Integral Equation for the Finite Depth Green Function at Surface

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We want to solve

\phi(x) = \int_{-L}^{L}G(x,\xi) \left( \alpha\phi(\xi) - w(\xi) \right)d \xi

where G(x,ξ) is the Free-Surface Green Function for two-dimensional waves, with singularity at the water surface. We break the surface into N evenly spaced point xn = − L = hn where h = 2L / N and n=0,1,\dots,N


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

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