How integral equations help you solve PDEs

Alex Barnett

Mathematics, Dartmouth College.

I will introduce potential theory, which lets you reformulate PDEs with piecewise-constant coefficients as an integral equation problem on the material interfaces (boundary) alone. This allows much more efficient solution that, say, finite element methods, especially in the case of wave scattering. However, it also has certain challanges that I will discuss, such as quadrature schemes.

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