Substitution of subspace collections with nonorthogonal subspaces to accelerate Fast Fourier Transform methods applied to conducting composites.

摘要: We show the power of algebra subspace collections developed in Chapter 7 book "Extending Theory Composites to Other Areas Science (edited by Milton, 2016). Specifically we accelerate Fast Fourier Transform schemes Moulinec and Suquet Eyre Milton (1994, 1998) for computing fields effective tensor a conducting periodic medium substituting collection with nonorthogonal subspaces inside one orthogonal subspaces. This can be done when conductivity as function $\sigma_1$ inclusion phase (with matrix set $1$) has its singularities confined an interval $[-\beta,-\alpha]$ negative real axis. Numerical results accelerated convergence model example square array squares at $25\%$ volume fraction. For other problems how $Q^*_C$-convex functions used restrict region where component tensors might found.