High frequency boundary integral equations in a linearly stratified medium

Alex Barnett

Mathematics, Dartmouth College, and Simons Center for Data Analysis

We present a high-order Nyström method for scattering from a smooth obstacle embedded in an unbounded continuously-graded medium, in which the square of the wavenumber varies linearly in the vertical coordinate. This models quantum particles in a uniform gravitational field, with broader applications in acoustics, optics and seismology. We approximate the Green's function exponentially accurately with wavenumber-independent effort via numerical steepest descent (quadrature) applied to a contour integral. 50λ diameter, 11 digits, in 1 minute.

Joint work with Brad Nelson '13 and Matt Mahoney PhD '09

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