Uniform approximations for bodies with defects and asymptotics of Green's kernels for singularly perturbed domains
Lead Research Organisation:
University of Liverpool
Department Name: Mathematical Sciences
Abstract
The issue of uniform asymptotic approximations for Green's kernelsin singularly perturbed domains has been addressed for the firsttime in the recent papers by the authors of this proposal. Themain challenge in this work is the presence of singularities ofthe Green's kernels, which make the known asymptotic methodsinefficient and require additional analysis.
Organisations
Publications
Maz'ya V
(2011)
Mesoscale Asymptotic Approximations to Solutions of Mixed Boundary Value Problems in Perforated Domains
in Multiscale Modeling & Simulation
Maz'ya V
(2009)
Asymptotic treatment of perforated domains without homogenization
in Mathematische Nachrichten
| Description | The project has lead to a breakthrough in modelling of large-scale clusters of impurities in solids and analysis of rapidly oscillating fields in the multi-physics context. The new rigorous method of meso-scale asymptotic approximations have been developed and implemented in a wide range of important applications. In addition to high quality journal publications, the project has lead to several research monographs. |
| Exploitation Route | The findings of this research are of great interest to physicists, engineers and industrialists. Numerical algorithms using the ideas of meso-scale asymptotic approximations have proved to be robust accurate and highly efficient. |
| Sectors | Aerospace, Defence and Marine,Chemicals,Education |
| Description | Engineers working on composite structures use the novel method of meso-scale asymptotic approximations successfully to design and study rapidly oscillatory fields in a wide range of important applications. |
| First Year Of Impact | 2008 |
| Sector | Aerospace, Defence and Marine,Chemicals,Construction,Education |
| Impact Types | Cultural,Societal |