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1. Discretisation of an Oldroyd-B viscoelastic fluid flow using a Lie derivative formulation NSTL国家科技图书文献中心

Ashby, Ben S. | Pryer, Tristan - 《Advances in computational mathematics》 - 2025,51(1) - 共26页

摘要：In this article, we present a numerical method | for the Stokes flow of an Oldroyd-B fluid. The | viscoelastic stress evolves according to a constitutive law | formulated in terms of the upper convected time derivative | . A finite difference method is used to discretise

关键词： Non-Newtonian fluid dynamics | Upper convected time derivative | Finite element methods | Finite difference methods | Lie derivative approximation

2. A reduced-order model for advection-dominated problems based on the Radon Cumulative Distribution Transform NSTL国家科技图书文献中心

Long, Tobias | Barnett, Robert ... - 《Advances in computational mathematics》 - 2025,51(1) - 共30页

摘要：Problems with dominant advection | , discontinuities, travelling features, or shape variations are | widespread in computational mechanics. However, classical | linear model reduction and interpolation methods | typically fail to reproduce even relatively small

关键词： Reduced order model | Non-linear transformations | Advection-dominated problems | Radon transform | Cumulative distribution | Proper orthogonal decomposition | 65-XX

3. On the recovery of two function-valued coefficients in the Helmholtz equation for inverse scattering problems via neural networks NSTL国家科技图书文献中心

Zhou, Zehui - 《Advances in computational mathematics》 - 2025,51(1) - 共54页

摘要：Recently, deep neural networks (DNNs) have | become powerful tools for solving inverse scattering | problems. However, the approximation and generalization | rates of DNNs for solving these problems remain | largely under-explored. In this work, we introduce two

关键词： Inverse scattering problem | Neural network | Approximation | Generalization | Two function-valued coefficients

4. A nonsingular-kernel Dirichlet-to-Dirichlet mapping method for the exterior Stokes problem NSTL国家科技图书文献中心

Liu, Xiaojuan | Li, Maojun ... - 《Advances in computational mathematics》 - 2025,51(1) - 共24页

摘要：This paper studies the finite element method | for solving the exterior Stokes problem in two | dimensions. A nonlocal boundary condition is defined using | a nonsingular-kernel Dirichlet-to-Dirichlet (DtD | ) mapping, which maps the Dirichlet data on an interior

关键词： Exterior Stokes problem | Dirichlet-to-Dirichlet mapping | Mixed finite elements | Bubble function | Error estimates

5. An all-frequency stable integral system for Maxwell's equations in 3-D penetrable media: continuous and discrete model analysis NSTL国家科技图书文献中心

Ganesh, Mahadevan | Hawkins, Stuart C.... - 《Advances in computational mathematics》 - 2025,51(1) - 共37页

摘要：We introduce a new system of surface integral | equations for Maxwell's transmission problem in three | dimensions (3-D). This system has two remarkable features | , both of which we prove. First, it is well-posed at | all frequencies. Second, the underlying linear

关键词： Electromagnetic scattering | Dielectric | Weakly singular integral equations | Surface integral equations | Stabilization | Spectral numerical convergence

6. Parametric model order reduction for a wildland fire model via the shifted POD-based deep learning method NSTL国家科技图书文献中心

Shubhaditya,Burela | Philipp,Krah ... - 《Advances in computational mathematics》 - 2025,51(1) - 共43页

摘要：Abstract Parametric model order reduction | techniques often struggle to accurately represent transport | -dominated phenomena due to a slowly decaying Kolmogorov n | -width. To address this challenge, we propose a non | -intrusive, data-driven methodology that combines the

关键词： Model order reduction | Shifted proper orthogonal decomposition | Data-driven models | Deep learning | Artificial neural networks | Wildland fires | 68T07 | 65F55 | 35Q35 | 76-10

7. A difference finite element method based on nonconforming finite element methods for 3D elliptic problems NSTL国家科技图书文献中心

Song, Jianjian | Sheen, Dongwoo ... - 《Advances in computational mathematics》 - 2025,51(1) - 共31页

摘要：In this paper, a class of 3D elliptic | equations is solved by using the combination of the finite | difference method in one direction and nonconforming finite | element methods in the other two directions. A finite | -difference (FD) discretization based on P1documentclass

关键词： Difference finite element method | Crouzeix-Raviart element | Park-Sheen element | 3D elliptic equation | Error estimation

8. Strong convergence of a fully discrete scheme for stochastic Burgers equation with fractional-type noise NSTL国家科技图书文献中心

Wang, Yibo | Cao, Wanrong - 《Advances in computational mathematics》 - 2025,51(2) - 共32页

摘要：We investigate numerical approximations for | the stochastic Burgers equation driven by an | additive cylindrical fractional Brownian motion with | Hurst parameter H is an element of(12,1)documentclass | [12pt]{minimal} usepackage{amsmath} usepackage{wasysym

