Difference between revisions of "Integral Equation for the Finite Depth Green Function at Surface"

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</math></center>
 
</math></center>
 
where  
 
where  
−
G(x,\xi) is the [[Free-Surface Green Function]] for two-dimensional waves, with singularity at
+
<math>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>N</math> evenly spaced point
 
the water surface. We break the surface into <math>N</math> evenly spaced point
 
<math>x_n = -L = hn</math> where <math>h=2L/N</math> and <math>n=0,1,\dots,N</math>
 
<math>x_n = -L = hn</math> where <math>h=2L/N</math> and <math>n=0,1,\dots,N</math>

Revision as of 23:08, 9 November 2008

We want to solve

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

where [math]\displaystyle{ G(x,\xi)\lt \math\gt is the [[Free-Surface Green Function]] for two-dimensional waves, with singularity at the water surface. We break the surface into \lt math\gt 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

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