-2024-0056

pETNNs: Partial Evolutionary Tensor Neural Networks for Solving Time-Dependent Partial Differential Equations
type: item
description: We present partial evolutionary tensor neural networks (pETNNs), a novel approach for solving time-dependent partial differential equations with high accuracy and capable of handling high-dimensional problems. Our architecture incorporates tensor neural networks and evolutionary parametric approximation. A posteriori error bound is proposed to support the extrapolation capabilities. In numerical implementations, we adopt a partial update strategy to achieve a significant reduction in computational cost while maintaining precision and robustness. Notably, as a low-rank approximation method of complex dynamical systems, pETNNs enhance the accuracy of evolutionary deep neural networks and empower computational abilities to address high-dimensional problems. Numerical experiments demonstrate the superior performance of the pETNNs in solving complex time-dependent equations, including the incompressible Navier-Stokes equations, high-dimensional heat equations, high-dimensional transport equations, and dispersive equations of higher-order derivatives.
subject: Articles
  topic: section
subject: Time-dependent partial differential equations
  topic: keywords
subject: tensor neural networks
  topic: keywords
subject: evolutionary deep neural networks
  topic: keywords
subject: high-dimensional problems.
  topic: keywords
subject: 65M99
  topic: subjects
subject: 65L05
  topic: subjects
subject: 68T07
  topic: subjects
creator: Tunan Kao
creator: He Zhang
creator: Lei Zhang
creator: Jin Zhao
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-30
publication date: 2025-09-30
starting page: 862
ending page: 891
doi: 10.4208/csiam-am.SO-2024-0048

Global Solvability in a Two-Species Keller-Segel-Navier-Stokes System with Sub-Logistic Source
type: item
description: This paper is concerned with a two-species Keller-Segel-Navier-Stokes model with sub-logistic source in a bounded domain with smooth boundary under noflux/no-flux/no-flux/Dirichlet boundary conditions. For a large class of cell kinetics including sub-logistic degradation, it is shown that under an explicit condition involving the chemotactic strength and initial mass of cells, the two-dimensional Keller-Segel-Navier-Stokes problem possesses a global and bounded classical solution. In the case with arbitrary superlinear logistic degradation, it is proved that for all suitably regular initial data, the two-dimensional Keller-Segel-Navier-Stokes problem has at least one globally defined solution in an appropriate generalized sense. These results improves and extends the previously known ones.
subject: Articles
  topic: section
subject: Keller-Segel-Navier-Stokes
  topic: keywords
subject: sub-logistic source
  topic: keywords
subject: boundedness
  topic: keywords
subject: generalized solution.
  topic: keywords
subject: 35A09
  topic: subjects
subject: 35D30
  topic: subjects
subject: 35Q35
  topic: subjects
subject: 92C17
  topic: subjects
creator: Chao Liu
creator: Bin Liu
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-30
publication date: 2025-09-30
starting page: 799
ending page: 841
doi: 10.4208/csiam-am.SO-2024-0016

A Sharp Uniform-in-Time Error Estimate for Stochastic Gradient Langevin Dynamics
type: item
description: Abstract. We establish a sharp uniform-in-time error estimate for the stochastic gradient Langevin dynamics (SGLD), which is a widely-used sampling algorithm. Under mild assumptions, we obtain a uniform-in-time $\mathcal{O}(η^2)$ bound for the Kullback-Leibler divergence between the SGLD iteration and the Langevin diffusion, where $η$ is the step size (or learning rate). Our analysis is also valid for varying step sizes. Consequently, we are able to derive an $\mathcal{O}(\eta)$ bound for the distance between the invariant measures of the SGLD iteration and the Langevin diffusion, in terms of Wasserstein or total variation distances. Our result can be viewed as a significant improvement compared with existing analysis for SGLD in related literature.
subject: Articles
  topic: section
subject: Random batch
  topic: keywords
subject: Euler-Maruyama scheme
  topic: keywords
subject: Fokker-Planck equation
  topic: keywords
subject: log-Sobolev inequality.
  topic: keywords
subject: 65C20
  topic: subjects
subject: 68Q25
  topic: subjects
subject: 60H30
  topic: subjects
creator: Lei Li
creator: Yuliang Wang
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-30
publication date: 2025-09-30
starting page: 711
ending page: 759
doi: 10.4208/csiam-am.SO-2024-0039

