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The Finite Difference Time Domain (FDTD) method is a widely used numerical technique for solving Maxwell's equations, particularly in computational electromagnetics and photonics. It enables accurate modeling of wave propagation in complex…

Computation and Language · Computer Science 2025-04-15 Yifei He , Måns I. Andersson , Stefano Markidis

Topology optimization enables the design of highly efficient and complex structures, but conventional iterative methods, such as SIMP-based approaches, often suffer from high computational costs and sensitivity to initial conditions.…

Computational Engineering, Finance, and Science · Computer Science 2025-09-18 Aaron Lutheran , Srijan Das , Alireza Tabarraei

We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn-Sham density-functional theory (DFT). To this end, we develop an…

Computational Physics · Physics 2015-06-05 Phani Motamarri , Michael R Nowak , Kenneth Leiter , Jaroslaw Knap , Vikram Gavini

In this work, we develop an adaptive nonconforming finite element algorithm for the numerical approximation of phase-field parameterized topology optimization governed by the Stokes system. We employ the conforming linear finite element…

Numerical Analysis · Mathematics 2026-04-20 Bangti Jin , Jing Li , Yifeng Xu , Shengfeng Zhu

Homogenization is a fundamental technique for estimating the macroscopic properties of materials with microscale heterogeneity. Among Homogenization methods, the FFT-based Homogenization algorithm has become widely used due to its…

Materials Science · Physics 2025-04-15 Sascha H. Hauck , Matthias Kabel , Mazen Ali , Nicolas R. Gauger

In the present work, we investigate the computational efficiency afforded by higher-order finite-element discretization of the saddle-point formulation of orbital-free density functional theory. We first investigate the robustness of viable…

Computational Physics · Physics 2015-05-30 Phani Motamarri , Mrinal Iyer , Jaroslaw Knap , Vikram Gavini

In this paper, we propose an efficient and flexible algorithm to solve dynamic mean-field planning problems based on an accelerated proximal gradient method. Besides an easy-to-implement gradient descent step in this algorithm, a crucial…

Optimization and Control · Mathematics 2021-03-01 Jiajia Yu , Rongjie Lai , Wuchen Li , Stanley Osher

Robust topology optimization (RTO), as a class of topology optimization problems, identifies a design with the best average performance while reducing the response sensitivity to input uncertainties, e.g. load uncertainty. Solving RTO is…

Machine Learning · Computer Science 2024-08-22 Rini Jasmine Gladstone , Mohammad Amin Nabian , Vahid Keshavarzzadeh , Hadi Meidani

Given a time series vector, how can we efficiently compute a specified part of Fourier coefficients? Fast Fourier transform (FFT) is a widely used algorithm that computes the discrete Fourier transform in many machine learning applications.…

Machine Learning · Computer Science 2020-08-31 Yong-chan Park , Jun-Gi Jang , U Kang

Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\em fast Fourier…

Optimization and Control · Mathematics 2012-09-05 Robert J. Vanderbei

We introduce a topology optimization method to design permanent magnets for advanced stellarators. Recent researches show that permanent magnets have great potentials to simplify stellarator coils. We adopt state-of-the-art numerical…

This paper introduces a new computational framework to derive electromagnetic field derivatives with respect to multiple design parameters up to any order with the Finite-Difference Time-Domain (FDTD) technique. Specifically, only one FDTD…

Signal Processing · Electrical Eng. & Systems 2019-10-23 Kae-An Liu , Costas D. Sarris

Meshing of geometric domains having curved boundaries by affine simplices produces a polytopial approximation of those domains. The resulting error in the representation of the domain limits the accuracy of finite element methods based on…

Numerical Analysis · Mathematics 2018-02-09 James Cheung , Mauro Perego , Pavel Bochev , Max Gunzburger

The computational efficiency of the Finite-Difference Time-Domain (FDTD) method can be significantly reduced by the presence of complex objects with fine features. Small geometrical details impose a fine mesh and a reduced time step,…

Computational Engineering, Finance, and Science · Computer Science 2021-06-30 Xinyue Zhang , Fadime Bekmambetova , Piero Triverio

An efficient finite-difference time-domain (FDTD) algorithm is built to solve the transverse electric 2D Maxwell's equations with inhomogeneous dielectric media where the electric fields are discontinuous across the dielectric interface.…

Computational Physics · Physics 2023-07-14 Timothy Meagher , Bin Jiang , Peng Jiang

In this letter, a fast Fourier transform (FFT)-enhanced low-complexity super-resolution sensing algorithm for near-field source localization with both angle and range estimation is proposed. Most traditional near-field source localization…

Signal Processing · Electrical Eng. & Systems 2024-11-26 Yuxiao Wu , Huizhi Wang , Yong Zeng

In this work, we develop an adaptive algorithm for the efficient numerical solution of the minimum compliance problem in topology optimization. The algorithm employs the phase field approximation and continuous density field. The adaptive…

Optimization and Control · Mathematics 2024-04-18 Bangti Jin , Jing Li , Yifeng Xu , Shengfeng Zhu

Topology optimization methods face serious challenges when applied to structural design with fluid-structure interaction (FSI) loads, specially for high Reynolds fluid flow. This paper devises an explicit boundary method that employs…

In this paper a class of higher order finite element methods for the discretization of surface Stokes equations is studied. These methods are based on an unfitted finite element approach in which standard Taylor-Hood spaces on an underlying…

Numerical Analysis · Mathematics 2019-09-19 Thomas Jankuhn , Arnold Reusken

Fast Fourier transform (FFT) based methods have turned out to be an effective computational approach for numerical homogenisation. In particular, Fourier-Galerkin methods are computational methods for partial differential equations that are…

Numerical Analysis · Mathematics 2020-04-22 Jaroslav Vondřejc , Dishi Liu , Martin Ladecký , Hermann G. Matthies