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Transcript

In Figure 1.7 we present the stencil structure for Rouy-Tourin algorithm and the
algorithm is presented in Algorithm 1.
Ti,j+1
Ti-1,j
R
Ti+1,j
Ti,j-1
FIGURE 1.7. Grid points for Rouy-Tourin algorithm
Algorithm 1 The Rouy-Tourin algorithm
Consider S > diam(Ω).
Initialization:
Ti,j = 0 on ∂Ω
Ti,j = S, otherwise
Iteration:
repeat
for i = 0 to n do
for j = 0 to n do
compute R solution of local Eikonal equation at Xi,j
end
end
T˜i,j = min(Ti,j , R)
T = T̃
until kT − T̃ k ≤ ε ;
For any node (i, j) in the domain we should solve the equation:
2
−x
+x
[ max max(Di,j
T, 0), − min(Di,j
T, 0)
+
2
−y
+y
max max(Di,j
T, 0), − min(Di,j
T, 0) ]1/2 =
1
,
Fi,j
(1.24)
in order to compute its Ti,j .
Let us consider the case presented in the previous section, in Figure 1.5(a), where
the third quadrant is the upwind side of our domain and show how the Rouy-Tourin
algorithm satisfies the upwind-ing. All the other possible situations can be reduced
24

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