General enrichments of stable GFEM for interface problems: Theory and extreme learning machine construction: General enrichments of stable GFEM for interface problems: theory and extreme learning machine construction

Authors: Wang, Dongmei, Li, Hengguang, Zhang, Qinghui

Source: Applied Numerical Mathematics. 214:143-159

Subject Terms: SGFEM, extreme learning machine, machine learning, Numerical and other methods in solid mechanics, Numerical methods for partial differential equations, boundary value problems, interface, complex geometry, Elliptic equations and elliptic systems

File Description: application/xml

Access URL: https://zbmath.org/8034929
https://doi.org/10.1016/j.apnum.2025.03.009

Drug release from polymeric platforms for non smooth solutions

Authors: J.S. Borges, G.C.M. Campos, J.A. Ferreira, G. Romanazzi

Source: Applied Numerical Mathematics. 213:12-37

Subject Terms: Parabolic equations and parabolic systems, Numerical methods for partial differential equations, boundary value problems, Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems

File Description: application/xml

Access URL: https://zbmath.org/8034915
https://doi.org/10.1016/j.apnum.2025.02.016

Spectral element method for the solution of viscoelastic seismic wave propagation

Authors: Barzegar, Feze, Rashidinia, Jalil

Source: Applied Numerical Mathematics. 212:92-109

Subject Terms: Gauss-Legendre-Lobatto points, Numerical methods for partial differential equations, boundary value problems, Basic methods in fluid mechanics, spectral element method, Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, viscoelastic wave equations, error analysis

File Description: application/xml

Analysis of average bound preserving time-implicit discretizations for convection-diffusion-reaction equation

Authors: Fengna Yan, Yinhua Xia

Source: Applied Numerical Mathematics. 211:103-122

Subject Terms: Parabolic equations and parabolic systems, Numerical methods for partial differential equations, boundary value problems, average bound-preserving, KKT limiter, LDG methods, Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, convection-diffusion-reaction equation, implicit time discretization

File Description: application/xml

Strongly consistent low-dissipation WENO schemes for finite elements

Authors: Joshua Vedral, Andreas Rupp, Dmitri Kuzmin

Source: Applied Numerical Mathematics. 210:64-81

Subject Terms: consistency, a priori estimates, Numerical methods for partial differential equations, boundary value problems, residual-based nonlinear weights, Basic methods in fluid mechanics, hyperbolic conservation laws, Numerical Analysis (math.NA), continuous and discontinuous Galerkin methods, Mathematics - Analysis of PDEs, WENO scheme, FOS: Mathematics, Mathematics - Numerical Analysis, Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, Analysis of PDEs (math.AP)

File Description: application/xml

Access URL: http://arxiv.org/abs/2407.04646
https://zbmath.org/7984900
https://doi.org/10.1016/j.apnum.2024.12.008

The two-grid hybrid high-order method for the nonlinear strongly damped wave equation on polygonal mesh and its reduced-order model

Authors: Lu Wang, Youjun Tan, Minfu Feng

Source: Applied Numerical Mathematics. 210:1-24

Subject Terms: hybrid high-order method, proper orthogonal decomposition, semi-discrete scheme, nonlinear wave equation, Numerical methods for partial differential equations, boundary value problems, fully-discrete scheme, Hyperbolic equations and hyperbolic systems, Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, two-grid algorithm, polygonal mesh

File Description: application/xml

Property-preserving numerical approximation of a Cahn–Hilliard–Navier–Stokes model with variable density and degenerate mobility: Property-preserving numerical approximation of a Cahn-Hilliard-Navier-Stokes model with variable density and degenerate mobility

Authors: Daniel Acosta-Soba, Francisco Guillén-González, J. Rafael Rodríguez-Galván, Jin Wang

Contributors: Matemáticas

Source: Applied Numerical Mathematics, Vol. 209, 2025, pp. 68-83
RODIN. Repositorio de Objetos de Docencia e Investigación de la Universidad de Cádiz
Universidad de Cádiz

Subject Terms: Discrete pointwise bounds, Numerical methods for partial differential equations, boundary value problems, Finite elements, Basic methods in fluid mechanics, Numerical Analysis (math.NA), discrete energy stability, upwind scheme, Upwind scheme, Discontinuous Galerkin, discrete pointwise bounds, FOS: Mathematics, finite elements, Mass-conservation, Mathematics - Numerical Analysis, Discrete energy stability, Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, mass-conservation, discontinuous Galerkin

File Description: application/pdf; application/xml

Access URL: http://arxiv.org/abs/2310.01522
http://hdl.handle.net/10498/35726

The Local Subtraction Approach for EEG and MEG Forward Modeling: The local subtraction approach for EEG and MEG forward modeling

