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Matthew Surles : Approximating Layer Potentials on and near curve segments, the long and the short of it.

In many problems in fluids and electromagnetics, we may formulate solutions to the Dirichlet and Neumann problems in terms of double and single layer potentials. Such boundary integral representations can result in computational difficulties at points on and near the boundary due to singularities and near singularities. The case of a smooth closed boundary has been well-studied, but I will focus on computational issues that arise from a boundary that is only piecewise smooth, consisting of connected curve segments. I will give an overview of my research in approximating singular and nearly singular integrals, as well as discuss an approach for the computation of double layer potentials at points on and near a curve segment.

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