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

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

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

Subject Terms: 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

File Description: application/xml

Access URL: 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

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

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

Subject Terms: 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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Access URL: 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

Authors: Johannes Hertrich

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

Subject Terms: 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

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Access URL: 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

Authors: Babak Azarnavid, Mojtaba Fardi, Soheila Mohammadi

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

Subject Terms: 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

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Smaller stencil preconditioners for linear systems in RBF-FD discretizations

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

Source: Numerical Algorithms. 98:1313-1335

Subject Terms: 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

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Access URL: 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

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

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

Authors: Yadav, Rajesh, Yadav, Deepak Kumar, Kumar, Alpesh

Source: Numerical Algorithms. 97:645-685

Subject Terms: 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

File Description: application/xml

Access URL: 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

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

File Description: application/xml

Access URL: 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

Authors: Helmut Harbrecht, Rüdiger Kempf, Michael Multerer

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

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

File Description: application/xml

Access URL: 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

Authors: Barikbin, Mohammad Saeed

Source: Computational and Applied Mathematics. 44

Subject Terms: 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

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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

Authors: Jianming Liu, Xin Kai Li, Xiuling Hu

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

Subject Terms: 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

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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

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

Source: Journal of Computational Physics. 527:113798

Subject Terms: 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

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Access URL: 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

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

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

Subject Terms: 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

File Description: application/xml

Access URL: 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

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

Source: Applied Mathematics Letters. 160:109328

Subject Terms: 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

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$L^\infty$-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

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

Subject Terms: 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

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Access URL: http://arxiv.org/abs/2403.18809

An improved RBF based differential quadrature method

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

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

Subject Terms: 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

File Description: 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

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

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

Subject Terms: 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

File Description: application/xml

Access URL: 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

Authors: Zhang, Xueying, Ran, Luyu

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

Subject Terms: 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

File Description: application/xml

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

Authors: Mostafa Abbaszadeh, Mehdi Dehghan

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

Subject Terms: 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

File Description: application/xml

Access URL: 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

Authors: Jianming Liu, Xinkai Li, Xiuling Hu

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

Subject Terms: 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

File Description: application/xml

Access URL: 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