When two stiff inclusions are closely located, the gradient of the solution may become arbitrarily large as the distance between two inclusions tends to zero. Since blow-up of the gradient occurs in the narrow region, fine meshes should be required to compute the gradient. Thus, it is a challenging problem to numerically compute the gradient. Recent studies have shown that the major singularity can be extracted in an explicit way, so it suffices to compute the residual term for which only regular meshes are required. In this paper, we show through numerical simulations that the characterization of the singular term method can be efficiently used for the computation of the gradient when two strongly convex stiff domains of general shapes are closely located.

翻译：当两个刚性夹杂紧密分布时，随着夹杂间距趋近于零，解的梯度可能变得任意大。由于梯度在狭窄区域发生爆破，计算梯度需要精细网格，因此数值计算梯度是一项具有挑战性的问题。近期研究表明，主要奇异性可通过显式方式提取，因此只需计算残差项，而这一项仅需常规网格即可完成。本文通过数值模拟证明，当两个一般形状的强凸刚性区域紧密分布时，奇异项表征方法可高效用于梯度计算。