Search Results - Numerical methods for discrete and fast Fourier transforms

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

File Description: application/xml

Access URL: http://arxiv.org/abs/2401.08260
https://zbmath.org/7960206
https://doi.org/10.1137/24m1632085

A fast Fourier transform based method for computing the effective crack energy of a heterogeneous material on a combinatorially consistent grid

Authors: Felix Ernesti Matti Schneider

Source: International Journal for Numerical Methods in Engineering, 112 (21), 6283-6307

Subject Terms: ddc:620, FOS: Computer and information sciences, Finite element methods applied to problems in solid mechanics, alternating direction method of multipliers, FFT-based computational homogenization, Computational Engineering, Finance, and Science (cs.CE), Brittle fracture, combinatorial continuous maximum flow, effective crack energy, Computer Science - Computational Engineering, Finance, and Science, Engineering & allied operations, Numerical methods for discrete and fast Fourier transforms, Bauwissenschaften

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Access URL: https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/nme.6792
http://arxiv.org/abs/2103.05968
https://dblp.uni-trier.de/db/journals/corr/corr2103.html#abs-2103-05968
http://arxiv.org/pdf/2103.05968.pdf
https://ui.adsabs.harvard.edu/abs/2021arXiv210305968E/abstract
https://arxiv.org/pdf/2103.05968.pdf
https://arxiv.org/abs/2103.05968
https://publikationen.bibliothek.kit.edu/1000136993/125918703
https://onlinelibrary.wiley.com/doi/full/10.1002/nme.6792
https://publikationen.bibliothek.kit.edu/1000136993
https://publikationen.bibliothek.kit.edu/1000136993
https://publikationen.bibliothek.kit.edu/1000136993/125918703
https://doi.org/10.5445/IR/1000136993

Discrete Pseudo-differential Operators and Applications to Numerical Schemes.

Authors: Faou, Erwan Grébert, Benoît

Source: Foundations of Computational Mathematics. Apr2025, Vol. 25 Issue 2, p587-630. 44p.

Subject Terms: *DISCRETE Fourier transforms, *FINITE difference method, *FAST Fourier transforms, *FINITE differences, *CALCULUS

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

Authors: Jiachuan Cao Buyang Li Yanping Lin et al.

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

Subject Terms: 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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Access URL: http://arxiv.org/abs/2312.10392
https://zbmath.org/7981229
https://doi.org/10.1137/24m1635879

A dual‐space multilevel kernel‐splitting framework for discrete and continuous convolution: A dual-space multilevel kernel-splitting framework for discrete and continuous convolution

Authors: Jiang, Shidong Greengard, Leslie

Source: Communications on Pure and Applied Mathematics. 78:1086-1143

Subject Terms: discrete convolution, 31A10, 65F30, 65E05, 65Y20, 0103 physical sciences, FOS: Mathematics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), 0101 mathematics, continuous convolution, 01 natural sciences, Numerical methods for discrete and fast Fourier transforms

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Access URL: http://arxiv.org/abs/2308.00292
https://zbmath.org/8023947
https://doi.org/10.1002/cpa.22240

Fast numerical derivatives of univariate functions on non-uniform grids

Authors: Egidi, Nadaniela Giacomini, Josephin Maponi, Pierluigi

Source: Journal of Computational and Applied Mathematics. 467:116619

Subject Terms: Numerical differentiation, numerical derivative, discrete Fourier transformation, Numerical derivative, Singular value expansion, singular value expansion, Approximation, approximation, Numerical methods for discrete and fast Fourier transforms, Discrete Fourier transformation

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Access URL: https://zbmath.org/8031367
https://doi.org/10.1016/j.cam.2025.116619
https://hdl.handle.net/11581/492805
https://doi.org/10.1016/j.cam.2025.116619

Anderson‐accelerated polarization schemes for fast Fourier transform‐based computational homogenization: Anderson-accelerated polarization schemes for fast Fourier transform-based computational homogenization

Authors: Daniel Wicht Matti Schneider Thomas Böhlke

Source: International journal for numerical methods in engineering, 122 (9), 2287-2311

Subject Terms: ddc:620, directionally solidified eutectics, computational homogenization, 02 engineering and technology, fiber-reinforced composites, 01 natural sciences, metal-matrix composites, Numerical and other methods in solid mechanics, 0203 mechanical engineering, Homogenization in equilibrium problems of solid mechanics, Anderson acceleration, 0101 mathematics, Engineering & allied operations, Numerical methods for discrete and fast Fourier transforms, Bauwissenschaften, FFT-based method

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Access URL: https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/nme.6622
http://ui.adsabs.harvard.edu/abs/2021IJNME.122.2287W/abstract
https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6622
https://onlinelibrary.wiley.com/doi/full/10.1002/nme.6622
https://publikationen.bibliothek.kit.edu/1000130188
https://publikationen.bibliothek.kit.edu/1000130188/104455558
https://doi.org/10.5445/IR/1000130188
https://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&origin=inward&scp=85100509395
https://doi.org/10.1002/nme.6622