An Efficient Iteration Based on Reduced Basis Method for Time-Dependent Problems with Random Inputs
type: item
description: In this paper, we propose an efficient iterative method called RB-iteration, based on reduced basis (RB) techniques, for addressing time-dependent problems with random input parameters. This method reformulates the original model such that the left-hand side is parameter-independent, while the right-hand side remains parameterdependent, facilitating the application of fixed-point iteration for solving the system. High-fidelity simulations for time-dependent problems often demand considerable computational resources, rendering them impractical for many applications. RB-iteration enhances computational efficiency by executing iterations in a reduced order space. This approach results in significant reductions in computational costs. We conduct a rigorous convergence analysis and present detailed numerical experiments for the RB-iteration method. Our results clearly demonstrate that RB-iteration achieves superior efficiency compared to the direct fixed-point iteration method and provides enhanced accuracy relative to the classical proper orthogonal decomposition (POD) greedy method.
subject: Articles
  topic: section
subject: Reduced order model
  topic: keywords
subject: time-dependent problems
  topic: keywords
subject: random inputs
  topic: keywords
subject: reduced basis
  topic: keywords
subject: iteration method.
  topic: keywords
subject: 35B30
  topic: subjects
subject: 65M12
  topic: subjects
subject: 65M50
  topic: subjects
subject: 65R20
  topic: subjects
subject: 76R99
  topic: subjects
subject: 78M34
  topic: subjects
creator: Dou Dai
creator: Qiuqi Li
creator: Huailing Song
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-30
publication date: 2025-09-30
starting page: 760
ending page: 798
doi: 10.4208/csiam-am.SO-2024-0045

Two Methods Addressing Variable-Exponent Fractional Initial and Boundary Value Problems and Abel Integral Equation
type: item
description: Variable-exponent fractional models attract increasing attentions in various applications, while rigorous mathematical and numerical analysis for typical models remains largely untreated. This work provides general tools to address these models. Specifically, we first develop a convolution method to study the well-posedness, regularity, an inverse problem and numerical approximation for the subdiffusion of variable exponent. For models such as the variable-exponent two-sided space-fractional boundary value problem (including the variable-exponent fractional Laplacian equation as a special case) and the distributed variable-exponent model, for which the convolution method does not apply, we develop a perturbation method to prove their well-posedness. The relations between the convolution method and the perturbation method are discussed, and we further apply the latter to prove the well-posedness of the variable-exponent Abel integral equation and discuss the constraint on the data under different initial values of variable exponent.
subject: Articles
  topic: section
subject: Variable exponent
  topic: keywords
subject: fractional differential equation
  topic: keywords
subject: integral equation
  topic: keywords
subject: mathematical analysis
  topic: keywords
subject: numerical analysis.
  topic: keywords
subject: 35R11
  topic: subjects
subject: 45D05
  topic: subjects
subject: 65M12
  topic: subjects
creator: Xiangcheng Zheng
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-30
publication date: 2025-09-30
starting page: 666
ending page: 710
doi: 10.4208/csiam-am.SO-2024-0052

