Abstract:

Inverse problems in wave scattering involve determining the shape or material properties of an object by illuminating the object with a wave and measuring the scattered field. They are important for their applications, which include imaging and non-destructive testing, and design of materials with particular characteristics. We present a computational method for the particular inverse problem of using electromagnetic waves to reconstruct the refractive index of an unknown medium that contains metal inclusions. Our algorithm is based on a Newton-type method for the inverse problem and simulates wave scattering from the complex medium and metal system by coupling the well-known finite element and boundary element methods. Key components of our algorithm are a novel hybrid surface-volume integral equation that generalises the Lippman-Schwinger equation, and use of a thin plate spline ansatz to represent the refractive index in complex domains.

Bio:

Stuart Hawkins is a senior lecturer in Mathematics at Macquarie University. Stuart was awarded a PhD in 1999 from the University of Bath and held postdoctoral positions at the University of Liverpool and the University of New South Wales. He has been at Macquarie University since 2009. Stuart's research interests are forward and inverse wave scattering, and uncertainty quantification.