Authors: Malte B. Höltershinken, Pia Lange, Tim Erdbrügger, Yvonne Buschermöhle, Fabrice Wallois, Alena Buyx, Sampsa Pursiainen, Johannes Vorwerk, Christian Engwer, Carsten H. Wolters

Source: SIAM Journal on Scientific Computing. 47:B160-B189

Subject Terms: Computational Engineering, Finance, and Science (cs.CE), FOS: Computer and information sciences, 03 medical and health sciences, MEG, 0302 clinical medicine, Numerical methods for partial differential equations, boundary value problems, finite element method, source analysis, EEG, Computer Science - Computational Engineering, Finance, and Science, source modeling

File Description: application/xml

Access URL: http://arxiv.org/abs/2302.12785

A Finite Expression Method for Solving High-Dimensional Committor Problems: A finite expression method for solving high-dimensional committor problems

Authors: Zezheng Song, Maria K. Cameron, Haizhao Yang

Source: SIAM Journal on Scientific Computing. 47:C1-C21

Subject Terms: Computer Science - Symbolic Computation, FOS: Computer and information sciences, Computer Science - Machine Learning, Numerical methods for partial differential equations, boundary value problems, deep neural network, Computational learning theory, Numerical Analysis (math.NA), Symbolic Computation (cs.SC), Symbolic computation and algebraic computation, committor functions, rare events, Machine Learning (cs.LG), finite expression method, high dimensions, Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics, FOS: Mathematics, symbolic learning, PDEs with randomness, stochastic partial differential equations, Mathematics - Numerical Analysis, Brownian motion, Artificial neural networks and deep learning, PDEs in connection with statistical mechanics

File Description: application/xml

Access URL: http://arxiv.org/abs/2306.12268

Treatment of 3D diffusion problems with discontinuous coefficients and Dirac curvilinear sources

Authors: Bejaoui, E., Ben Belgacem, F.

Source: Applied Numerical Mathematics. 207:400-413

Subject Terms: variable coefficients, Numerical methods for partial differential equations, boundary value problems, Physiological, cellular and medical topics, dual variational formulation, Elliptic equations and elliptic systems, singular-regular expansion, Dirac curvilinear sources

File Description: application/xml

Access URL: https://zbmath.org/7952196
https://doi.org/10.1016/j.apnum.2024.09.012

A Selectively Relaxed Splitting Preconditioning Strategy for the Flux-Limited Multi-Group Radiation Diffusion Equations in Three Dimensions: A selectively relaxed splitting preconditioning strategy for the flux-limited multi-group radiation diffusion equations in three dimensions

Authors: Yue, Xiaoqiang, Zhang, Chenxi, Chen, Chunyan, Xu, Xiaowen, Shu, Shi

Source: East Asian Journal on Applied Mathematics. 15:113-137

Subject Terms: radiation diffusion equation, algebraic multigrid, parallel computing, Numerical methods for partial differential equations, boundary value problems, Preconditioners for iterative methods, Parallel numerical computation, selective relaxation, matrix splitting preconditioner

File Description: application/xml

A Local Model Reduction Method Based on $k$-Nearest-Neighbors for Parametrized Nonlocal Problems: A local model reduction method based on \(k\)-nearest-neighbors for parametrized nonlocal problems

Authors: Nan, Caixia, Li, Qiuqi, Song, Huailing

Source: Communications in Computational Physics. 37:220-249

Subject Terms: proper orthogonal decomposition, Numerical methods for partial differential equations, boundary value problems, dynamic mode decomposition, quadratic finite element method, parametrized nonlocal PDEs, surrogate model, Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, \(k\)-nearest-neighbors

File Description: application/xml

Access URL: https://zbmath.org/8013537
https://doi.org/10.4208/cicp.oa-2024-0028

Multi-physics model bias correction with data-driven reduced order techniques: Application to nuclear case studies: Multi-physics model bias correction with data-driven reduced order techniques: application to nuclear case studies

Authors: Stefano Riva, Carolina Introini, Antonio Cammi

Source: Applied Mathematical Modelling. 135:243-268

Subject Terms: reduced order modelling, Approximations and expansions, nuclear reactors, Numerical methods for partial differential equations, boundary value problems, FOS: Mathematics, multi-physics, data driven, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, model correction

File Description: application/xml

Access URL: http://arxiv.org/abs/2401.07300

A bi-fidelity DeepONet approach for modeling hysteretic systems under uncertainty

