Learning PDEs from Data on Closed Surfaces with Sparse Optimization: Learning PDEs from data on closed surfaces with sparse optimization

Συγγραφείς: Sun, Zhengjie, Ling, Leevan, Zhang, Ran

Πηγή: Communications in Computational Physics. 37:289-314

Θεματικοί όροι: meshless methods, data-driven modeling, Numerical radial basis function approximation, FOS: Mathematics, FOS: Physical sciences, surface PDE, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Mathematical Physics (math-ph), sparse optimization, Interpolation in approximation theory, Mathematical Physics

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Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2405.06199
https://zbmath.org/8033878
https://doi.org/10.4208/cicp.oa-2024-0112

Robust Radial Basis Function Interpolation Based on Geodesic Distance for the Numerical Coupling of Multiphysics Problems: Robust radial basis function interpolation based on geodesic distance for the numerical coupling of multiphysics problems

Συγγραφείς: Michele Bucelli, Francesco Regazzoni, Luca Dede’, Alfio Quarteroni

Πηγή: SIAM Journal on Scientific Computing. 46:B981-B1002

Θεματικοί όροι: 65D05, 65D12, 65M60, Numerical interpolation, Numerical radial basis function approximation, intergrid interpolation, FOS: Mathematics, radial basis functions, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), cardiac electromechanics, multiphysics modeling

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Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2403.03665

Fast Kernel Summation in High Dimensions via Slicing and Fourier Transforms: Fast kernel summation in high dimensions via slicing and Fourier transforms

Συγγραφείς: Johannes Hertrich

Πηγή: SIAM Journal on Mathematics of Data Science. 6:1109-1137

Θεματικοί όροι: FOS: Computer and information sciences, Computer Science - Machine Learning, Numerical radial basis function approximation, slicing, Numerical Analysis (math.NA), 01 natural sciences, Machine Learning (cs.LG), nonequispaced Fourier transforms, Algorithms for approximation of functions, fast kernel summation, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, Numerical methods for discrete and fast Fourier transforms

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2401.08260
https://zbmath.org/7960206
https://doi.org/10.1137/24m1632085

Numerical simulation of coupled Klein–Gordon–Schrödinger equations: RBF partition of unity: Numerical simulation of coupled Klein-Gordon-Schrödinger equations: RBF partition of unity

Συγγραφείς: Babak Azarnavid, Mojtaba Fardi, Soheila Mohammadi

Πηγή: Engineering Analysis with Boundary Elements. 163:562-575

Θεματικοί όροι: NLS equations (nonlinear Schrödinger equations), Finite difference methods for initial value and initial-boundary value problems involving PDEs, Numerical radial basis function approximation, implicit central finite difference scheme, radial basis function partition of unity, polyharmonic splines kernels, coupled Klein-Gordon-Schrödinger system, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

Περιγραφή αρχείου: application/xml

Smaller stencil preconditioners for linear systems in RBF-FD discretizations

Συγγραφείς: Koch, Michael, Le Borne, Sabine, Leinen, Willi

Πηγή: Numerical Algorithms. 98:1313-1335

Θεματικοί όροι: polyharmonic spline, preconditioner, Polynomial augmentation, meshfree method, 65F08, 65M12, 65N22, Numerical radial basis function approximation, Radial basis function finite difference (RBF-FD), Polyharmonic spline, radial basis function finite difference (RBF-FD), 01 natural sciences, Numerical computation using splines, Meshfree method, polynomial augmentation, Iterative solver, Preconditioners for iterative methods, iterative solver, 0101 mathematics, Preconditioner, 65D12, 65F10, 65F55, 65D25

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/7985680
https://doi.org/10.1007/s11075-024-01835-7

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

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

Πηγή: International Journal for Numerical Methods in Engineering. 126

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/7991422
https://doi.org/10.1002/nme.70002

RBF-FD based some implicit-explicit methods for pricing option under regime-switching jump-diffusion model with variable coefficients

Συγγραφείς: Yadav, Rajesh, Yadav, Deepak Kumar, Kumar, Alpesh

Πηγή: Numerical Algorithms. 97:645-685

Θεματικοί όροι: local volatility, options pricing, Integro-partial differential equations, Derivative securities (option pricing, hedging, etc.), regime-switching jump-diffusion, Numerical methods (including Monte Carlo methods), Numerical radial basis function approximation, Finite difference methods for initial value and initial-boundary value problems involving PDEs, stability analysis, radial basis function, operator splitting

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/7925688
https://doi.org/10.1007/s11075-023-01719-2

