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Table 1 Continuity constraints in the second analyzed topology, where \({\mathcal {N}}_1\) and \({\mathcal {N}}_2\) are the same in all the subdomains

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

Continuity constraint Equations
1 \(\varvec{U}_{1n}^1 = \varvec{U}_{2n}^2\) , \(\varvec{U}_{2n}^1 |_1 = \varvec{U}_{1n}^2 |_1\)
2 \(\varvec{U}_{2n}^2 = \mathrm {Flip} (\varvec{U}_{1n}^3)\) , \(\varvec{U}_{1n}^2 |_{{\mathcal {N}}_1} = \varvec{U}_{2n}^3 |_1\)
3 \(\varvec{U}_{1n}^3 = \varvec{U}_{2n}^4\) , \(\varvec{U}_{2n}^3 |_{{\mathcal {N}}_2} = \varvec{U}_{1n}^4 |_{{\mathcal {N}}_1}\)
4 \(\varvec{U}_{2n}^4 = \mathrm {Flip} (\varvec{U}_{1n}^1)\) , \(\varvec{U}_{1n}^4 |_1 = \varvec{U}_{2n}^1 |_{{\mathcal {N}}_2}\)