Authors: Subhayan De, Patrick T. Brewick

Source: Applied Mathematical Modelling. 135:708-728

Subject Terms: Artificial intelligence, deep operator networks (DeepONets), nonlinear hysteretic systems, Numerical methods for partial differential equations, boundary value problems, multi-fidelity modeling, degrading hysteresis, residual modeling, Basic methods in fluid mechanics, seismic isolation systems

File Description: application/xml

Prediction of mechanical property of open-hole composite laminates using generalized regression neural network method

Authors: Hou, Junling, Zhao, Mengfan, Chen, Yujie, Li, Qun, Wang, Chunguang

Source: Acta Mechanica. 235:7553-7568

Subject Terms: open-hole composite laminates, Numerical methods for partial differential equations, boundary value problems, finite element models, General nonlinear regression, Computational learning theory, Random materials and composite materials, PDEs with randomness, stochastic partial differential equations, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Composite and mixture properties, machine learning-based method, neural network model, Artificial neural networks and deep learning

File Description: application/xml

Integral formulation of Klein–Gordon singular waveguides: Integral formulation of Klein-Gordon singular waveguides

Authors: Bal, Guillaume, Hoskins, Jeremy, Quinn, Solomon, Rachh, Manas

Source: Communications on Pure and Applied Mathematics. 78:323-365

Subject Terms: Numerical methods for partial differential equations, boundary value problems, FOS: Physical sciences, Mathematical Physics (math-ph), Numerical Analysis (math.NA), 01 natural sciences, Mathematics - Analysis of PDEs, Boundary value problems for second-order elliptic equations, FOS: Mathematics, Klein-Gordon equation, boundary integral equation, Mathematics - Numerical Analysis, 0101 mathematics, algorithm for solving integral equations, Mathematical Physics, Analysis of PDEs (math.AP)

File Description: application/xml

Access URL: http://arxiv.org/abs/2212.12619

A 3-D extension of the Multiscale Control Volume method for the simulation of the single-phase flow in anisotropic and heterogeneous porous media: A 3-D extension of the multiscale control volume method for the simulation of the single-phase flow in anisotropic and heterogeneous porous media

Authors: Filipe Antônio Cumaru Silva Alves, Artur Castiel Reis de Souza, Paulo Roberto Maciel Lyra, Darlan Karlo Elisiário de Carvalho

Source: Applied Mathematical Modelling. 134:198-222

Subject Terms: single-phase flow, GLS, MsCV, Flows in porous media, filtration, seepage, Numerical methods for partial differential equations, boundary value problems, background grid, Basic methods in fluid mechanics, MPFA-D

File Description: application/xml

Access URL: https://zbmath.org/8011661
https://doi.org/10.1016/j.apm.2024.05.045

An efficient variable step numerical method for the three-dimensional nonlinear evolution equation

Authors: Wang, Ruru, Chen, Yanping, Qiao, Leijie

Source: Journal of Applied Mathematics and Computing. 70:6131-6163

Subject Terms: orthogonal spline collocation method, alternating direction implicit method, Numerical methods for partial differential equations, boundary value problems, variable step BDF2 method, stability and convergence, Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, Numerical methods for integral equations, integral transforms, nonlinear fractional evolution equation

File Description: application/xml

Access URL: https://zbmath.org/8036697
https://doi.org/10.1007/s12190-024-02206-0

Simulating time-harmonic acoustic wave effects induced by periodic holes/inclusions on surfaces

Authors: Wen Hu, Zhuojia Fu, Leevan Ling

Source: Applied Mathematical Modelling. 132:630-644

Subject Terms: 35J05, 65N35, 74J05, surface PDEs, Numerical methods for partial differential equations, boundary value problems, FOS: Physical sciences, Numerical Analysis (math.NA), Mathematical Physics (math-ph), Computational Physics (physics.comp-ph), Parabolic equations and parabolic systems, generalized finite difference method, acoustic wave propagation, FOS: Mathematics, extrinsic technique, Mathematics - Numerical Analysis, Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, Physics - Computational Physics, Mathematical Physics

File Description: application/xml

Access URL: http://arxiv.org/abs/2307.10009
https://zbmath.org/7991781
https://doi.org/10.1016/j.apm.2024.05.009

Improved multi-scale fusion network for solving non-smooth elliptic interface problems with applications

Authors: Jinyong Ying, Jiao Li, Qiong Liu, Yinghao Chen

Source: Applied Mathematical Modelling. 132:274-297

Subject Terms: Artificial intelligence, solvation free energy, size-modified dielectric continuum model, deep learning method, Numerical methods for partial differential equations, boundary value problems, elliptic interface problem, the discontinuity-capturing method, Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, convergence analysis

File Description: application/xml

Access URL: https://zbmath.org/7991766
https://doi.org/10.1016/j.apm.2024.04.039