# Table 2 Continuity constraints to be enforced in the second use case, with $${\mathcal {N}}_1 = {\mathcal {N}}_2 \equiv {\mathcal {N}}$$ for all the subdomains

Continuity constraint

Equations

1

$$\varvec{U}_{2n}^1 = \varvec{U}_{2n}^2$$ ,

$$\varvec{U}_{1n}^1 |_{\mathcal {N}} = \varvec{U}_{1n}^2 |_1$$

2

$$\varvec{U}_{2n}^2 = \varvec{U}_{2n}^3$$ ,

$$\varvec{U}_{1n}^2 |_{\mathcal {N}}= \varvec{U}_{1n}^3 |_1$$

3

$$\varvec{U}_{2n}^3 = \varvec{U}_{2n}^4$$ ,

$$\varvec{U}_{1n}^3 |_{\mathcal {N}} = \varvec{U}_{1n}^4 |_1$$

4

$$\varvec{U}_{2n}^4 = \varvec{U}_{2n}^1$$ ,

$$\varvec{U}_{1n}^4 |_{\mathcal {N}} = \varvec{U}_{1n}^1 |_1$$

5

$$\varvec{U}_{1n}^2 = \mathrm {Flip} ( \varvec{U}_{1n}^8)$$ ,

$$\varvec{U}_{2n}^2 |_1 = \varvec{U}_{2n}^8 |_1$$

6

$$\varvec{U}_{2n}^5 = \varvec{U}_{2n}^6$$ ,

$$\varvec{U}_{1n}^5 |_{\mathcal {N}} =\varvec{U}_{1n}^6 |_1$$

7

$$\varvec{U}_{2n}^6 = \varvec{U}_{2n}^7$$ ,

$$\varvec{U}_{1n}^6 |_{\mathcal {N}} =\varvec{U}_{1n}^7 |_1$$

8

$$\varvec{U}_{2n}^7 = \varvec{U}_{2n}^8$$ ,

$$\varvec{U}_{1n}^7 |_{\mathcal {N}} =\varvec{U}_{1n}^8 |_1$$

9

$$\varvec{U}_{2n}^8 = \varvec{U}_{2n}^5$$ ,

$$\varvec{U}_{1n}^8 |_{\mathcal {N}} =\varvec{U}_{1n}^5 |_1$$