首页/论文/0908.4448

arXiv 0908.44482009-08math.NAcs.NA

使用离散外微积分在流形上计算麦克斯韦方程组

Computation of Maxwell's equations on Manifold using DEC

Zhejiang University（浙江大学）；Chinese Academy of Sciences（中国科学院）

Zheng Xie, Yujie Ma

备注：: 19 pages,6 figures

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

摘要英文摘要相关论文

AI总结：

本文采用离散外微积分方法，在空间流形上数值求解麦克斯韦方程组，并分析其稳定性条件和误差，最后在C++平台上模拟真空中的TE/M波。

摘要：

本文讨论了在空间流形和时间上使用离散外微积分方法数值求解麦克斯韦方程组，这是一种格点规范理论。还完成了其稳定性条件和误差的分析。该算法已在C++平台上实现，用于模拟真空中的TE/M波。

英文摘要：

In this paper, the method of discrete exterior calculus for numerically solving Maxwell's equations in space manifold and the time is discussed, which is a kind of lattice gauge theory. The analysis of its stable condition and error is also accomplished. This algorithm has been implemented on C++ plateform for simulating TE/M waves in vacuum.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

摘要英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

使用隐式DEC格式在流形上计算麦克斯韦方程组

Computation of Maxwell's equations on manifold using implicit DEC scheme

Zhejiang University（浙江大学）；Chinese Academy of Sciences（中国科学院）

针对离散外微积分求解麦克斯韦方程组稳定性限制严格的问题，提出结合隐式时间格式与离散外微积分的无条件稳定方案，并分析了其稳定性和误差。

2009-12-29cs.NAmath.NA

流形上的多面体离散de Rham复形及其在Maxwell方程中的应用

A polytopal discrete de Rham complex on manifolds, with application to the Maxwell equations

本文在流形上构造了任意阶精度的离散de Rham复形，并应用于无边界二维流形上的Maxwell方程，数值验证于球面和环面。

2025-02-20cs.NAmath.NA

微分形式与Maxwell型问题的边界积分方程

Differential Forms and Boundary Integral Equations for Maxwell-Type Problems

Robert Bosch GmbH（罗伯特·博世有限公司）；CERN（欧洲核子研究组织）

本文基于微分形式框架，推导Maxwell型问题的边界积分方程，建立Sobolev空间框架，引入积分变换和基本解，推导表示公式，并探讨边界积分方程的性质与对称性。

2014-11-17cs.NAmath.NA

A low-rank projector-splitting integrator for the Vlasov--Maxwell equations with divergence correction

The Vlasov--Maxwell equations are used for the kinetic description of magnetized plasmas. As they are posed in an up to 3+3 dimensional phase space, solving this problem is extremely expensive from a computational point of view. In this paper, we exploit the low-rank structure in the solution of the Vlasov equation. More specifically, we consider the Vlasov--Maxwell system and propose a dynamic low-rank integrator. The key idea is to approximate the dynamics of the system by constraining it to a low-rank manifold. This is accomplished by a projection onto the tangent space. There, the dynamics…

2019-08-21cs.NAmath.NA

Stability and convergence analysis of a domain decomposition FE/FD method for the Maxwell's equations in time domain

Stability and convergence analysis for the domain decomposition finite element/finite difference (FE/FD) method is presented. The analysis is designed for semi-discrete finite element scheme for the time-dependent Maxwell's equations. The explicit finite element schemes in different settings of the spatial domain are constructed and domain decomposition algorithm is formulated. Several numerical examples validate convergence rates obtained in the theoretical studies.

2021-07-07cs.NAmath.NA

Convergence of HX Preconditioner for Maxwell's Equations with Jump Coefficients (i): Various Extensions of The Regular Helmholtz Decomposition

This paper is the first one of two serial articles, whose goal is to prove convergence of HX Preconditioner (proposed by Hiptmair and Xu 2007) for Maxwell's equations with jump coefficients. In this paper we establish various extensions of the regular Helmholtz decomposition for edge finite element functions defined in three dimensional domains. The functions defined by the regular Helmholtz decompositions can preserve the zero tangential complement on faces and edges of polyhedral domains and some non-Lipchitz domains, and possess stability estimates with only a $logarithm$ factor. These regu…

2020-01-16cs.NAmath.NA

更多相关论文收起更多论文

基于精确离散特征分解的快速麦克斯韦求解器 I. 二维情形

Fast Maxwell Solvers Based on Exact Discrete Eigen-Decompositions I. Two-Dimensional Case