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

Συγγραφείς: Farzaneh Safari, Tong Qingshan, Wen Chen

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

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/7783949
https://doi.org/10.1016/j.camwa.2023.10.014

Construction of quasi-localized dual bases in reproducing kernel Hilbert spaces

Συγγραφείς: Helmut Harbrecht, Rüdiger Kempf, Michael Multerer

Πηγή: Journal of Computational and Applied Mathematics. 465:116545

Θεματικοί όροι: reproducing kernel Hilbert spaces, preconditioning, Numerical radial basis function approximation, dual pairs, Approximation by other special function classes

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Σύνδεσμος πρόσβασης: https://zbmath.org/8015353
https://doi.org/10.1016/j.cam.2025.116545

A radial basis function partition of unity for coupled Klein–Gordon–Zakarov equations: A radial basis function partition of unity for coupled Klein-Gordon-Zakarov equations

Συγγραφείς: Barikbin, Mohammad Saeed

Πηγή: Computational and Applied Mathematics. 44

Θεματικοί όροι: Numerical radial basis function approximation, coupled Klein-Gordon-Zakharov system, Spectral, collocation and related methods for boundary value problems involving PDEs, Lagrangian polyharmonic splines, radial basis function partition of unity, finite difference schemes

Περιγραφή αρχείου: application/xml

A novel local Hermite radial basis function‐based differential quadrature method for solving two‐dimensional variable‐order time fractional advection–diffusion equation with Neumann boundary conditions: A novel local Hermite radial basis function-based differential quadrature method for solving two-dimensional variable-order time fractional advection-diffusion equation with Neumann boundary conditions

Συγγραφείς: Jianming Liu, Xin Kai Li, Xiuling Hu

Πηγή: Numerical Methods for Partial Differential Equations. 39:2998-3019

Θεματικοί όροι: variable-order time fractional, Neumann boundary condition, Hermite RBF-DQ, meshfree method, Numerical radial basis function approximation, Fractional partial differential equations, 01 natural sciences, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Numerical differentiation, Fractional derivatives and integrals, Finite difference methods for initial value and initial-boundary value problems involving PDEs, 0103 physical sciences, Spectral, collocation and related methods for boundary value problems involving PDEs, 0101 mathematics, differential quadrature method, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

Περιγραφή αρχείου: application/xml

FE-PIRBN: Feature-enhanced physics-informed radial basis neural networks for solving high-frequency electromagnetic scattering problems: FE-PIRBN: feature-enhanced physics-informed radial basis neural networks for solving high-frequency electromagnetic scattering problems

Συγγραφείς: Huajian Zhang, Chao Li, Rui Xia, Xinhai Chen, Tiaojie Xiao, Xiao-Wei Guo, Jie Liu

Πηγή: Journal of Computational Physics. 527:113798

Θεματικοί όροι: radial basis neural network, hash encoding, Numerical radial basis function approximation, physics-informed neural network, Spectral, collocation and related methods for boundary value problems involving PDEs, high-frequency electromagnetic scattering, Diffraction, scattering, Artificial neural networks and deep learning

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/8021098
https://doi.org/10.1016/j.jcp.2025.113798

Numerical approximation of the first-passage time distribution of time-varying diffusion decision models: A mesh-free approach: Numerical approximation of the first-passage time distribution of time-varying diffusion decision models: a mesh-free approach

Συγγραφείς: Amir Hosein Hadian Rasanan, Nathan J. Evans, Jörg Rieskamp, Jamal Amani Rad

Πηγή: Engineering Analysis with Boundary Elements. 151:227-243

Θεματικοί όροι: moving boundary, first passage-time, Numerical radial basis function approximation, 05 social sciences, Moving boundary problems for PDEs, diffusion model, Fokker-Planck equation, stability analysis, Decision theory, convergence analysis, 03 medical and health sciences, 0302 clinical medicine, Cognitive psychology, human decision making, 0501 psychology and cognitive sciences, Fokker-Planck equations, radial basis function, numerical approximation

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/7698646
https://doi.org/10.1016/j.enganabound.2023.03.005

A POD based reduced-order local RBF collocation approach for time-dependent nonlocal diffusion problems

Συγγραφείς: Jiashu Lu, Lei Zhang, Xuncheng Guo, Qiong Qi

Πηγή: Applied Mathematics Letters. 160:109328

Θεματικοί όροι: nonlocal models, Numerical interpolation, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Numerical radial basis function approximation, fast algorithm, model reduction, radial basis functions, Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, Methods of ordinary differential equations applied to PDEs, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs, Numerical computation using splines

