Efficient Partition-of-Unity Radial-Basis-Function Interpolation for Coupled Problems: Efficient partition-of-unity radial-basis-function interpolation for coupled problems

Συγγραφείς: David Schneider, Benjamin Uekermann

Πηγή: SIAM Journal on Scientific Computing. 47:B558-B582

Θεματικοί όροι: partition-of-unity, Algorithms for approximation of functions, data mapping, radial-basis functions, Numerical interpolation, math software, high-performance computing, multiphysics coupling, Parallel numerical computation

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Numerical Approximation of Discontinuous Solutions of the Semilinear Wave Equation: Numerical approximation of discontinuous solutions of the semilinear wave equation

Συγγραφείς: Jiachuan Cao, Buyang Li, Yanping Lin, Fangyan Yao

Πηγή: SIAM Journal on Numerical Analysis. 63:214-238

Θεματικοί όροι: Smoothness and regularity of solutions to PDEs, high-/low-frequency decomposition, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, Numerical Analysis (math.NA), Series expansions (e.g., Taylor, Lidstone series, but not Fourier series), Error bounds for initial value and initial-boundary value problems involving PDEs, KdV equations (Korteweg-de Vries equations), error estimates, Numerical interpolation, semilinear wave equation, discontinuous solution, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, low regularity, Numerical methods for discrete and fast Fourier transforms, numerical approximation

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Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2312.10392
https://zbmath.org/7981229
https://doi.org/10.1137/24m1635879

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

A Meshfree RBF-FD Constant along Normal Method for Solving PDEs on Surfaces: A meshfree RBF-FD constant along normal method for solving PDEs on surfaces

Συγγραφείς: Víctor Bayona, Argyrios Petras, Cécile Piret, Steven J. Ruuth

Συνεισφορές: Comunidad de Madrid

Πηγή: e-Archivo. Repositorio Institucional de la Universidad Carlos III de Madrid
Universidad Carlos III de Madrid (UC3M)

Θεματικοί όροι: Finite difference methods for boundary value problems involving PDEs, Matemáticas, Closest point method, Meshfree, Numerical Analysis (math.NA), meshfree, Numerical differentiation, Approximation by polynomials, Spline approximation, High-order methods, Numerical interpolation, Finite difference methods for initial value and initial-boundary value problems involving PDEs, high-order methods, PDEs on surfaces, FOS: Mathematics, RBF-FD, Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, Interpolation in approximation theory, Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs, closest point method

Περιγραφή αρχείου: application/pdf; application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2412.14761
https://hdl.handle.net/10016/46963

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

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

Πηγή: Applied Numerical Mathematics. 205:87-100

Θεματικοί όροι: 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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Classification-Based Framework for Remaining Useful Life Prediction With Limited Images and Unequal Time Intervals

Συγγραφείς: Zhu, X., Lu, C., Zhang, P.

Πηγή: IEEE Transactions on Instrumentation and Measurement IEEE Trans. Instrum. Meas. Instrumentation and Measurement, IEEE Transactions on. 72:1-11 2023

Zipper rational fractal interpolation functions

Συγγραφείς: R. Pasupathi, null Vijay, A. K. B. Chand, N. S. Upadhye

Πηγή: The Journal of Analysis. 32:3197-3226

Θεματικοί όροι: Approximation by rational functions, Fractals, convexity, positivity, Numerical interpolation, rational cubic spline, zipper, fractal interpolation function, monotonicity, Interpolation in approximation theory, Real rational functions, Numerical computation using splines

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Σύνδεσμος πρόσβασης: https://zbmath.org/7965080
https://doi.org/10.1007/s41478-024-00796-3

Structure Preserving Nodal Continuous Finite Elements via Global Flux Quadrature: Structure preserving nodal continuous finite elements via global flux quadrature

Συγγραφείς: Wasilij Barsukow, Mario Ricchiuto, Davide Torlo

Συνεισφορές: Ricchiuto, Mario

Πηγή: Numerical Methods for Partial Differential Equations. 41

Θεματικοί όροι: OSS, Hydro- and aero-acoustics, Numerical Analysis (math.NA), [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, PDE constrained optimization (numerical aspects), Euler equations, Numerical quadrature and cubature formulas, global flux quadrature, Finite difference methods applied to problems in fluid mechanics, stabilization, divergence preserving, finite elements, SUPG, very high-order, Numerical interpolation, 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, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Finite element methods applied to problems in fluid mechanics