本文基于最低阶矩形 Nédélec 元的精确离散特征分解，提出二维矩形区域麦克斯韦方程的快速求解器，利用快速正弦/余弦变换实现 $\mathcal{O}(n^2\log n)$ 复杂度，并可用于变系数问题的预条件处理。

2025-03-13cs.NAmath.NA

具有正则分解技术的连续有限元方法用于Maxwell特征值问题

Continuous Finite Element Method For Maxwell Eigenvalue Problems With Regular Decomposition Technique

本文提出了一种基于正则分解技术的连续有限元方法，用于求解Maxwell特征值问题，通过高阶拉格朗日有限元实现高阶收敛性，并通过数值实验验证了理论结果。

2025-12-17cs.NAmath.NA

Parallel domain decomposition solvers for the time harmonic Maxwell equations

The time harmonic Maxwell equations are of current interest in computational science and applied mathematics with many applications in modern physics. In this work, we present parallel finite element solver for the time harmonic Maxwell equations and compare different preconditioners. We show numerically that standard preconditioners like incomplete LU and the additive Schwarz method lead to slow convergence for iterative solvers like generalized minimal residuals, especially for high wave numbers. Even more we show that also more specialized methods like the Schur complement method also yield…

2021-05-25cs.NAmath.NA

时谐Maxwell方程的双层域分解预条件器

A two-level domain-decomposition preconditioner for the time-harmonic Maxwell's equations

Université Côte d’Azur, CNRS, LJAD（蔚蓝海岸大学，法国国家科学研究中心，拉格朗日分析几何实验室）；University of Strathclyde（思克莱德大学）；University of Bath（巴斯大学）；UPMC Univ Paris 06, LJLL（巴黎第六大学皮埃尔和玛丽·居里大学，拉格朗日分析实验室）

本文研究了针对时谐Maxwell方程的双层域分解预条件器，探讨了其在理论和数值上的有效性，以解决中高频下的快速迭代求解问题。

2018-02-21cs.NAmath.NA

Solution of time-harmonic Maxwell's equations by a domain decomposition method based on PML transmission conditions

Numerical discretization of the large-scale Maxwell's equations leads to an ill-conditioned linear system that is challenging to solve. The key requirement for successive solutions of this linear system is to choose an efficient solver. In this work we use Perfectly Matched Layers (PML) to increase this efficiency. PML have been widely used to truncate numerical simulations of wave equations due to improving the accuracy of the solution instead of using absorbing boundary conditions (ABCs). Here, we will develop an efficient solver by providing an alternative use of PML as transmission conditi…

2023-01-30cs.NAmath.NA

Domain Decomposition with Neural Network Interface Approximations for time-harmonic Maxwell's equations with different wave numbers

In this work, we consider the time-harmonic Maxwell's equations and their numerical solution with a domain decomposition method. As an innovative feature, we propose a feedforward neural network-enhanced approximation of the interface conditions between the subdomains. The advantage is that the interface condition can be updated without recomputing the Maxwell system at each step. The main part consists of a detailed description of the construction of the neural network for domain decomposition and the training process. To substantiate this proof of concept, we investigate a few subdomains in …

2023-03-05cs.NAmath.NA

波导中Maxwell方程域分解方法的模态分析

Modal analysis of a domain decomposition method for Maxwell's equations in a waveguide

Eindhoven University of Technology（埃因霍温理工大学）；INSA Rouen Normandie, Normandie Univ（鲁昂诺曼底高等师范学院，诺曼底大学）；Sorbonne Université, Université Paris Cité, CNRS, Inria, Laboratoire Jacques-Louis Lions, LJLL（索邦大学，巴黎西岱大学，法国国家科学研究中心，法国国家数字技术研究所，雅克-路易·利翁斯实验室）

本文分析了波导中基于Maxwell方程的一级Schwarz域分解方法的弱可扩展性，结合Toeplitz矩阵的极限谱分析和Maxwell解的模态分解，提出新的理论框架，并通过数值实验验证了其在复杂几何和传输条件下的有效性。

2026-04-14cs.NAmath.NAphysics.comp-ph

A Matrix Basis Formulation For The Green's Functions Of Maxwell's Equations And The Elastic Wave Equations In Layered Media

A matrix basis formulation is introduced to represent the 3 x 3 dyadic Green's functions in the frequency domain for the Maxwell's equations and the elastic wave equation in layered media. The formulation can be used to decompose the Maxwell's Green's functions into independent TE and TM components, each satisfying a Helmholtz equation, and decompose the elastic wave Green's function into the S-wave and the P-wave components. In addition, a derived vector basis formulation is applied to the case for acoustic wave sources from a non-viscous fluid layer.

2020-08-03cs.NAmath-phmath.MP