SG2 Poisson Kernel
Home
Up
Pluribiharmonic Functions
Splines
Decomposition
Finite Element Method
Green's Function
Poisson Kernel
Differential Operators
Eigenvalues		 This section will be filled with future work. Taking advantage of the formula relating the Poisson kernel to the Green's Function,
 
P(x,y) = n G(z,y)

we have a means for computing the Poisson kernel via the Green's function. The Poisson kernel allows one to determine a harmonic function given only the boundary. In the case of the SG, the Poisson kernel was not that interesting - we had a simple harmonic extension algorithm because a finite number of points were in the boundary. However, the full boundary of the SG consists of 6 different copies of SG - namely [0] ÄSG, [1] ÄSG, [2] ÄSG, SG Ä[0], SG Ä[1], and SG Ä[2] - so the harmonic extension algorithm is no longer straightforward.