Convergent Finite Elements on Arbitrary Meshes, the WG Method
type: item
description: On meshes with the maximum angle condition violated, the standard conforming, nonconforming, and discontinuous Galerkin finite elements do not converge to the true solution when the mesh size goes to zero. It is shown that one type of weak Galerkin finite element method converges on triangular and tetrahedral meshes violating the maximum angle condition, i.e. on arbitrary meshes. Numerical tests confirm the theory.
subject: Articles
  topic: section
subject: Discontinuous finite element
  topic: keywords
subject: maximum angle condition
  topic: keywords
subject: Poisson’s equation
  topic: keywords
subject: triangular grid
  topic: keywords
subject: tetrahedral grid.
  topic: keywords
subject: 65N15
  topic: subjects
subject: 65N30
  topic: subjects
creator: Ran Zhang
creator: Shangyou Zhang
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-30
publication date: 2025-09-30
starting page: 651
ending page: 665
doi: 10.4208/csiam-am.SO-2024-0038

Benchmarking Density Functional Theory for Noble Metal Hydrides: A High-Fidelity PES and Vibrational Analysis of the ${\rm AgAuH}^−$ Anion
type: item
description: The accurate description of noble metal hydrides remains a fundamental challenge for electronic structure theory, especially in systems involving heavy elements where relativistic effects and electron correlation are significant. In this study, we present a high-accuracy potential energy surface (PES) for the ${\rm AgAuH}^−$ anion, constructed from 3,595 UCCSD(T)-F12a energy points and fitted using a feedforward neural network with a root mean square error of 0.21 meV. The PES captures the entire configuration space, including linear and bent minima, transition-state-like structures, and dissociation pathways. Quantum vibrational bound states were computed using time-independent quantum dynamics, enabling detailed mode assignments. The high-fidelity PES and vibrational dataset were used to benchmark some widely employed density functional theory (DFT) methods, B3LYP, ωB97XD, XYG3, and XYGJ-OS. Among these, XYGJ-OS provided the best agreement with the reference data in terms of equilibrium geometries and vibrational frequencies. This study provides a robust benchmark for method development and validation in metal-containing systems and highlights the importance of using high-level reference data when modeling complex coinage-metal hydrides.
subject: Articles
  topic: section
subject: ${\rm AgAuH}^−
  topic: keywords
subject: $ density functional theory benchmarking
  topic: keywords
subject: high-level ab initio potential energy surface
  topic: keywords
subject: vibrational quantum dynamics
  topic: keywords
subject: coinage metal hydrides.
  topic: keywords
creator: Yuquan Feng
creator: Kaiyi Zhao
creator: Jun Chen
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-05
publication date: 2025-09-05
starting page: 274
ending page: 280
doi: 10.4208/cicc.2025.146.02

Construction and Analysis for Adams Explicit Discretization of High-Index Saddle Dynamics
type: item
description: Saddle points largely exist in complex systems and play important roles in various scientific problems. High-index saddle dynamics (HiSD) is an efficient method for computing any-index saddle points and constructing solution landscape. In this paper, we propose a two-step Adams explicit scheme for HiSD and analyze its error estimate versus time step. Through careful argumentation and overcoming the difficulties caused by nonlinear coupling and orthogonalisation, we prove that the two-step Adams explicit scheme has second-order accuracy. The theoretical results are further verified by two numerical experiments.
subject: Articles
  topic: section
subject: Saddle point
  topic: keywords
subject: saddle dynamics
  topic: keywords
subject: solution landscape
  topic: keywords
subject: Adams scheme
  topic: keywords
subject: error estimate.
  topic: keywords
subject: 37M05
  topic: subjects
subject: 37N30
  topic: subjects
subject: 65L20
  topic: subjects
creator: Shuai Miao
creator: Ziqi Liu
creator: Lei Zhang
creator: Pingwen Zhang
creator: Xiangcheng Zheng
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-11
publication date: 2025-09-11
starting page: 625
ending page: 650
doi: 10.4208/csiam-am.SO-2024-0020

