论文标题
涡流模型中磁性电势的角渐近学
Corner asymptotics of the magnetic potential in the eddy-current model
论文作者
论文摘要
在本文中，我们描述了在二维环境中嵌入介电介质中的导电体角附近的磁力。我们将其显式渐近扩展为此潜力，因为与角落的距离为零。这种扩展涉及单数功能和奇异系数。我们介绍了一种计算角附近奇异函数的方法，并提供了两种计算奇异系数的方法：矩的方法和准偶性奇异函数的方法。证明了两种近似方法的收敛性的估计。我们最终通过有限元计算说明了理论结果。此问题的特定非标准特征在于其奇异函数的结构：它们具有串联的形式，其第一项是谐波多项式，而进一步的术语是操作员的分段恒定零件订单产生的真正的非平滑函数。
In this paper, we describe the magnetic potential in the vicinity of a corner of a conducting body embedded in a dielectric medium in a bidimensional setting. We make explicit the corner asymptotic expansion for this potential as the distance to the corner goes to zero. This expansion involves singular functions and singular coefficients. We introduce a method for the calculation of the singular functions near the corner and we provide two methods to compute the singular coefficients: the method of moments and the method of quasi-dual singular functions. Estimates for the convergence of both approximate methods are proven. We eventually illustrate the theoretical results with finite element computations. The specific non-standard feature of this problem lies in the structure of its singular functions: They have the form of series whose first terms are harmonic polynomials and further terms are genuine non-smooth functions generated by the piecewise constant zeroth order term of the operator.
