Numerical methods for the close evaluation of layer potentials in 3D (Camille Carvalho, MCF INSA Lyon, ICJ)

It is well-known that, when using boundary integral equation methods, quadrature rules approximating layer potentials (representing the solution of a linear, partial differential equation) may suffer from poor resolution when integral representations are evaluated closed to (but not on) the boundary: this is the close evaluation problem. In this talk we present some techniques to address this challenge in three dimensions. In particular we perform an asymptotic analysis at the evaluation points, providing valuable insights in designing adapted numerical methods. Several numerical examples illustrating the efficiency of the technique will be provided. Additionally, we present ad hoc layer potential modifications to gain more accuracy.