关键词： Stochastic Burgers equation | Fractional Brownian motion | Tamed exponential Euler method | Strong convergence | Non-globally monotone nonlinearity

9. A scaling fractional asymptotical regularization method for linear inverse problems NSTL国家科技图书文献中心

Yuan, Lele | Zhang, Ye - 《Advances in computational mathematics》 - 2025,51(1) - 共37页 - 被引量：1

摘要：In this paper, we propose a Scaling Fractional | Asymptotical Regularization (S-FAR) method for solving linear | ill-posed operator equations in Hilbert spaces | , inspired by the work of (2019 Fract. Calc. Appl. Anal. 22 | (3) 699-721). Our method is incorporated into the

关键词： Linear operator equation | Ill-posed problems | Fractional asymptotical regularization | Convergence rates | De-biasing | Sparse thresholding

10. Quasi-Monte Carlo methods for mixture distributions and approximated distributions via piecewise linear interpolation NSTL国家科技图书文献中心

Tiangang,Cui | Josef,Dick ... - 《Advances in computational mathematics》 - 2025,51(1) - 共44页

摘要：Abstract We study numerical integration over | bounded regions in Rsdocumentclass[12pt]{minimal | } usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts | } usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs | } usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin

摘要：In this article, we present a numerical method | for the Stokes flow of an Oldroyd-B fluid. The | viscoelastic stress evolves according to a constitutive law | formulated in terms of the upper convected time derivative | . A finite difference method is used to discretise

关键词： Non-Newtonian fluid dynamics | Upper convected time derivative | Finite element methods | Finite difference methods | Lie derivative approximation

摘要：Problems with dominant advection | , discontinuities, travelling features, or shape variations are | widespread in computational mechanics. However, classical | linear model reduction and interpolation methods | typically fail to reproduce even relatively small

关键词： Reduced order model | Non-linear transformations | Advection-dominated problems | Radon transform | Cumulative distribution | Proper orthogonal decomposition | 65-XX

摘要：Recently, deep neural networks (DNNs) have | become powerful tools for solving inverse scattering | problems. However, the approximation and generalization | rates of DNNs for solving these problems remain | largely under-explored. In this work, we introduce two

关键词： Inverse scattering problem | Neural network | Approximation | Generalization | Two function-valued coefficients

摘要：This paper studies the finite element method | for solving the exterior Stokes problem in two | dimensions. A nonlocal boundary condition is defined using | a nonsingular-kernel Dirichlet-to-Dirichlet (DtD | ) mapping, which maps the Dirichlet data on an interior

关键词： Exterior Stokes problem | Dirichlet-to-Dirichlet mapping | Mixed finite elements | Bubble function | Error estimates

摘要：We introduce a new system of surface integral | equations for Maxwell's transmission problem in three | dimensions (3-D). This system has two remarkable features | , both of which we prove. First, it is well-posed at | all frequencies. Second, the underlying linear

关键词： Electromagnetic scattering | Dielectric | Weakly singular integral equations | Surface integral equations | Stabilization | Spectral numerical convergence

摘要：Abstract Parametric model order reduction | techniques often struggle to accurately represent transport | -dominated phenomena due to a slowly decaying Kolmogorov n | -width. To address this challenge, we propose a non | -intrusive, data-driven methodology that combines the

关键词： Model order reduction | Shifted proper orthogonal decomposition | Data-driven models | Deep learning | Artificial neural networks | Wildland fires | 68T07 | 65F55 | 35Q35 | 76-10

摘要：In this paper, a class of 3D elliptic | equations is solved by using the combination of the finite | difference method in one direction and nonconforming finite | element methods in the other two directions. A finite | -difference (FD) discretization based on P1documentclass

关键词： Difference finite element method | Crouzeix-Raviart element | Park-Sheen element | 3D elliptic equation | Error estimation

摘要：We investigate numerical approximations for | the stochastic Burgers equation driven by an | additive cylindrical fractional Brownian motion with | Hurst parameter H is an element of(12,1)documentclass | [12pt]{minimal} usepackage{amsmath} usepackage{wasysym

关键词： Stochastic Burgers equation | Fractional Brownian motion | Tamed exponential Euler method | Strong convergence | Non-globally monotone nonlinearity

摘要：In this paper, we propose a Scaling Fractional | Asymptotical Regularization (S-FAR) method for solving linear | ill-posed operator equations in Hilbert spaces | , inspired by the work of (2019 Fract. Calc. Appl. Anal. 22 | (3) 699-721). Our method is incorporated into the

关键词： Linear operator equation | Ill-posed problems | Fractional asymptotical regularization | Convergence rates | De-biasing | Sparse thresholding

摘要：Abstract We study numerical integration over | bounded regions in Rsdocumentclass[12pt]{minimal | } usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts | } usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs | } usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin

关键词： Weighted integration | Quasi-Monte Carlo | Digital sequences | Mixture distributions | 65C05 | 11K45 | 65D30

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