A High-Order Perturbation of Envelopes (HOPE) Method for Vector Electromagnetic Scattering by Periodic Inhomogeneous Media: Joint Analyticity: A high-order perturbation of envelopes (HOPE) method for vector electromagnetic scattering by periodic inhomogeneous media: joint analyticity

Authors: David P. Nicholls, Liet Vo

Source: SIAM Journal on Applied Mathematics. 85:755-778

Subject Terms: Spectral, collocation and related methods applied to problems in optics and electromagnetic theory, high-order spectral methods, Boundary value problems for second-order elliptic equations, Maxwell equations, inhomogeneous media, high-order perturbation of envelopes methods, linear wave scattering, Spectral, collocation and related methods for boundary value problems involving PDEs, layered media, PDEs in connection with optics and electromagnetic theory, PDEs in connection with geophysics, Diffraction, scattering

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Access URL: https://zbmath.org/8035693
https://doi.org/10.1137/24m1643189

On action ground states of defocusing nonlinear Schrödinger equations

Authors: Wei Liu, Chushan Wang, Xiaofei Zhao

Source: Mathematical Models and Methods in Applied Sciences. 35:39-74

Subject Terms: energy ground state, NLS equations (nonlinear Schrödinger equations), Asymptotic behavior of solutions to PDEs, action ground state, Numerical Analysis (math.NA), Variational principles in infinite-dimensional spaces, Computational methods for problems pertaining to quantum theory, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, rotation, numerical simulations, Mathematics - Analysis of PDEs, 35B38, 35Q55, 58E30, 81-08, asymptotics, Time-dependent Schrödinger equations and Dirac equations, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, defocusing nonlinear Schrödinger equation, Spectral, collocation and related methods for boundary value problems involving PDEs, Mathematics - Numerical Analysis, quantized vortices, Critical points of functionals in context of PDEs (e.g., energy functionals), Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2311.02890
https://zbmath.org/8005753
https://doi.org/10.1142/s0218202525500022

A Boundary Mapped Collocation Method for the Analysis of the Arbitrarily Shaped Plates: A boundary mapped collocation method for the analysis of the arbitrarily shaped plates

Authors: Huang, Zhentian, Lei, Dong, Han, Zi, Xie, Heping, Zhu, Jianbo

Source: Advances in Applied Mathematics and Mechanics. 17:350-372

Subject Terms: moving least squares, Software, source code, etc. for problems pertaining to partial differential equations, Boundary value problems for higher-order elliptic equations, boundary mapped collocation method, Software, source code, etc. for problems pertaining to computer science, meshless method, Spectral, collocation and related methods for boundary value problems involving PDEs, Kirchhoff plate

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Access URL: https://zbmath.org/7976962
https://doi.org/10.4208/aamm.oa-2022-0166

A Second-Order, Global-in-Time Energy Stable Implicit-Explicit Runge–Kutta Scheme for the Phase Field Crystal Equation: A second-order, global-in-time energy stable implicit-explicit Runge-Kutta scheme for the phase field crystal equation

Authors: Hong Zhang, Haifeng Wang, Xueqing Teng

Source: SIAM Journal on Numerical Analysis. 62:2667-2697

Subject Terms: global-in-time energy stability, phase field crystal equation, linear stabilization, optimal rate convergence analysis, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Integro-partial differential equations, Error bounds for initial value and initial-boundary value problems involving PDEs, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Spectral, collocation and related methods for boundary value problems involving PDEs, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Crystals in solids, Statistical mechanics of crystals, implicit-explicit Runge-Kutta method, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs, PDEs in connection with statistical mechanics

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The enriched multinode Shepard collocation method for solving elliptic problems with singularities

Authors: Dell'Accio F., Di Tommaso F., Francomano E.

