Details of Grant 

EPSRC Reference:	EP/C510941/1
Title:	Mathematical methods for Wave Interaction with Large Arrays
Principal Investigator:	Linton, Professor C
Other Investigators:	McIver, Professor P
Researcher Co-Investigators:
Project Partners:
Department:	School of Mathematics
Organisation:	Loughborough University
Scheme:	Standard Research (Pre-FEC)
Starts:	01 July 2005	Ends:	30 June 2008	Value (£):	146,601
EPSRC Research Topic Classifications:	Coastal & Waterway Engineering Continuum Mechanics
EPSRC Industrial Sector Classifications:	Water
Related Grants:
Panel History:
Summary on Grant Application Form
Many methods exist for studying wave interactions with arrays of scatterers. As the size of an array increases, solutions to scattering problems rapidly become computationally expensive. By contrast, the case of an infinite periodic array is usually a much simpler proposition. This is because the periodicity allows us to formulate the problem on a single cell of the array.The first part of our proposal is to develop methods by which scattering by infinite periodic arrays can be used to shed light on associated large array problems. The basic idea is simple: instead of solving for unknowns relevant to the large array case, we formulate equations for the difference between the unknowns in the infinite and large array problems. Used effectively, this can increase the efficiency of solution procedures dramatically. It also enables the effects of the edges of an array to be easily isolated.In applications, interest may be in the global properties of the scattering problem, such as the far-field waves, or in the large-scale variations of the wave field within the array, and accurate determination of the wave field throughout the fluid domain may not be necessary. In such cases d is appropriate to seek approximate methods of solution that do not involve the small-scale variations of the wave field. Such approaches are called homogenization techniques and those presently available yield useful results for long wavelengths or for unstructured arrays. However, for large periodic arrays of structures the approximate theory obtained by homogenization cannot reproduce those phenomena, such as Bragg reflection, that arise from the periodic nature of the array. The second strand of our proposal is to devise extended homogenization techniques which can model these phenomena.
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Organisation Website:	http://www.lboro.ac.uk