2014/01/14 by Gilles Chardon, Chardon, Gilles
Engineering · Environmental Science · Physics and Astronomy · #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Landslides and related hazards #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1401.3177
openalex publication_date 2014/01/14 · openalex created_date 2019/06/07 · openalex updated_date 2026/07/28
The scattering of waves by obstacles in a 2D setting is considered, in particular the computation of the scattered field via the collocation or the least-squares methods. In the case of multiple scattering by smooth obstacles, we prove that the scattered field can be uniformly approximated by sums of multipoles. For a unique obstacle, the choice of the number of points and their positions for the estimation of the error on the border of the scatterer is studied, showing the benefit of using a non-uniform distribution of points dependent on the scatterer and the approximation scheme. In general, using a denser discretization near the singularities of the scattered field does not improve the stability of the method. The analysis can also be used to estimate the discretization size needed to ensure stability given a density of points and an approximation scheme, e.g. in the case of multiple scatterers.