Computing the effective response of heterogeneous materials with thermomechanically coupled constituents by an implicit fast Fourier transform‐based approach: Computing the effective response of heterogeneous materials with thermomechanically coupled constituents by an implicit fast Fourier transform-based approach

Authors: Daniel Wicht Matti Schneider Thomas Böhlke

Source: International journal for numerical methods in engineering, 122 (5), 1307-1332

Subject Terms: ddc:620, homogenization, FFT-based micromechanics, 02 engineering and technology, composites, 01 natural sciences, Thermal effects in solid mechanics, 0203 mechanical engineering, 0101 mathematics, Engineering & allied operations, Numerical methods for discrete and fast Fourier transforms, thermomechanical coupling, viscoelasticity, Bauwissenschaften, Bounds on effective properties in solid mechanics

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Access URL: https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/nme.6579
https://zbmath.org/7863113
https://doi.org/10.1002/nme.6579
https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.6579
http://ui.adsabs.harvard.edu/abs/2021IJNME.122.1307W/abstract
https://publikationen.bibliothek.kit.edu/1000127673/104569802
https://publikationen.bibliothek.kit.edu/1000127673
https://doi.org/10.5445/IR/1000127673
https://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&origin=inward&scp=85096765187
https://doi.org/10.1002/nme.6579

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

A Simple and Efficient Finite Difference Method for the Tempered Nonlocal Laplacian: A simple and efficient finite difference method for the tempered nonlocal Laplacian

Authors: Xuehong Cui Rui Du Zhaopeng Hao

Source: Journal of Scientific Computing. 103

Subject Terms: Finite difference methods for boundary value problems involving PDEs, convergence, Fractional derivatives and integrals, fast algorithm, Stability and convergence of numerical methods for boundary value problems involving PDEs, stability, Fractional partial differential equations, Numerical methods for discrete and fast Fourier transforms, tempered nonlocal Laplacian, finite difference method

File Description: application/xml

Access URL: https://zbmath.org/8016237
https://doi.org/10.1007/s10915-025-02823-2

A Fast Method for the Numerical Evaluation of Continuous Fourier and Laplace Transforms: A fast method for the numerical evaluation of continuous Fourier and Laplace transforms

Authors: David H. Bailey Paul N. Swarztrauber

Source: SIAM Journal on Scientific Computing. 15:1105-1110

Subject Terms: Laplace transform, continuous Fourier transforms, Laplace transforms, Numerical methods for trigonometric approximation and interpolation, 02 engineering and technology, fractional Fourier transform, fast Fourier transform, 01 natural sciences, Complexity and performance of numerical algorithms, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, 0202 electrical engineering, electronic engineering, information engineering, 0101 mathematics, Numerical methods for integral transforms, Numerical methods for discrete and fast Fourier transforms, Gaussian probability density function

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Access URL: https://zbmath.org/681429
https://doi.org/10.1137/0915067
http://core.ac.uk/display/20910652
https://doi.org/10.1137/0915067
https://epubs.siam.org/doi/10.1137/0915067
https://dblp.uni-trier.de/db/journals/siamsc/siamsc15.html#BaileyS94

A Grid-Overlay Finite Difference Method for Inhomogeneous Dirichlet Problems of the Fractional Laplacian on Arbitrary Bounded Domains: A grid-overlay finite difference method for inhomogeneous Dirichlet problems of the fractional Laplacian on arbitrary bounded domains

Authors: Weizhang Huang Jinye Shen

Source: Journal of Scientific Computing. 102

Subject Terms: Finite difference methods for boundary value problems involving PDEs, overlay grid, finite difference, mesh adaptation, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, Fractional partial differential equations, Computational methods for sparse matrices, Error bounds for initial value and initial-boundary value problems involving PDEs, Fractional derivatives and integrals, inhomogeneous fractional Laplacian, Preconditioners for iterative methods, arbitrary domain, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Numerical methods for discrete and fast Fourier transforms

File Description: application/xml

Access URL: https://zbmath.org/7975323
https://doi.org/10.1007/s10915-024-02782-0

Unconditional error estimate of linearly-implicit and energy-preserving schemes for nonlocal wave equations

Authors: Li, Lingling Fu, Yayun

Source: Computers & Mathematics with Applications. 176:492-509

Subject Terms: GSAV method, Spectral methods applied to problems in fluid mechanics, nonlocal wave equation, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Wave equation, energy-preserving, error estimate, unique solvability, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Fractional partial differential equations, Numerical methods for discrete and fast Fourier transforms

File Description: application/xml

Access URL: https://zbmath.org/7967267
https://doi.org/10.1016/j.camwa.2024.11.002

An augmented fourth order domain-decomposed method with fast algebraic solvers for three-dimensional Helmholtz interface problems

Authors: Yang, Huanfeng Long, Guangqing Ren, Yiming et al.

