POP Quadrature: Painless high-order-accurate layer potentials

Andreas Kloeckner

Courant Institute, NYU


Boundary integral equations yield very efficient solvers for a special (but large and important) class of partial differential equations. They hinge crucially on the accurate computation of the singular integrals involved. I will present a new scheme that computes these integrals, discretized by Nyström methods, for even hypersingular kernels very simply and accurately to high order. Moreover, the scheme is dimension-independent and lends itself to acceleration via FMMs or related techniques.

(joint work with Leslie Greengard and Alexander Barnett)

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