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

01/22/2020
by   Graeme W. Milton, et al.
0

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.

READ FULL TEXT
research
06/21/2023

Accelerated Griffin-Lim algorithm: A fast and provably converging numerical method for phase retrieval

The recovery of a signal from the magnitudes of its transformation, like...
research
06/05/2013

Quaternion Fourier Transform on Quaternion Fields and Generalizations

We treat the quaternionic Fourier transform (QFT) applied to quaternion ...
research
07/02/2019

Robust Tensor Completion Using Transformed Tensor SVD

In this paper, we study robust tensor completion by using transformed te...
research
05/27/2022

Exact bounds on the amplitude and phase of the interval discrete Fourier transform in polynomial time

We elucidate why an interval algorithm that computes the exact bounds on...
research
07/20/2018

Fast transforms over finite fields of characteristic two

An additive fast Fourier transform over a finite field of characteristic...
research
10/23/2017

Tensor Matched Subspace Detection

The problem of testing whether an incomplete tensor lies in a given tens...
research
08/19/2018

Fourier analysis perspective for sufficient dimension reduction problem

A theory of sufficient dimension reduction (SDR) is developed from an op...

Please sign up or login with your details

Forgot password? Click here to reset