Design of optimal Runge-Kutta methods - FEniCS Project
Design of optimal Runge-Kutta methods - FEniCS Project
Design of optimal Runge-Kutta methods - FEniCS Project
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Optimizing for the SD spectrum<br />
On regular grids, SD leads to a block-Toeplitz operator<br />
We perform a von Neumann-like analysis using a ”generating pattern”<br />
dWi,j<br />
dt<br />
i − 1,j<br />
i − 1,j+1<br />
�g2<br />
i − 1,j− 1 i, j − 1<br />
i, j<br />
�g1<br />
i, j +1 i +1,j+1<br />
i +1,j− 1<br />
a � 0,0<br />
+ T Wi,j + T<br />
∆g<br />
−1,0 Wi−1,j + T 0,−1 Wi,j−1<br />
+T +1,0 Wi+1,j + T 0,+1 �<br />
Wi,j+1 = 0<br />
D. Ketcheson (KAUST) 31 / 36<br />
i +1,j
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