Source: Applied Numerical Mathematics. 205:87-100

Subject Terms: Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, approximation by rational functions, multinode Shepard method, Elliptic PDEs, elliptic PDEs, Asymptotic expansions of solutions to PDEs, Approximation by rational functions, Motz problem, Approximation by polynomials, collocation method, Numerical interpolation, Multinode Shepard method, Spectral, collocation and related methods for boundary value problems involving PDEs, Collocation method

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Conformal structure-preserving SVM methods for the nonlinear Schrödinger equation with weakly linear damping term

Authors: Xin Li, Luming Zhang

Source: Applied Numerical Mathematics. 205:120-136

Subject Terms: Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Numerical optimization and variational techniques, damped nonlinear Schrödinger equation, high-order accuracy, NLS equations (nonlinear Schrödinger equations), conformal properties, supplementary variable method, Time-dependent Schrödinger equations and Dirac equations, optimization model, Spectral, collocation and related methods for boundary value problems involving PDEs, PDE constrained optimization (numerical aspects), Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

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Access URL: https://zbmath.org/7901899
https://doi.org/10.1016/j.apnum.2024.06.024

Stability analysis and error estimation based on difference spectral approximation for Allen–Cahn equation in a circular domain: Stability analysis and error estimation based on difference spectral approximation for Allen-Cahn equation in a circular domain

Authors: Zhenlan Pan, Jihui Zheng, Jing An

Source: Mathematical Methods in the Applied Sciences. 48:3214-3232

Subject Terms: Error bounds for initial value and initial-boundary value problems involving PDEs, circular domain, differential spectral approximation, stability and error estimation, Spectral, collocation and related methods for boundary value problems involving PDEs, Allen-Cahn equation, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

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A dimension reduction method of two‐grid finite element solution coefficient vectors for the Allen–Cahn equation: A dimension reduction method of two-grid finite element solution coefficient vectors for the Allen-Cahn equation

Authors: Yuejie Li, Fei Teng, Yihui Zeng, Zhendong Luo

Source: Mathematical Methods in the Applied Sciences. 48:678-698

Subject Terms: Error bounds for initial value and initial-boundary value problems involving PDEs, proper orthogonal decomposition, two-grid Crank-Nicolson finite element method, unconditional stability and errors, Spectral, collocation and related methods for boundary value problems involving PDEs, Stability and convergence of numerical methods for boundary value problems involving PDEs, 0101 mathematics, nonlinear Allen-Cahn equation, 01 natural sciences, reduced-dimension extrapolated two-grid Crank-Nicolson finite element method

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An Efficient Quasi-Newton Method with Tensor Product Implementation for Solving Quasi-Linear Elliptic Equations and Systems: An efficient quasi-Newton method with tensor product implementation for solving quasi-linear elliptic equations and systems

Authors: Wenrui Hao, Sun Lee, Xiangxiong Zhang

Source: J Sci Comput

Subject Terms: Kronecker product, Quasilinear elliptic equations, quasi-linear elliptic equations and systems, FOS: Mathematics, 65N35, 90C53, 35J62, quasi-Newton method, tensor product, Spectral, collocation and related methods for boundary value problems involving PDEs, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Methods of quasi-Newton type, Article

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Access URL: https://pubmed.ncbi.nlm.nih.gov/40321660
http://arxiv.org/abs/2502.03611
https://zbmath.org/8036990
https://doi.org/10.1007/s10915-025-02897-y

A barycentric Floater–Hormann interpolation with time splitting for numerical simulation of multi-dimensional regularized long wave equation: A barycentric Floater-Hormann interpolation with time splitting for numerical simulation of multi-dimensional regularized long wave equation

Authors: Ömer Oruç

Source: Computational and Applied Mathematics. 44

Subject Terms: barycentric Floater-Hormann interpolation, Spectral, collocation and related methods for boundary value problems involving PDEs, multi-dimensional RLW equation, Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs, operator splitting

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Access URL: https://zbmath.org/8034224
https://doi.org/10.1007/s40314-025-03183-1

A collaborating approach for hole detection with the numerical manifold method and Elman neural network

Authors: Zheng, G. Y., Li, C. L., Guo, D. L., Zhang, H. H., Ji, X. L., Han, S. Y.

