Integral Equation for the Finite Depth Green Function at Surface
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We want to solve
where [math]\displaystyle{ G(x,\xi) }[/math] is the Free-Surface Green Function for two-dimensional waves, with singularity at the water surface. We break the surface into [math]\displaystyle{ N }[/math] evenly spaced point [math]\displaystyle{ x_n = -L = hn }[/math] where [math]\displaystyle{ h=2L/N }[/math] and [math]\displaystyle{ n=0,1,\dots,N }[/math]
Matlab Code
A program to calculate the coefficients for the semi-infinite dock problems can be found here matrix_G_surface.m
Additional code
This program requires