Source: Journal of Computational Physics. 524:113742

Subject Terms: Helmholtz interface problems, domain decomposition, matched interface and boundary (MIB) method, fast Fourier transform (FFT), Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, Finite difference methods for initial value and initial-boundary value problems involving PDEs, mixed boundary conditions, high order finite difference methods, Numerical methods for discrete and fast Fourier transforms

File Description: application/xml

Access URL: https://zbmath.org/7996154
https://doi.org/10.1016/j.jcp.2025.113742

A modified incremental harmonic balance method based on the fast Fourier transform and Broyden’s method: A modified incremental harmonic balance method based on the fast Fourier transform and Broyden's method

Authors: Xuefeng Wang Weidong Zhu

Source: Nonlinear Dynamics. 81:981-989

Subject Terms: Broyden's method, Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc, harmonic balance, 02 engineering and technology, nonlinear system, 15. Life on land, fast Fourier transform, 01 natural sciences, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, bifurcation, 0103 physical sciences, arc-length method, 0210 nano-technology, Special ordinary differential equations (Mathieu, Hill, Bessel, etc.), Numerical methods for discrete and fast Fourier transforms, Jacobian

File Description: application/xml

Access URL: https://link.springer.com/article/10.1007/s11071-015-2045-x
https://www.infona.pl/resource/bwmeta1.element.springer-c01e3d81-ba48-31fc-b8fe-c407bc7b4341

A mesh free method using hyperinterpolation and fast Fourier transform for solving differential equations: A mesh-free method using hyperinterpolation and fast Fourier transform for solving differential equations

Authors: Ching-Shyang Chen Xin Li

Source: Engineering Analysis with Boundary Elements. 28:1253-1260

Subject Terms: linear boundary value problems, numerical examples, Boundary value problems for second-order elliptic equations, particular solutions, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, 0101 mathematics, Sloan hyperinterpolation, fast Fourier transform, 01 natural sciences, Numerical methods for discrete and fast Fourier transforms, mesh-free method

File Description: application/xml

Access URL: https://zbmath.org/2211140
https://doi.org/10.1016/j.enganabound.2003.05.001
https://www.sciencedirect.com/science/article/pii/S0955799704000190

Very fast algorithms for implied barriers and moving-barrier options pricing

Authors: Yu-Ming Lu Yuh-Dauh Lyuu

Source: Mathematics and Computers in Simulation. 205:251-271

Subject Terms: algorithm, Derivative securities (option pricing, hedging, etc.), moving-barrier option, Numerical methods (including Monte Carlo methods), 0502 economics and business, 05 social sciences, implied barrier, translation invariance, option pricing, fast Fourier transform, Numerical methods for discrete and fast Fourier transforms

File Description: application/xml

Access URL: https://zbmath.org/7627995
https://doi.org/10.1016/j.matcom.2022.09.018

Fully-decoupled conservative exponential approaches for the coupled nonlinear Schrödinger-Boussinesq equations

Authors: Cai, Jiaxiang Chen, Juan

Source: Discrete and Continuous Dynamical Systems - B. 29:2453-2470

Subject Terms: discrete gradient method, NLS equations (nonlinear Schrödinger equations), Finite difference methods for initial value and initial-boundary value problems involving PDEs, Hamiltonian system, Numerical methods for Hamiltonian systems including symplectic integrators, Schrödinger-Boussinesq equation, fast Fourier transform, Numerical methods for discrete and fast Fourier transforms, exponential method, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

File Description: application/xml

Access URL: https://zbmath.org/7815409
https://doi.org/10.3934/dcdsb.2023186

A Fourier spectral immersed boundary method with exact translation invariance, improved boundary resolution, and a divergence-free velocity field

Authors: Zhe Chen Charles S. Peskin

Source: Journal of Computational Physics. 509:113048

Subject Terms: nonuniform fast Fourier transform, viscous incompressible flow, Fluid Dynamics (physics.flu-dyn), fluid-structure interaction, FOS: Physical sciences, Physics - Fluid Dynamics, Numerical Analysis (math.NA), Fourier spectral method, 01 natural sciences, Boundary element methods for initial value and initial-boundary value problems involving PDEs, immersed boundary method, 0103 physical sciences, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, thin elastic boundary, Numerical methods for discrete and fast Fourier transforms, 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/2302.08694
https://zbmath.org/8021012
https://doi.org/10.1016/j.jcp.2024.113048

Retrospective and perspective for modification of digital methods for discrete Fourier transform.

Authors: Burova, Adeliya Usatenko, Timur

Source: AIP Conference Proceedings; 2023, Vol. 2700 Issue 1, p1-6, 6p

Subject Terms: SEPARATION of variables, DISCRETE Fourier transforms, FOURIER transforms, DIGITAL transformation, DIGITAL signal processing, DIGITAL technology, FAST Fourier transforms