Source: Engineering Analysis with Boundary Elements. 161:214-225

Subject Terms: hole detection, numerical manifold method, Elman neural network, Finite element methods applied to problems in solid mechanics, Brittle fracture, inverse analysis, Spectral, collocation and related methods for boundary value problems involving PDEs, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

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A high-order compact ADI scheme for two-dimensional nonlinear Schrödinger equation with time fractional derivative

Authors: Yuting Zhang, Xinlong Feng, Lingzhi Qian

Source: Computational and Applied Mathematics. 44

Subject Terms: Caputo fractional derivative, convergence, compact ADI scheme, Spectral, collocation and related methods for boundary value problems involving PDEs, \(L2\)-\(1_\sigma\) formula, nonlinear Schrödinger equation, Stability and convergence of numerical methods for ordinary differential equations, Fractional partial differential equations, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

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Access URL: https://zbmath.org/8034167
https://doi.org/10.1007/s40314-025-03127-9

A Hybrid Collocation Method for Long‐Time Simulation of Heat Conduction in Anisotropic Functionally Graded Materials: A hybrid collocation method for long-time simulation of heat conduction in anisotropic functionally graded materials

Authors: Lin Qiu, Fajie Wang, Wenzhen Qu, Ji Lin, Yan Gu, Qing‐Hua Qin

Source: International Journal for Numerical Methods in Engineering. 126

Subject Terms: Iterative numerical methods for linear systems, anisotropic heat conduction, Numerical radial basis function approximation, Numerical computation of solutions to systems of equations, Diffusive and convective heat and mass transfer, heat flow, radial basis function collocation method, Finite difference methods applied to problems in solid mechanics, Computational methods for sparse matrices, Thermal effects in solid mechanics, Krylov deferred correction technique, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Spectral, collocation and related methods for boundary value problems involving PDEs, long-time simulation, PDEs in connection with mechanics of deformable solids, functionally graded materials, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

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Access URL: https://zbmath.org/7991422
https://doi.org/10.1002/nme.70002

Error estimates of general linear and spectral Galerkin methods for the fractional diffusion equation with spectral fractional Laplacian

Authors: Yanming Zhang, Yu Li, Yuexin Yu, Wansheng Wang

Source: Computational and Applied Mathematics. 44

Subject Terms: Boundary value problems for PDEs with pseudodifferential operators, fractional diffusion equation, spectral fractional Laplacian, spectral Galerkin method, convergence, Spectral, collocation and related methods for boundary value problems involving PDEs, stability, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Stability and convergence of numerical methods for ordinary differential equations, Fractional partial differential equations, general linear method, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

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New third-order convex splitting methods and analysis for the phase field crystal equation

Authors: Ye, Zhijian, Zheng, Zhoushun, Li, Zhilin

Source: Numerical Algorithms. 98:47-84

Subject Terms: Iterative numerical methods for linear systems, third-order backward difference formula, energy stability, Liquid crystals, Numerical computation of solutions to systems of equations, phase field crystal equation, PDEs in connection with fluid mechanics, convex splitting method, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Statistical mechanics of superfluids, Preconditioners for iterative methods, Spectral, collocation and related methods for boundary value problems involving PDEs, unique solvability, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

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Deep Neural Network for Solving Differential Equations Motivated by Legendre-Galerkin Approximation: Deep neural network for solving differential equations motivated by Legendre-Galerkin approximation

Authors: Chudomelka, Bryce, Hong, Youngjoon, Morgan, John, Kim, Hyunwoo, Park, Jinyoung

Source: International Journal of Numerical Analysis and Modeling. 21:652-673

Subject Terms: data driven numerical method, Numerical algorithms for specific classes of architectures, neural network, deep learning, spectral element method, Legendre-Galerkin method, Spectral, collocation and related methods for boundary value problems involving PDEs, Numerical solution of discretized equations for boundary value problems involving PDEs, Computational aspects of data analysis and big data, Artificial neural networks and deep learning

