Solving integral equations on non-smooth domains
iterative solver. I show how to alleviate them in certain situations.
Then I turn to the main topic of the talk – a method to enhance the
efficiency of integral equation based schemes for elliptic PDEs on
domains with corners, multi-wedge points, and mixed boundary
conditions. The key ingredients are a block-diagonal inverse
preconditioner 'R' and a fast recursion, 'i=1,...,n', where step 'i'
inverts and compresses contributions to 'R' from the outermost
quadrature panels on level 'i' of a locally 'n'-ply refined mesh. From
an efficiency point of view, this method converts a non-smooth
boundary into a smooth boundary and mixed boundary conditions into
pure boundary conditions. The spectral properties of the system
matrices in the linear systems that eventually have to be solved are
essentially the same. The corner difficulties are gone.
The talk is available as a pdf-file: