## UC Berkeley / Lawrence Berkeley Laboratory

#### Recent Progress in Integral Equation Methods

**James Bremer, **

##### December 7th, 2011 at 4PM–5PM in 939 Evans Hall [Map]

Despite offering significant advantages over more direct approaches, integral
equation methods are not widely used for the numerical solution of elliptic
boundary value problems. This is primarily due to several unresolved issues
which hamper the competitiveness of integral equation methods in certain
situations. In this talk, I will describe several of these unresolved issues
and discuss one in detail.

In particular, I will focus on recent work regarding the numerical solution of
integral equations given on domains with singularities. Solutions of integral
equations arising from elliptic boundary value problems given on irregular
domains often exhibit singularities which are more severe than those exhibited
by the solution of the original equation. This is sometimes cited as a serious
drawback of integral equation methods. In fact, as I will show, it turns out to
be essentially harmless.

If time permits, I will also discuss the efficient evaluation of a class of
singular integrals which arises from the discretization of integral equations
on surfaces.