Time-reversed infinite elements and their application to scatterer and source identification

Recently, it has been shown that time reversed absorbing conditions can be used to determine the location and size of an unknown scatterer for Helmholtz problems. This was done by removing a region from the computational domain and applying time reversed first order Bayliss-Turkel absorbing boundary conditions on the edge of this domain. If the region is placed at the right location, the time reversed absorbing condition works as a sink that effectively removes the energy from the system after convergence of the back propagated sound wave at the scatterer location. Thus, the scatterer or source location can be determined by reviewing the energy decay of the system. In this paper, a similar approach is adopted, but then with time reversed Astley-Leis infinite elements. This has several advantages as compared to the time reversed first order Bayliss- Turkel absorbing boundary condition. Firstly, it is shown that the resulting formulation of the time reversed infinite elements is the same as the classical infinite elements, meaning that the implementation of the time reversed infinite elements is basically the same as for classical infinite elements. Secondly, it is possible to easily adjust the accuracy of the infinite elements by changing the radial order. The effectiveness of the method is shown with several numerical examples.