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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

From: Domain decomposition involving subdomain separable space representations for solving parametric problems in complex geometries

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 \(\varvec{U}_{2n}^8 = \varvec{U}_{2n}^5\) , \(\varvec{U}_{1n}^8 |_{\mathcal {N}} =\varvec{U}_{1n}^5 |_1\)