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An FFT based method is proposed to simulate chemo-mechanical problems at the microscale including fracture, specially suited to predict crack formation during the intercalation process in batteries. The method involves three fields fully…
This paper presents a comprehensive exploration of Fast Fourier Transform (FFT) and linear convolution implementations, integrating both conventional methods and novel approaches leveraging the Bit Slicing Multiplier (BSM) technique. The…
In this paper, we first introduce the reader to the Basic Scheme of Moulinec and Suquet in the setting of quasi-static linear elasticity, which takes advantage of the fast Fourier transform on homogenized microstructures to accelerate…
In this work, we present a framework for the matrix-free solution to a monolithic quasi-static phase-field fracture model with geometric multigrid methods. Using a standard matrix based approach within the Finite Element Method requires…
Deep learning has delivered its powerfulness in many application domains, especially in image and speech recognition. As the backbone of deep learning, deep neural networks (DNNs) consist of multiple layers of various types with hundreds to…
The algorithm behind the Fast Fourier Transform has a simple yet beautiful geometric interpretation that is often lost in translation in a classroom. This article provides a visual perspective which aims to capture the essence of it.
The nonuniform discrete Fourier transform (NUDFT) and its inverse are widely used in various fields of scientific computing. In this article, we propose a novel superfast direct inversion method for type-III NUDFT. The proposed method…
The variational approach to fracture is effective for simulating the nucleation and propagation of complex crack patterns, but is computationally demanding. The model is a strongly nonlinear non-convex variational inequality that demands…
In Convolutional Neural Network (CNN) based image processing, most of the studies propose networks that are optimized for a single-level (or a single-objective); thus, they underperform on other levels and must be retrained for delivery of…
Large sparse linear algebraic systems can be found in a variety of scientific and engineering fields, and many scientists strive to solve them in an efficient and robust manner. In this paper, we propose an interpretable neural solver, the…
In this paper, we develop a nonlinear reduction framework based on our recently introduced extended group finite element method. By interpolating nonlinearities onto approximation spaces defined with the help of finite elements, the…
For nonlinear reduced-order models, especially for those with non-polynomial nonlinearities, the computational complexity still depends on the dimension of the original dynamical system. As a result, the reduced-order model loses its…
The precise analysis and accurate measurement of harmonic provides a reliable scientific industrial application. However, the high-performance DSP processor is the important method of electrical harmonic analysis. Hence, in this research…
Resolving sources beyond the diffraction limit is important in imaging, communications, and metrology. Current image-based methods of super-resolution require phase information (either of the source points or an added filter) and perfect…
The modeling of electric machines and power transformers typically involves systems of nonlinear magnetostatics or -quasistatics, and their efficient and accurate simulation is required for the reliable design, control, and optimization of…
The nonlinear Schr\"odinger equation (NSE) is well-known to model an ideal fiber-optic communication channel. Even though the NSE is a nonlinear evolution equation, it can be solved analytically using a nonlinear Fourier transform (NFT).…
This paper presents a novel boundary-optimized fast Fourier extension algorithm for efficient approximation of non-periodic functions. The proposed methodology constructs periodic extensions through strategic utilization of boundary…
Secure signal processing is becoming a de facto model for preserving privacy. We propose a model based on the Fully Homomorphic Encryption (FHE) technique to mitigate security breaches. Our framework provides a method to perform a Fast…
We developed fast direct solver for 3D Helmholtz and Maxwell equations in layered medium. The algorithm is based on the ideas of cyclic reduction for separable matrices. For the grids with major uniform part (within the survey domain in the…
An additive fast Fourier transform over a finite field of characteristic two efficiently evaluates polynomials at every element of an $\mathbb{F}_2$-linear subspace of the field. We view these transforms as performing a change of basis from…