Title: Solving integral equations on boundaries with singular points

Recursively compressed inverse preconditioning (RCIP) is a kernel-independent and purely numerical method for solving Fredholm second kind boundary integral equations in situations where the boundary shape induces a non-smooth behavior in the solution. The method can be viewed as an accelerator and stabilizer for Nyström schemes when intense local mesh refinement is needed. A key feature is that refinement and compression are done in tandem. No precomputed quantities or large intermediate matrices are required. The method automatically achieves, rapidly and for practical purposes, the equivalent of infinite mesh refinement.

In the talk, I will first review basic features of the RCIP method (what the method can and cannot do) and then present a medley of my greatest hits regarding applications to Laplace's, Helmholtz, biharmonic, and the Maxwell equations.

For more information, see: this