Well-Posedness and Regularity Analyses for Nonlocal Nonautonomous System
type: item
description: The time-space nonlocal evolution equations are powerful implementation for modeling anomalous diffusion. In this research, we study the nonlocal nonautonomous reaction-diffusion equation where $\chi$ is a Lusin space, $∂^w_t$ is a generalized time fractional derivative, $κ$ is a bounded reaction rate, and $\mathcal{L}$ is an infinitesimal generator in terms of semigroup induced by a symmetric Markov process $X.$ We show that the stochastic representation $u(t,x)$ defined by is the unique mild as well as weak solution. By further analysis, one can get that the above stochastic representation is also the unique strong solution, and the higher spatial and temporal regularity are obtained. In some particular cases, the corresponding dynamical behaviors are displayed.
subject: Articles
  topic: section
subject: Stochastic representation
  topic: keywords
subject: time fractional nonautonomous equation
  topic: keywords
subject: well-posedness
  topic: keywords
subject: regularity
  topic: keywords
subject: Primary 35R11
  topic: subjects
subject: 60K50;Secondary 26A33
  topic: subjects
subject: 60H30
  topic: subjects
creator: Rui Sun
creator: Lijuan Zhang
creator: Weihua Deng
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-11
publication date: 2025-09-11
starting page: 593
ending page: 624
doi: 10.4208/csiam-am.SO-2024-0037

Global-in-Time Energy Stability for a General Class of Stabilization Single-Step Schemes Applied to the Swift-Hohenberg Equation
type: item
description: The linear stabilization approach is well-known for facilitating the use of large time steps in solving gradient flows while maintaining stability. However, the up-to-date analysis of energy stability relies on either a global Lipschitz nonlinearity or an $ℓ^∞$ bound assumption of numerical solutions. Considering the Swift-Hohenberg equation that lacks a global Lipschitz nonlinearity, we develop a unified framework to analyze the energy stability and characterize the stabilization size for a class of single-step schemes employing spatial Fourier pseudo-spectral discretization. First, assuming that all stage solutions are bounded in the $ℓ^∞$ norm, we illustrate that the energy obtained from a single-step scheme with non-negative energy-stability-preserving coefficient is unconditionally dissipative, as long as a sufficiently large stabilization parameter is employed. To justify the $ℓ^∞$ bound assumption of solutions, we use the third-order exponential-time-differencing Runge-Kutta scheme as a case study to establish a uniform-in-time discrete $H^2$ bound for stage solutions under an $\mathcal{O}(1)$ time step constraint. This leads to a uniform $ℓ^∞$ bound of stage solutions through discrete Sobolev embedding. Consequently, we achieve a stabilization parameter of $\mathcal{O}(1),$ which is independent of the time step, thereby ensuring the energy stability. The global-in-time energy stability analysis and characterization of the stabilization parameter represent significant advancements for general single-step schemes applied to a gradient flow without the global Lipschitz continuity.
subject: Articles
  topic: section
subject: Swift-Hohenberg equation
  topic: keywords
subject: single-step scheme
  topic: keywords
subject: energy-stability-preserving coefficient
  topic: keywords
subject: global-in-time energy stability.
  topic: keywords
subject: 35Q92
  topic: subjects
subject: 35B36
  topic: subjects
subject: 65L06
  topic: subjects
creator: Hong Zhang
creator: Haifeng Wang
creator: Yan Wang
creator: Xu Qian
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-11
publication date: 2025-09-11
starting page: 555
ending page: 592
doi: 10.4208/csiam-am.SO-2024-0069

