École Nationale Supérieure de
Techniques Avancées

Abstract

Today we know several methods to solve the wave equation depending on the parameters of the problem we are interested in. In the case of an unbounded domain, we can restrict our study to the boundary of the domain thanks to the integral formulation of the problem. However, not always knowing an explicit form of the solution, we sometimes discretize our equation thanks to the method of Convolution Qua- drature. But the problem persists when the boundary of the domain remains unbounded, making discretisation impossible. Perfectly Matched Layers (PML) are a way to truncate a domain artificially without any conse- quence on the wave propagation and we have tried to see if they can be used in our case. The objective of this internship was to discover and understand these different methods and then to consider to what extent it is possible to truncate the domain using PMLs after integral formulation.