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Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2407.10579
https://hal.science/hal-04779510v2/document
https://hal.science/hal-04779510v2

One-Second GPS Orbits: A Comparison Between Numerical Integration and Interpolation

Συγγραφείς: Gaur, Deepak, Prasad, Mani Shankar

Πηγή: 2019 6th International Conference on Signal Processing and Integrated Networks (SPIN) Signal Processing and Integrated Networks (SPIN), 2019 6th International Conference on. :973-977 Mar, 2019

Relation: 2019 6th International Conference on Signal Processing and Integrated Networks (SPIN)

Numerical analysis and comparison of fractional physics-informed neural networks in unsaturated flow process

Συγγραφείς: Xin Wang, Xiaoping Wang, Huanying Xu, Haitao Qi

Πηγή: Communications in Nonlinear Science and Numerical Simulation. 147:108833

Θεματικοί όροι: unsaturated flow, neural network, Numerical interpolation, Flows in porous media, filtration, seepage, deep learning, Richards equation, Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs, fractional calculus, Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, Fractional partial differential equations, Artificial neural networks and deep learning

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Σύνδεσμος πρόσβασης: https://zbmath.org/8035197
https://doi.org/10.1016/j.cnsns.2025.108833

The Fekete problem in segmental polynomial interpolation

Συγγραφείς: Ludovico Bruni Bruno, Wolfgang Erb

Πηγή: BIT Numerical Mathematics. 65

Θεματικοί όροι: Numerical interpolation, polynomial approximation of differential forms, FOS: Mathematics, segmental polynomial interpolation, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), optimal design of segments, Interpolation in approximation theory, Fekete problem, 41A05, 41A25, A1A30, 65D05

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Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2403.09378
https://zbmath.org/7964459
https://doi.org/10.1007/s10543-024-01047-4

A fast H3N3‐2σ$_\sigma$‐based compact ADI difference method for time fractional wave equations: A fast H3N3-2\(_\sigma\)-based compact ADI difference method for time fractional wave equations

Συγγραφείς: Ruilian Du

Πηγή: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik. 104

Θεματικοί όροι: Finite difference methods for boundary value problems involving PDEs, Error bounds for initial value and initial-boundary value problems involving PDEs, alternating direction implicit (ADI) schemes, Fractional derivatives and integrals, Numerical interpolation, Smoothness and regularity of solutions to PDEs, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Fractional partial differential equations

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Two Numerical Schemes Via an Auxiliary Function for Nonlocal Problems With Integrable Kernels: Two numerical schemes via an auxiliary function for nonlocal problems with integrable kernels

Συγγραφείς: Yutong Li, Xiaobo Yin

Πηγή: Numerical Methods for Partial Differential Equations. 41

Θεματικοί όροι: Integro-partial differential equations, Error bounds for boundary value problems involving PDEs, Numerical interpolation, Smoothness and regularity of solutions to PDEs, nonlocal problems, Spectral, collocation and related methods for boundary value problems involving PDEs, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Numerical methods for integral equations, Stability and convergence of numerical methods for boundary value problems involving PDEs, integrable kernel, auxiliary problem

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Σύνδεσμος πρόσβασης: https://zbmath.org/8005890
https://doi.org/10.1002/num.23153

Brezzi–Douglas–Marini interpolation on anisotropic simplices and prisms: Brezzi-Douglas-Marini interpolation on anisotropic simplices and prisms

Συγγραφείς: Kempf, Volker

Πηγή: Comptes Rendus. Mathématique, Vol 361, Iss G1, Pp 437-443 (2023)

Θεματικοί όροι: Numerical interpolation, QA1-939, FOS: Mathematics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, 0101 mathematics, 01 natural sciences, Mathematics, 65D05, 65N30

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Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2205.04734
https://zbmath.org/7652660
https://doi.org/10.5802/crmath.424
https://doaj.org/article/de109b52989547fe986838e9a8a11dfc

Image restoration of medical images with streaking artifacts by Euler's elastica inpainting

Συγγραφείς: Zhang, Xiaochen, Wan, Justin W.L.

