THOMPSON, I. and LINTON, C.M., 2008. An interaction theory for scattering by defects in arrays. SIAM Journal on Applied Mathematics, 68 (6), pp. 1783-1806
Wave scattering by an array of bodies that is periodic except for a finite number
of missing or irregular elements is considered. The field is decomposed into contributions from a
set of canonical problems, which are solved using a modified array scanning method. The resulting
interaction theory for defects is very efficient and can be used to construct the field in a large number
of different situations. Numerical results are presented for several cases, and particular attention is
paid to the amplitude with which surface waves are excited along the array. We also show how other
approaches can be incorporated into the theory so as to increase the range of problems that can be solved.