Discrete Geometric Homogenisation and Inverse Homogenisation of an Elliptic Operator

Exponential Estimates in Averaging and Homogenisation

Many partial differential equations with rapid spatial or temporal scales have effective descriptions which can be derived by homogenisation or averaging. In this article we deal with examples, where quantitative estimates of the error is possible for higher order homogenisation and averaging. In particular, we provide theorems, which allow homogenisation and averaging beyond all orders by givi...

Homogenisation of Exponential Order for Elliptic Systems in Infinite Cylinders

Homogenisation with application to layered materials

In this paper we are concerned with the elliptic PDEs with highly oscillating coefficients which model the behaviour of composite linear elastic materials. Analytical expressions for the effective coefficients are obtained for the case of layered materials using the theory of homogenisation. Some properties of the homogenised materials are analysed. An efficient algorithm for the numerical dete...

Spectral convergence for high contrast elliptic periodic problems with a defect via homogenisation

We consider an eigenvalue problem for a divergence form elliptic operator Aε with high contrast periodic coefficients with period ε in each coordinate, where ε is a small parameter. The coefficients are perturbed on a bounded domain of ‘order one’ size. The local perturbation of coefficients for such operator could result in emergence of localised waves eigenfunctions with corresponding eigenva...

Merging expert and empirical data for rare event frequency estimation: Pool homogenisation for empirical Bayes models

Empirical Bayes provides one approach to estimating the frequency of rare events as a weighted average of the frequencies of an event and a pool of events. The pool will draw upon, for example, events with similar precursors. The higher the degree of homogeneity of the pool, then the Empirical Bayes estimator will be more accurate. We propose and evaluate a new method using homogenisation facto...