A boundary element method with a new Green's function kernel solves the mild-slope equation for waves over unidirectional variable bathymetry.
Belibassakis, The Green’s function of the mild-slope equation: The case of a monotonic bed profile, Wave Motion 32 (2000), 339–361
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Boundary element formulation of the Mild-Slope Equation for harmonic water waves propagating over unidirectional variable bathymetries
A boundary element method with a new Green's function kernel solves the mild-slope equation for waves over unidirectional variable bathymetry.