English
Related papers

Related papers: Jacobi-accelerated FFT-based solver for smooth hig…

200 papers

FFT-based solvers introduced in the 1990s for the numerical homogenization of heterogeneous elastic materials have been extended to a wide range of physical properties. In parallel, alternative algorithms and modified discrete Green…

Materials Science · Physics 2015-05-20 Lionel Gélébart , Franck Ouaki

The Fourier-Galerkin method (in short FFTH) has gained popularity in numerical homogenisation because it can treat problems with a huge number of degrees of freedom. Because the method incorporates the fast Fourier transform (FFT) in the…

Numerical Analysis · Mathematics 2020-02-14 Jaroslav Vondřejc , Tom W. J. de Geus

The linear conjugate gradient method is widely used in physical simulation, particularly for solving large-scale linear systems derived from Newton's method. The nonlinear conjugate gradient method generalizes the conjugate gradient method…

Optimization and Control · Mathematics 2024-05-15 Xing Shen , Runyuan Cai , Mengxiao Bi , Tangjie Lv

The problem of fast computation of multivariate kernel density estimation (KDE) is still an open research problem. In our view, the existing solutions do not resolve this matter in a satisfactory way. One of the most elegant and efficient…

Computation · Statistics 2016-09-08 Artur Gramacki , Jarosław Gramacki

Most of the FFT methods available for homogenization of the mechanical response use the strain/deformation gradient as unknown, imposing their compatibility using Green's functions or projection operators. This implies the allocation of…

Computational Engineering, Finance, and Science · Computer Science 2019-08-27 Sergio Lucarini , Javier Segurado

Computationally efficient numerical methods for high-order approximations of convolution integrals involving weakly singular kernels find many practical applications including those in the development of fast quadrature methods for…

Numerical Analysis · Mathematics 2018-10-10 Akash Anand , Awanish Kumar Tiwari

The graph fractional Fourier transform (GFRFT) for unitary graph Fourier transform (GFT) matrices can be interpreted through the scalar function $e^{j\alpha\theta}$ on the unit circle. Under the principal branch, its Fourier-series…

Signal Processing · Electrical Eng. & Systems 2026-05-19 Ziqi Yan , Mingzhi Wang , Sen Shi , Feiyue Zhao , Manjun Cui , Yangfan He , Zhichao Zhang

We consider the Fast Fourier Transform (FFT) based numerical method for thin film magnetization problems [Vestg{\aa}rden and Johansen, SuST, 25 (2012) 104001], compare it with the finite element methods, and evaluate its accuracy. Proposed…

Computational Physics · Physics 2018-05-09 Leonid Prigozhin , Vladimir Sokolovsky

To address limitations of the graph fractional Fourier transform (GFRFT) Wiener filtering and the traditional joint time-vertex fractional Fourier transform (JFRFT) Wiener filtering, this study proposes a filtering method based on the…

Signal Processing · Electrical Eng. & Systems 2025-07-30 Ziqi Yan , Zhichao Zhang

The non-equidistant fast Fourier transform (NFFT) is an extension of the famous fast Fourier transform (FFT), which can be applied to non-equidistantly sampled data in time/space or frequency domain. It is an approximative algorithm that…

Mathematical Software · Computer Science 2023-01-31 Tobias Knopp , Marija Boberg , Mirco Grosser

Fourier-accelerated micromechanical homogenization has been developed and applied to a variety of problems, despite being prone to ringing artifacts. In addition, the majority of Fourier-accelerated solvers applied to FFT-accelerated…

Numerical Analysis · Mathematics 2022-07-22 Ali Falsafi , Richard J. Leute , Martin Ladecký , Till Junge

Fast-Fourier Transform (FFT) methods have been widely used in solid mechanics to address complex homogenization problems. However, current FFT-based methods face challenges that limit their applicability to intricate material models or…

Materials Science · Physics 2024-10-15 Mohit Pundir , David S. Kammer

In this paper we propose an efficiently preconditioned Newton method for the computation of the leftmost eigenpairs of large and sparse symmetric positive definite matrices. A sequence of preconditioners based on the BFGS update formula is…

Numerical Analysis · Mathematics 2013-12-06 Luca Bergamaschi , Angeles Martinez

The Fast Fourier Transform (FFT) is an algorithm of paramount importance in signal processing as it allows to apply the Fourier transform in O(n log n) instead of O(n 2) arithmetic operations. Graph Signal Processing (GSP) is a recent…

Numerical Analysis · Computer Science 2017-06-19 Luc Le Magoarou , Rémi Gribonval , Nicolas Tremblay

This paper presents a large-scale parallel solver, specifically designed to tackle the challenges of solving high-dimensional and high-contrast linear systems in heat transfer topology optimization. The solver incorporates an interpolation…

Numerical Analysis · Mathematics 2025-01-14 Yingjie Zhou , Changqing Ye , Yucheng Liu , Shubin Fu , Eric T. Chung

This paper presents an efficient Krylov subspace iterative solver for the three-dimensional (3D) Helmholtz equation with non-constant coefficients and absorbing boundary conditions, combining high-resolution compact schemes with low-order…

Numerical Analysis · Mathematics 2026-02-10 Yury Gryazin , Ron Gonzales , Xiaoye Sherry Li

Discrete normalizing flows are promising generative models with advantages such as analytical log-likelihood computation and end-to-end training. However, the architectural constraints to ensure invertibility and tractable Jacobian…

Machine Learning · Computer Science 2026-05-06 Jiaru Zhang , Juanwu Lu , Xiaoyu Wu , Ziran Wang , Ruqi Zhang

The construction of robust solvers for linear systems obtained from the discretization of partial differential equations using Isogeometric Analysis is challenging since the condition number of the system matrix not only grows with the…

Numerical Analysis · Mathematics 2025-12-24 Monica Montardini , Stefan Takacs , Mattia Tani

Fourier transform methods are used to analyze functions and data sets to provide frequencies, amplitudes, and phases of underlying oscillatory components. Fast Fourier transform (FFT) methods offer speed advantages over evaluation of…

Data Analysis, Statistics and Probability · Physics 2015-07-08 Elya Courtney , Michael Courtney

In this article, we present an $O(N \log N)$ rapidly convergent algorithm for the numerical approximation of the convolution integral with radially symmetric weakly singular kernels and compactly supported densities. To achieve the reduced…

Numerical Analysis · Mathematics 2021-07-09 Awanish Kumar Tiwari , Ambuj Pandey , Jagabandhu Paul , Akash Anand