File Description: application/xml

Access URL: https://zbmath.org/7954065
https://doi.org/10.4208/ijnam2024-1026

A Simple GPU Implementation of Spectral-Element Methods for Solving 3D Poisson Type Equations on Rectangular Domains and Its Applications: A simple GPU implementation of spectral-element methods for solving 3D Poisson type equations on rectangular domains and its applications

Authors: Liu, Xinyu, Shen, Jie, Zhang, Xiangxiong

Source: Communications in Computational Physics. 36:1157-1185

Subject Terms: Numerical computation of matrix exponential and similar matrix functions, Finite difference methods for boundary value problems involving PDEs, FOS: Computer and information sciences, tensor matrix multiplication, rectangular domain, GPU, Parallel numerical computation, spectral element methods, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Direct numerical methods for linear systems and matrix inversion, direct solver, Computer Science - Distributed, Parallel, and Cluster Computing, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Spectral, collocation and related methods for boundary value problems involving PDEs, Mathematics - Numerical Analysis, Distributed, Parallel, and Cluster Computing (cs.DC), 3D Poisson equation, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

File Description: application/xml

Access URL: http://arxiv.org/abs/2310.00226

A High–Order Perturbation of Envelopes (HOPE) method for vector electromagnetic scattering by periodic inhomogeneous media: Analytic continuation: A high-order perturbation of envelopes (HOPE) method for vector electromagnetic scattering by periodic inhomogeneous media: analytic continuation

Authors: David P. Nicholls, Liet Vo

Source: Journal of Differential Equations. 422:106-151

Subject Terms: Spectral, collocation and related methods applied to problems in optics and electromagnetic theory, high-order spectral methods, Composite media, random media in optics and electromagnetic theory, Perturbations in context of PDEs, 4. Education, inhomogeneous media, Analyticity in context of PDEs, Numerical Analysis (math.NA), Best approximation, Chebyshev systems, analytic continuation, Mathematics - Analysis of PDEs, Boundary value problems for second-order elliptic equations, Maxwell equations, high-order perturbation of envelopes methods, FOS: Mathematics, Spectral, collocation and related methods for boundary value problems involving PDEs, Mathematics - Numerical Analysis, Waves and radiation in optics and electromagnetic theory, layered media, PDEs in connection with optics and electromagnetic theory, Numerical methods for discrete and fast Fourier transforms, Diffraction, scattering, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2407.03351

Enhancing RBF-FD Efficiency for Highly Non-Uniform Node Distributions via Adaptivity: Enhancing RBF-FD efficiency for highly non-uniform node distributions via adaptivity

Authors: Li, Siqing, Ling, Leevan, Liu, Xin, Mishra, Pankaj K., Sen, Mrinal K., Zhang, Jing

Source: Numerical Mathematics: Theory, Methods and Applications. 17:331-350

Subject Terms: adaptive stencil, 0103 physical sciences, partial differential equations, FOS: Mathematics, radial basis functions, Spectral, collocation and related methods for boundary value problems involving PDEs, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Stability and convergence of numerical methods for boundary value problems involving PDEs, polynomial refinement, convergence order, 01 natural sciences, meshless finite difference

File Description: application/xml

Access URL: http://arxiv.org/abs/2004.06319

Time discretization for modeling migration of groundwater contaminant in the presence of micro-organisms via a semi-analytic method

Authors: Farzaneh Safari, Tong Qingshan, Wen Chen

Source: Computers & Mathematics with Applications. 151:397-407

Subject Terms: groundwater viscosity, Spectral methods applied to problems in fluid mechanics, Fractional derivatives and integrals, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Numerical radial basis function approximation, numerical scheme, Nonlinear parabolic equations, Spectral, collocation and related methods for boundary value problems involving PDEs, Fractional partial differential equations, nonlinear parabolic PDE, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs, time discretization

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Access URL: https://zbmath.org/7783949
https://doi.org/10.1016/j.camwa.2023.10.014