An optimization-based domain decomposition method for nonlinear wall laws in coupled systems. (English) Zbl 1185.65223
Summary: We study an optimization-based domain decomposition method for a nonlinear wall law in a coupled system. The problem is restated as a saddle-point problem by introducing as a new variable the displacement jump across the interface. Then the minimization step of the saddle-point problem corresponds to the equilibrium equations stated in each subdomain with Lagrange multiplier as interface force. The maximization step corresponds to maximizing a (nonlinear) strictly concave functional. This could have a lot of applications in geophysical flows such as coupling ocean and atmosphere, free surface and groundwater flows.
MSC:
| 65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |
| 49K10 | Optimality conditions for free problems in two or more independent variables |
| 49M30 | Other numerical methods in calculus of variations (MSC2010) |
| 74B05 | Classical linear elasticity |
| 74G15 | Numerical approximation of solutions of equilibrium problems in solid mechanics |
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