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Mesh adaptation by Optimal Control of a continuous model

Abstract : The problem of finding the best mesh in a numerical simulation is addressed with the introduction of a scalar output and of an adjoint state in combination with an a priori error model. This strategy is organised around a continuous modelling of mesh description and numerical error. The mesh description is done by the specification of a continuous metric. This is a scalar field defining the mesh fineness over the domain. A truncation error is modelled from an a priori estimate in function of the metric. The numerical error is then derived from the truncation error using a "state system" having the truncation error as right hand side. This allows to formulate the optimal mesh problem under the form of a continuous Optimal Control problem, with a control, the metric, a state equation, the error equation, and a functional, the error on scalar output. The minimisation with respect to the metric is applied under a control constraint expressing the fact that the equivalent mesh has a specified number of nodes. Examples dealing with elliptic model problems will be presented. The optimisation process is implemented with a gradient method and produce the optimal metric. Then an adapted mesh is generated. This process is reiterated a few times.
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https://hal.inria.fr/inria-00070422
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Submitted on : Friday, May 19, 2006 - 8:26:47 PM
Last modification on : Monday, July 23, 2018 - 2:20:01 PM
Long-term archiving on: : Sunday, April 4, 2010 - 9:10:50 PM

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  • HAL Id : inria-00070422, version 1

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François Courty, Tristan Roy, Bruno Koobus, Alain Dervieux. Mesh adaptation by Optimal Control of a continuous model. [Research Report] RR-5585, INRIA. 2006, pp.31. ⟨inria-00070422⟩

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