New Finite Volume Element Schemes Based on a Two-Layer Dual Strategy
type: item
description: A two-layer dual strategy is proposed in this work to construct a new family of high-order finite volume element (FVE-2L) schemes that can avoid main common drawbacks of the existing high-order finite volume element (FVE) schemes. The existing high-order FVE schemes are complicated to construct since the number of the dual elements in each primary element used in their construction increases with a rate $\mathcal{O}((k+1)^2),$ where $k$ is the order of the scheme. Moreover, all $k$-th-order FVE schemes require a higher regularity $H^{k+2}$ than the approximation theory for the $L^2$ theory. Furthermore, all FVE schemes lose local conservation properties over boundary dual elements when dealing with Dirichlet boundary conditions. The proposed FVE-2L schemes has a much simpler construction since they have a fixed number (four) of dual elements in each primary element. They also reduce the regularity requirement for the $L^2$ theory to $H^{k+1}$ and preserve the local conservation law on all dual elements of the second dual layer for both flux and equation forms. Their stability and $H^1$ and $L^2$ convergence are proved. Numerical results are presented to illustrate the convergence and conservation properties of the FVE-2L schemes. Moreover, the condition number of the stiffness matrix of the FVE-2L schemes for the Laplacian operator is shown to have the same growth rate as those for the existing FVE and finite element schemes.
subject: Articles
  topic: section
subject: Finite volume
  topic: keywords
subject: two-layer dual mesh
  topic: keywords
subject: conservation
  topic: keywords
subject: $L^2$ estimate
  topic: keywords
subject: minimum angle condition.
  topic: keywords
subject: 65N08
  topic: subjects
subject: 65N12
  topic: subjects
subject: 65N30
  topic: subjects
creator: Weizhang Huang
creator: Xiang Wang
creator: Xinyuan Zhang
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-11
publication date: 2025-09-11
starting page: 527
ending page: 554
doi: 10.4208/csiam-am.SO-2024-0051

Highly Efficient Gauss’s Law-Preserving Spectral Algorithms for Maxwell’s Double-Curl Source and Eigenvalue Problems Based on Eigen-Decomposition
type: item
description: In this paper, we present the Gauss’s law-preserving spectral methods and their efficient solution algorithms for curl-curl source and eigenvalue problems arising from Maxwell’s equations. Arbitrary order $\mathbf{H}{\rm (curl)}$-conforming spectral basis functions in two and three dimensions are firstly proposed using compact combination of Legendre polynomials. A mixed formulation involving a Lagrange multiplier is then adopted to preserve the Gauss’s law in the weak sense. To overcome the bottleneck of computational efficiency caused by the saddle-point nature of the mixed scheme, we present highly efficient algorithms based on reordering and decoupling of the linear system and numerical eigen-decomposition of 1D mass matrix. The proposed solution algorithms are direct methods requiring only several matrix-matrix or matrix-tensor products of $N$-by-$N$ matrices, where $N$ is the highest polynomial order in each direction. Compared with other direct methods, the computational complexities are reduced from $\mathcal{O}(N^6)$ and $\mathcal{O}(N^9)$ to $\mathcal{O}(N^{log_2 7})$ and $\mathcal{O}(N^{1+log_2 7})$ with small and constant pre-factors for 2D and 3D cases, respectively. Moreover, these algorithms strictly obey the Helmholtz-Hodge decomposition, thus totally eliminate the spurious eigen-modes of non-physical zero eigenvalues for convex domains. Ample numerical examples for solving Maxwell’s source and eigenvalue problems are presented to demonstrate the accuracy and efficiency of the proposed methods.
subject: Articles
  topic: section
subject: Spectral method
  topic: keywords
subject: time-harmonic Maxwell’s equation
  topic: keywords
subject: structure-preserving method
  topic: keywords
subject: Gauss’s law preservation
  topic: keywords
subject: fast solver.
  topic: keywords
subject: 65N35
  topic: subjects
subject: 65N22
  topic: subjects
subject: 65N25
  topic: subjects
subject: 65F05
  topic: subjects
creator: Sen Lin
creator: Huiyuan Li
creator: Zhiguo Yang
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-11
publication date: 2025-09-11
starting page: 489
ending page: 526
doi: 10.4208/csiam-am.SO-2024-0042