Πηγή: 2017 IEEE 14th International Symposium on Biomedical Imaging (ISBI 2017) Biomedical Imaging (ISBI 2017), 2017 IEEE 14th International Symposium on. :235-239 Apr, 2017

Relation: 2017 IEEE 14th International Symposium on Biomedical Imaging (ISBI 2017)

Structured barycentric forms for interpolation-based data-driven reduced modeling of second-order systems

Συγγραφείς: Ion Victor Gosea, Serkan Gugercin, Steffen W. R. Werner

Πηγή: Advances in Computational Mathematics

Θεματικοί όροι: 0209 industrial biotechnology, second-order systems, rational functions, Systems and Control (eess.SY), Dynamical Systems (math.DS), 02 engineering and technology, Electrical Engineering and Systems Science - Systems and Control, 01 natural sciences, Approximation by rational functions, Numerical interpolation, Realizations from input-output data, FOS: Mathematics, FOS: Electrical engineering, electronic engineering, information engineering, barycentric forms, Mathematics - Numerical Analysis, Mathematics - Dynamical Systems, 0101 mathematics, Mathematics - Optimization and Control, Numerical Analysis (math.NA), interpolation, reduced-order modeling, data-driven modeling, Linear systems in control theory, Optimization and Control (math.OC), Frequency-response methods in control theory, 41A20, 65D05, 93B15, 93C05, 93C80

Περιγραφή αρχείου: application/xml; application/pdf

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2303.12576
http://hdl.handle.net/21.11116/0000-000C-D2F1-6
http://hdl.handle.net/21.11116/0000-000C-D2F3-4
http://hdl.handle.net/21.11116/0000-000F-32C1-E

Numerical experiments using the barycentric Lagrange treecode to compute correlated random displacements for Brownian dynamics simulations

Συγγραφείς: Lei Wang, Robert Krasny

Πηγή: Journal of Computational Physics. 525:113743

Θεματικοί όροι: Iterative numerical methods for linear systems, hydrodynamic interactions, correlated random displacements, Brownian dynamics, Numerical interpolation, Stochastic particle methods, matrix square root, Krylov subspace, Orthogonalization in numerical linear algebra, RPY tensor, Lanczos iteration, barycentric Lagrange treecode

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Σύνδεσμος πρόσβασης: https://zbmath.org/8021064
https://doi.org/10.1016/j.jcp.2025.113743

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

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$$H^1$$-analysis of H3N3-2$$_\sigma $$-based difference method for fractional hyperbolic equations: \(H^1\)-analysis of H3N3-\(2_\sigma\)-based difference method for fractional hyperbolic equations

Συγγραφείς: Rui-lian Du, Changpin Li, Zhi-zhong Sun

Πηγή: Computational and Applied Mathematics. 43

Θεματικοί όροι: Finite difference methods for boundary value problems involving PDEs, Error bounds for initial value and initial-boundary value problems involving PDEs, Fractional derivatives and integrals, Numerical interpolation, Smoothness and regularity of solutions to PDEs, \(H^1\)-analysis, Finite difference methods for initial value and initial-boundary value problems involving PDEs, H3N3-\(2_\sigma\) approximation, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Fractional partial differential equations, finite difference scheme, Caputo derivative, time fractional hyperbolic equation

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High-order weighted compact nonlinear scheme for solving degenerate parabolic equations

Συγγραφείς: Yinggang Hu, Yanqun Jiang, Xiaoqian Huang, Wei Zhang

Πηγή: Computational and Applied Mathematics. 43

Θεματικοί όροι: Finite difference methods for boundary value problems involving PDEs, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, discontinuity-capturing ability, Numerical interpolation, Finite difference methods for initial value and initial-boundary value problems involving PDEs, weighted compact nonlinear scheme, high-order accurate, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, Direct numerical methods for linear systems and matrix inversion, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Degenerate parabolic equations, nonlinear degenerate parabolic equations, non-oscillatory property

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Σύνδεσμος πρόσβασης: https://zbmath.org/7803448
https://doi.org/10.1007/s40314-023-02551-z