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In the past decades, the finite difference methods for space fractional operators develop rapidly; to the best of our knowledge, all the existing finite difference schemes, including the first and high order ones, just work on uniform…

Numerical Analysis · Mathematics 2016-04-04 Lijing Zhao , Weihua Deng

Over the past decade, Finite Element Method (FEM) has served as a foundational numerical framework for approximating the terms of Time Series Expansion (TSE) as solutions to transient Partial Differential Equation (PDE). However, the…

Numerical Analysis · Mathematics 2024-09-04 Ahmad Deeb , Denys Dutykh

Currently existing energy-stable parametric finite element methods for surface diffusion flow and other flows are usually limited to first-order accuracy in time. Designing a high-order algorithm for geometric flows that can also be…

Numerical Analysis · Mathematics 2024-07-15 Meng Li , Yihang Guo , Jingjiang Bi

A finite difference method (FDM) applicable to a two dimensional (2D) quantum dot was developed as a non-conventional approach to the theoretical understandings of quantum devices. This method can be applied to a realistic potential with an…

Mesoscale and Nanoscale Physics · Physics 2013-12-16 Jai Seok Ahn

The finite difference time domain method is one of the simplest and most popular methods in computational electromagnetics. This work considers two possible ways of generalising it to a meshless setting by employing local radial basis…

Computational Physics · Physics 2026-02-27 Andrej Kolar-Požun , Gregor Kosec

We propose a class of temporally high-order parametric finite element methods for simulating solid-state dewetting of thin films in two dimensions using a sharp-interface model. The process is governed by surface diffusion and contact point…

Numerical Analysis · Mathematics 2025-10-21 Xiaowen Gan , Yuqian Teng , Sisheng Wang

We present a corrective subcell averaging technique that improves on the accuracy of the volume-averaged finite-difference time-domain (FDTD) method in the presence of dispersive material interfaces. The method is based on an alternative…

Computational Physics · Physics 2015-06-15 Joachim Hamm , Fabian Renn , Ortwin Hess

In this paper we focus on high order finite element approximations of the electric field combined with suitable preconditioners, to solve the time-harmonic Maxwell's equations in waveguide configurations. The implementation of high order…

Numerical Analysis · Mathematics 2017-05-16 Marcella Bonazzoli , Victorita Dolean , Frédéric Hecht , Francesca Rapetti

Although many 3D One-Way Wave-equation Migration (OWEM) methods exist for VTI media, most of them struggle either with the stability, the anisotropic noise or the computational cost. In this paper we present a new method based on a mixed…

In wave propagation problems, finite difference methods implemented on staggered grids are commonly used to avoid checkerboard patterns and to improve accuracy in the approximation of short-wavelength components of the solutions. In this…

Numerical Analysis · Mathematics 2026-01-15 Micol Bassanini , Simone Deparis , Paolo Ricci

We develop a new, efficient, and accurate method to simulate frequency-domain borehole electromagnetic (EM) measurements acquired in the presence of three-dimensional (3D) variations of the anisotropic subsurface conductivity. The method is…

This paper introduces an innovative end-to-end model-based deep learning approach for efficient electromagnetic analysis of high-dimensional frequency selective surfaces (FSS). Unlike traditional data-driven methods that require large…

Machine Learning · Computer Science 2024-10-23 Cheima Hammami , Lucas Polo-López , Luc Le Magoarou

A new method for implementing the kinetic energy operator for real-space, grid-based electronic structure codes is developed. It is based on multi-order Adaptive Finite Differencing (AFD) and uses atomic pseudo orbitals produced by the…

Computational Physics · Physics 2023-05-23 E. L. Briggs , Wenchang Lu , J. Bernholc

We present a proof of concept for solving a 1+1D complex-valued, delay partial differential equation (PDE) that emerges in the study of waveguide quantum electrodynamics (QED) by adapting the finite-difference time-domain (FDTD) method. The…

Mathematical Software · Computer Science 2018-11-19 Yao-Lung L. Fang

We present a novel end-to-end deep learning-based adaptation control algorithm for frequency-domain adaptive system identification. The proposed method exploits a deep neural network to map observed signal features to corresponding…

Audio and Speech Processing · Electrical Eng. & Systems 2022-03-07 Thomas Haubner , Andreas Brendel , Walter Kellermann

The time-dependent equations of computational electrodynamics (CED) are evolved consistent with the divergence constraints. As a result, there has been a recent effort to design finite volume time domain (FVTD) and discontinuous Galerkin…

Computational Physics · Physics 2018-11-14 Dinshaw S. Balsara , Roger Kappeli

A higher-order accurate finite element method is proposed which uses automatically generated meshes based on implicit level-set data for the description of boundaries and interfaces in two and three dimensions. The method is an alternative…

Numerical Analysis · Computer Science 2017-06-06 T. P. Fries

In this paper, the concept of cross-correlation Green's functions (CGF) is used in conjunction with the finite difference time domain (FDTD) technique for calculation of envelope correlation coefficient (ECC) of any arbitrary MIMO antenna…

Classical Physics · Physics 2016-11-28 Debdeep Sarkar , Kumar Vaibhav Srivastava

In the present work, a high order finite element type residual distribution scheme is designed in the framework of multidimensional compressible Euler equations of gas dynamics. The strengths of the proposed approximation rely on the…

Numerical Analysis · Mathematics 2023-01-16 Remi Abgrall , Paola Bacigaluppi , Tokareva Svetlana

Recently, large offshore wind power plants have been installed far from the shore, using long HVAC three-core armored cables to export power. Its high capacitance may contribute to the appearance of unwanted phenomena, such as overvoltages…

Systems and Control · Electrical Eng. & Systems 2024-01-25 Juan Carlos del-Pino-López , Pedro Cruz-Romero
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