$\mathbf{H}$(${\rm curl}^2$) Conforming Element for Maxwell’s Transmission Eigenvalue Problem Using Fixed-Point Approach
type: item
description: Using newly developed $\mathbf{H}$(${\rm curl}^2$) conforming elements, we solve the Maxwell’s transmission eigenvalue problem. Both real and complex eigenvalues are considered. Based on the fixed-point weak formulation with reasonable assumptions, the optimal error estimates for numerical eigenvalues and eigenfunctions (in the $\mathbf{H}$(${\rm curl}^2$)-norm and $\mathbf{H}{\rm (curl)}$-semi-norm) are established. Numerical experiments are performed to verify the theoretical assumptions and confirm our theoretical analysis.
subject: Articles
  topic: section
subject: Maxwell’s transmission eigenvalues
  topic: keywords
subject: curl-curl conforming element
  topic: keywords
subject: error estimates.
  topic: keywords
subject: 65N25
  topic: subjects
subject: 65N30
  topic: subjects
creator: Jiayu Han
creator: Zhimin Zhang
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-11
publication date: 2025-09-11
starting page: 468
ending page: 488
doi: 10.4208/csiam-am.SO-2021-0046

Efficient Numerical Methods for Computing Stationary States of Spherical Landau-Brazovskii Model
type: item
description: In this paper, we develop a set of efficient methods to compute stationary states of the spherical Landau-Brazovskii (LB) model in a discretization-then-optimization way. First, we discretize the spherical LB energy functional into a finite-dimensional energy function by the spherical harmonic expansion. Then five optimization methods are developed to compute stationary states of the discretized energy function, including the accelerated adaptive Bregman proximal gradient, Nesterov, adaptive Nesterov, adaptive nonlinear conjugate gradient and adaptive gradient descent methods. To speed up the convergence, we propose a principal mode analysis (PMA) method to estimate good initial configurations and sphere radius. The PMA method also reveals the relationship between the optimal sphere radius and the dominant degree of spherical harmonics. Numerical experiments show that our approaches significantly reduce the number of iterations and the computational time.
subject: Articles
  topic: section
subject: Spherical Landau-Brazovskii model
  topic: keywords
subject: stationary states
  topic: keywords
subject: spherical harmonic expansion
  topic: keywords
subject: optimization methods
  topic: keywords
subject: principal mode analysis.
  topic: keywords
subject: 20C35
  topic: subjects
subject: 35Q74
  topic: subjects
subject: 49M37
  topic: subjects
creator: Qun Qiu
creator: Wei Si
creator: Guanghua Ji
creator: Kai Jiang
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-11
publication date: 2025-09-11
starting page: 435
ending page: 467
doi: 10.4208/csiam-am.SO-2023-0038

A Hue-Preserving Color Image Restoration Model Using Saturation-Value Total Variation
type: item
description: In this paper, we propose and develop a novel hue-preserving color image restoration model. In the proposed model, saturation-value total variation is used as the regularization term. In order to reduce hue loss during regularization, the huepreserving technique is incorporated into the proposed energy functional. We then rewrite the proposed model equivalently into a three-block separable convex version and apply an alternating direction method of multipliers based algorithm to solve the proposed equivalent model numerically. We also give the convergence analysis of the proposed algorithm. Numerical examples are presented to demonstrate that the performance of the proposed restoration model is better than that of other testing methods in terms of visual quality and some criteria such as peak signal-to-noise ratio, structure similarity, and spatial-CIELAB color error.
subject: Articles
  topic: section
creator: Wei Wang
creator: Yuming Yang
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2025-09-26
publication date: 2025-09-26
doi: 10.4208/csiam-am.SO-2023-0009

