Presented by:
Matthew Priddin University of Cambridge
Date:
Thursday 15th August 2019 - 14:30 to 15:00
Venue:
INI Seminar Room 1
Abstract:
Wiener-Hopf equations involving $n\times n$ matrices can
arise when solving mixed boundary value problems with $n$ junctions at which
the boundary condition to be imposed changes form. The offset Fourier transforms of the unknown
boundary values lead to exponential factors which require careful consideration
when applying the Wiener-Hopf technique. We consider the generalisation of an
iterative method introduced recently (Kisil
2018) from $2\times 2$ to $n\times n$ problems. This may
be effectively implemented numerically by employing a spectral method to
compute Cauchy transforms. We illustrate the approach through various examples
of scattering from collinear rigid plates and consider the merits of the
iterative method relative to alternative approaches to similar problems.