论文标题
用非正交子空间的子空间收集替换，以加速用于传导复合材料的快速傅立叶变换方法
Substitution of subspace collections with nonorthogonal subspaces to accelerate Fast Fourier Transform methods applied to conducting composites
论文作者
论文摘要
我们展示了“将复合材料理论扩展到其他科学领域的第7章中开发的子空间集合代数的力量（米尔顿编辑，2016年）。特别是，我们加速了穆林克和苏奎特和苏奎特和艾尔和米尔顿的快速傅立叶变换方案，并通过计算现场和有效的媒介，以替代范围的媒介，并有效地收集了范围的媒介。具有正交子空间的子空间可以做到当电导率的有效电导率$σ_1$（设置为$ 1 $的矩阵阶段电导率）限制为nive $ [ - β，-β，-α] $ converied $σ_1$ ACCER的奇异。正方形的$ 25 \％$体积分数。
We show the power of the algebra of subspace collections developed in Chapter 7 of the book "Extending the Theory of Composites to Other Areas of Science (edited by Milton, 2016). Specifically we accelerate the Fast Fourier Transform schemes of Moulinec and Suquet and Eyre and Milton (1994, 1998) for computing the fields and effective tensor in a conducting periodic medium by substituting a subspace collection with nonorthogonal subspaces inside one with orthogonal subspaces. This can be done when the effective conductivity as a function of the conductivity $σ_1$ of the inclusion phase (with the matrix phase conductivity set to $1$) has its singularities confined to an interval $[-β,-α]$ of the negative real $σ_1$ axis. Numerical results of Moulinec and Suquet show accelerated convergence for the model example of a square array of squares at $25\%$ volume fraction. For other problems we show how $Q^*_C$-convex functions can be used to restrict the region where singularities of the effective tensor as a function of the component tensors might be found.