Περιγραφή αρχείου: application/xml

$L^\infty$-error bounds for approximations of the Koopman operator by kernel extended dynamic mode decomposition: \( L^\infty\)-error bounds for approximations of the Koopman operator by kernel extended dynamic mode decomposition

Συγγραφείς: Köhne, Frederik, Philipp, Friedrich M., Schaller, Manuel, Schiela, Anton, Worthmann, Karl

Θεματικοί όροι: Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces), Linear composition operators, Numerical radial basis function approximation, Dynamical Systems (math.DS), Numerical Analysis (math.NA), Approximation methods and numerical treatment of dynamical systems, interpolation, kernel EDMD, 37M99, 41A05, 47B32, 47B33, 65D12, FOS: Mathematics, regression, uniform error bounds, Mathematics - Numerical Analysis, Mathematics - Dynamical Systems, Koopman operator, reproducing kernel Hilbert space, Interpolation in approximation theory

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2403.18809

An improved RBF based differential quadrature method

Συγγραφείς: Liang, Xu, Wang, Tao, Huang, Decai, Liu, Zhen, Zhu, Ronghua, Wang, Chizhong

Πηγή: Engineering Analysis with Boundary Elements. 135:299-314

Θεματικοί όροι: meshless methods, differential quadrature (DQ) method, smoothed particle hydrodynamics (SPH), radial basis function (RBF), Numerical radial basis function approximation, 0103 physical sciences, Spectral, collocation and related methods for boundary value problems involving PDEs, 01 natural sciences

Περιγραφή αρχείου: application/xml

Lagrangian radial basis function‐based particle hydrodynamics method and its application for viscous flows: Lagrangian radial basis function-based particle hydrodynamics method and its application for viscous flows

Συγγραφείς: Ronghua Zhu, Lizhong Wang, Tao Wang, Zhen Liu, Xu Liang, Decai Huang, Can Huang

Πηγή: International Journal for Numerical Methods in Engineering. 122:1964-1989

Θεματικοί όροι: meshless methods, smoothed particle hydrodynamics, Numerical radial basis function approximation, viscous flows, 0103 physical sciences, Particle methods and lattice-gas methods, finite particle method, 0101 mathematics, radial basis function, 01 natural sciences

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.6607
https://ui.adsabs.harvard.edu/abs/2021IJNME.122.1964L/abstract

Upwind Strategy for Localized Method of Approximate Particular Solutions with Applications to Convection Dominated Diffusion Problems: Upwind strategy for localized method of approximate particular solutions with applications to convection dominated diffusion problems

Συγγραφείς: Zhang, Xueying, Ran, Luyu

Πηγή: Advances in Applied Mathematics and Mechanics. 13:455-466

Θεματικοί όροι: upwind scheme, Numerical radial basis function approximation, Initial value problems for first-order hyperbolic equations, convection dominated problems, radial basis functions, LMAPS, 0101 mathematics, 01 natural sciences, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

Περιγραφή αρχείου: application/xml

Simulation flows with multiple phases and components via the radial basis functions-finite difference (RBF-FD) procedure: Shan-Chen model

Συγγραφείς: Mostafa Abbaszadeh, Mehdi Dehghan

Πηγή: Engineering Analysis with Boundary Elements. 119:151-161

Θεματικοί όροι: POD idea, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Numerical radial basis function approximation, RBF-FD procedure, 0103 physical sciences, shan-Chen model, 0101 mathematics, incompressible Navier-Stokes equation, variable density, 01 natural sciences, local meshless scheme, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs, flows with multiple phases

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://www.sciencedirect.com/science/article/pii/S0955799720301582

A RBF-based differential quadrature method for solving two-dimensional variable-order time fractional advection-diffusion equation

Συγγραφείς: Jianming Liu, Xinkai Li, Xiuling Hu

Πηγή: Journal of Computational Physics. 384:222-238

Θεματικοί όροι: variable-order time fractional, Error bounds for initial value and initial-boundary value problems involving PDEs, Neumann boundary condition, Numerical radial basis function approximation, 0103 physical sciences, Fractional partial differential equations, RBF-differential quadrature method, radial basis function, 01 natural sciences, differential quadrature method

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://dora.dmu.ac.uk/bitstream/2086/17579/1/1-s2.0-S0021999119300920-main.pdf
https://zbmath.org/7283530
https://doi.org/10.1016/j.jcp.2018.12.043
https://dora.dmu.ac.uk/handle/2086/17579
https://www.sciencedirect.com/science/article/pii/S0021999119300920
https://arxiv.org/abs/1809.02301
https://arxiv.org/pdf/1809.02301.pdf
http://ui.adsabs.harvard.edu/abs/2019JCoPh.384..222L/abstract