Differential Forms and Boundary Integral Equations for Maxwell-Type Problems
Differential Forms and Boundary Integral Equations for Maxwell-Type Problems
复制标题
麦克斯韦型问题的微分形式和边界积分方程
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
B. Auchmann
中科院分区：
文献类型：
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作者：
S. Kurz;B. Auchmann
我们提出的边界积分方程的麦克斯韦型问题的微分形式设置。麦克斯韦型问题由微分方程（δd − k 2）ω = 0控制，其中k ∈ ω成立，但受到一些限制。这个问题类概括了三维中的旋度、旋度和梯度类型的问题。本文的目标有三个：1）在具有Lipschitz边界的任意维光滑流形上建立Sobolev-空间框架。2)引入积分变换和基本解，并推导出Maxwell型问题的表示公式。3)利用微分形式微积分的力量来深入了解麦克斯韦型边界积分方程的性质和固有对称性。
We present boundary-integral equations for Maxwell-type problems in a differential-form setting. Maxwell-type problems are governed by the differential equation (δd − k 2)ω = 0, where k ∈ ℂ holds, subject to some restrictions. This problem class generalizes curl curl- and grad-types of problems in three dimensions. The goal of the paper is threefold: 1) Establish the Sobolev-space framework in the full generality of differential-form calculus on a smooth manifold of arbitrary dimension and with Lipschitz boundary. 2) Introduce integral transformations and fundamental solutions, and derive a representation formula for Maxwell-type problems. 3) Leverage the power of differential-form calculus to gain insight into properties and inherent symmetries of boundary-integral equations of Maxwell-type.