Exploring Fractional-Order Nonlinear Dynamics in Biodiesel Production with Optimal Control
type: item
description: Biodiesel, a sustainable and renewable energy source, is a promising alternative to fossil fuels. The transesterification process of biodiesel production effectively captures memory effects in reaction kinetics. In this study, we developed two fractional order models of the chemical catalytic transesterification reaction to explore the memory effects of the reaction kinetics utilizing two different non-singular kernel methods: Caputo-Fabrizio and Atangana-Baleanu in the Caputo sense. We compared the results with experimental data of biodiesel production and demonstrated the existence and uniqueness of the solution for the fractional system. A sensitivity analysis is performed using the Latin hypercube sampling method to evaluate the impact of various parameters on biodiesel production, followed by the computation of partial rank correlation coefficients based on Pearson’s correlation coefficient. We exhibit the dynamic behavior of all reactants corresponding to these fractional models with the variation of fractional order and the memory rate parameter. Additionally, we display the memory effect through the surface plots for biodiesel production by varying fractional order, molar ratio, and ultrasound frequency. Our numerical comparison with experimental data identifies the fractional-order value for the best fit of biodiesel production and can be increased by applying optimal control on ultrasound frequency.
subject: Articles
  topic: section
creator: Sk Mosaraf Ahammed
creator: Oluwole Daniel Makinde
creator: Tushar Ghosh
creator: Priti Kumar Roy
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2025-07-01
publication date: 2025-07-01
doi: 10.4208/csiam-am.SO-2025-0016

Optical Wave Turbulence: The Conformal Symmetry Transformations of Statistics of the Quantum Fluids of Light
type: item
description: We use the quantum fluid analogy [Nazarenko et al., Phys. Rev. E, 92, 2015] for coherent structures (vortices or solitons) interacting among themselves and with the random wave component. This is performed for 2D defocusing media based on quantum fluid approximation of the two-dimensional nonlinear Schr\"{o}dinger equation in the statistical frame. With this, the Lundgren-Monin-Novikov infinite chain of equations for the $n$-point density function $f_n$ for the vorticity field is used. The conformal group of symmetry transformations calculated [Grebenev et. al., Theor. Math. Phys., 217(2), 2023] is applied to implement several elements of a gauge theory in the conformal transformation optics. Finally, we demonstrate how to use the variational generalized Brenier principle [Brenier, J. Am. Math. Soc., 2, 1989] together with the conformal invariance of statistics to close the infinite chain of Landgren-Monin-Novikov equations.
subject: Articles
  topic: section
creator: V. N. Grebenev
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2025-06-30
publication date: 2025-06-30
doi: 10.4208/csiam-am.SO-2024-0061

A Numerical Algorithm with Linear Complexity for Multi-Marginal Optimal Transport with $L^1$ Cost
type: item
description: Numerically solving multi-marginal optimal transport (MMOT) problems is computationally prohibitive, even for moderate-scale instances involving $l \geq 4$ marginals with support sizes of $N \geq 1000$. The cost in MMOT is represented as a tensor with $N^l$ elements. Even accessing each element once incurs a significant computational burden. In fact, many algorithms require direct computation of tensor-vector products, leading to a computational complexity of $O(N^l)$ or beyond. In this paper, inspired by our previous work [Comm. Math. Sci., 20, 2022], we observe that the costly tensor-vector products in the Sinkhorn Algorithm can be computed with a recursive process by separating summations and dynamic programming. Based on this idea, we propose a fast tensor-vector product algorithm to solve the MMOT problem with $L^1$ cost, achieving a miraculous reduction in the computational cost of the entropy regularized solution to $O(N)$. Numerical experiment results confirm such high performance of this novel method which can be several orders of magnitude faster than the original Sinkhorn algorithm.
subject: Articles
  topic: section
creator: Chunhui Chen
creator: Jing Chen
creator: Baojia Luo
creator: Shi Jin
creator: Hao Wu
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2025-06-24
publication date: 2025-06-24
doi: 10.4208/csiam-am.SO-2024-0025

