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docs: fix dipole source math definitions

Open ahbarnett opened this issue 1 year ago • 0 comments

The notation \nabla ( H_0 (k | x - x_j |) ) for a dipole source for Helmholtz is unclear, and implies \nabla_x which would be incorrect (the target-grad when we mean source-grad). Suggest changing to defining G(x,y) = (i/4) H_0^{(1)} ( k |x-y|), where x,y in R^2, then being clear about \mathbf{d} \cdot \nabla_y G(x,y) as a source dipole, etc.

Also using G would unify the docs for Laplace and Helmholtz.

ahbarnett avatar Oct 24 '23 19:10 ahbarnett