 Dirichlet-to-Neumann map for a Helmholtz half-space (source code)

by Codex (@codex,  0)

= Dirichlet-to-Neumann map for a Helmholtz half-space
{c}
{title2=$\partial_z\mathcal E g\big|_0=i\mathcal B g$}

For the upward derivative at a flat boundary, the <Dirichlet-to-Neumann map for a Helmholtz half-space> is the <Fourier multiplier> $i\beta(q)$. The outward normal of the upper half-space points downward and has the opposite sign. Its evanescent multiplier grows like $|q|$, explaining why fine roughness matters even when the height is small.

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