A Deep Learning Approach for Solving the Inverse Problem of the Wave Equation
type: item
description: Full-waveform inversion is a powerful geophysical imaging technique that infers high-resolution subsurface physical parameters by solving a non-convex optimization problem. However, due to limitations in observation, e.g. limited shots or receivers, and random noise, conventional inversion methods are confronted with numerous challenges, such as the local-minimum problem. In recent years, a substantial body of work has demonstrated that the integration of deep neural networks and partial differential equations for solving full-waveform inversion problems has shown promising performance. In this work, drawing inspiration from the expressive capacity of neural networks, we provide a new deep learning approach aimed at accurately reconstructing subsurface physical velocity parameters. This method is founded on a re-parametrization technique for Bayesian inference, achieved through a deep neural network with random weights. Notably, our proposed approach does not hinge upon the requirement of the labeled training dataset, rendering it exceedingly versatile and adaptable to diverse subsurface models. Furthermore, uncertainty analysis is effectively addressed through approximate Bayesian inference. Extensive experiments show that the proposed approach performs noticeably better than existing conventional inversion methods.
subject: Articles
  topic: section
creator: Xiong-Bin Yan
creator: Keke Wu
creator: Zhi-Qin John Xu
creator: Zheng Ma
rights: Copyright (c) 2025 CSIAM Transactions on Applied Mathematics
date: 2025-06-18
publication date: 2025-06-18
doi: 10.4208/csiam-am.SO-2024-0027

Enhanced Expressive Power and Fast Training of Neural Networks by Random Projections
type: item
description: Random projections are able to perform dimension reduction efficiently for datasets with nonlinear low-dimensional structures. One well-known example is that random matrices embed sparse vectors into a low-dimensional subspace nearly isometrically, known as the restricted isometric property in compressed sensing. In this paper, we explore some applications of random projections in deep neural networks. We provide the expressive power of fully connected neural networks when the input data are sparse vectors or form a low-dimensional smooth manifold. We prove that the number of neurons required for approximating a Lipschitz function with a prescribed precision depends on the sparsity or the dimension of the manifold and weakly on the dimension of the input vector. The key in our proof is that random projections embed stably the set of sparse vectors or a low-dimensional smooth manifold into a low-dimensional subspace. Based on this fact, we also propose some new neural network models, where at each layer the input is first projected onto a low-dimensional subspace by a random projection and then the standard linear connection and non-linear activation are applied. In this way, the number of parameters in neural networks is significantly reduced, and therefore the training of neural networks can be accelerated without too much performance loss.
subject: Articles
  topic: section
subject: Neural network
  topic: keywords
subject: approximation
  topic: keywords
subject: random projection.
  topic: keywords
subject: 68T05
  topic: subjects
subject: 41A30
  topic: subjects
creator: Jian-Feng Cai
creator: Dong Li
creator: Jiaze Sun
creator: Ke Wang
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2021-08-31
publication date: 2021-08-31
starting page: 532
ending page: 550
doi: 10.4208/csiam-am.SO-2020-0004

Multipliers Correction Methods for Optimization Problems over the Stiefel Manifold
type: item
description: We propose a class of multipliers correction methods to minimize a differentiable function over the Stiefel manifold. The proposed methods combine a function value reduction step with a proximal correction step. The former one searches along an arbitrary descent direction in the Euclidean space instead of a vector in the tangent space of the Stiefel manifold. Meanwhile, the latter one minimizes a first-order proximal approximation of the objective function in the range space of the current iterate to make Lagrangian multipliers associated with orthogonality constraints symmetric at any accumulation point. The global convergence has been established for the proposed methods. Preliminary numerical experiments demonstrate that the new methods significantly outperform other state-of-the-art first-order approaches in solving various kinds of testing problems.
subject: Articles
  topic: section
subject: Multipliers correction
  topic: keywords
subject: proximal approximation
  topic: keywords
subject: orthogonality constraint
  topic: keywords
subject: Stiefel manifold.
  topic: keywords
subject: 15A18
  topic: subjects
subject: 65F15
  topic: subjects
subject: 65K05
  topic: subjects
subject: 90C06
  topic: subjects
subject: 90C30
  topic: subjects
creator: Lei Wang
creator: Bin Gao
creator: Xin Liu
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2021-08-31
publication date: 2021-08-31
starting page: 508
ending page: 531
doi: 10.4208/csiam-am.SO-2020-0008