[Amath-seminars] Thursday Seminar, May 24th, Lewis 208

Loyce M. Adams lma3 at uw.edu
Wed May 23 16:29:33 PDT 2018

Hi All,

We have a seminar this Thursday in Lewis Hall 208 from 3:30-4:30pm.
Please note the seminar has moved 1/2 hour earlier than usual. The
speaker, title, and abstract are below.

Loyce Adams

May 24: 3:30-4:30 Fred Wan Conference Room, Lewis Hall 208

Speaker: Prof. Ludvig af Klinteberg
Dept. of Mathematics
Simon Fraser

Title: Quadrature for layer potentials with near singularities


Boundary integral methods provide an efficient way of solving elliptic
partial differential equations, by representing the solution as a
layer potential. However, efficient evaluation of the solution close
to the boundary of the domain presents a significant problem. The root
cause of this is the fact that common quadrature methods for smooth
integrands, such as Gauss-Legendre quadrature and the trapezoidal rule,
are ill-suited for integrands that have a singularity near the interval
of integration. The nature of this error is however well understood,
and I will show how it can be approximated numericalyy. I will also
review two relatively recent methods for evaluating layer potentials
near a boundary; one (QBX) uses the smoothness of the solution to form
a local expansion of the solution, the other computes modified quadrature
weights using a compex variable formulation. These methods can in turn
be improved, at least in some cases, by applying the techniques developed
for the numerical approximation of quadrature errors.

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