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Two Level Correction Algorithms for Model Problems

Jichao Zhao 1 Jean-Antoine Desideri 1 Badr El Majd 1
1 OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
Abstract : In this report, we experiment a variant of the two-level ideal algorithm for parametric shape optimization that was proposed in [5]. In the linear case, the method, referred to as the Z' method, employs a permutation operator to rearrange the eigenstructure in such a way that the new high-frequency modes are associated with large eigenvalues. As a result, the classical steepest-descent iteration can be viewed as a Jacobi-type smoother, and standard multilevel stragegies be applied. An alternate method is also tested based on odd-even decoupling (L' method). For a linear model problem, both new methods are found efficient and superior to the original formulation, but the Z' method is more robust. Similar numerical results are obtained for a nonlinear model problem by considering the eigensystem of the Jacobian matrix.
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https://hal.inria.fr/inria-00161891
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Submitted on : Monday, July 16, 2007 - 10:02:37 AM
Last modification on : Monday, October 12, 2020 - 2:28:02 PM
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  • HAL Id : inria-00161891, version 2

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Jichao Zhao, Jean-Antoine Desideri, Badr El Majd. Two Level Correction Algorithms for Model Problems. [Research Report] RR-6246, INRIA. 2007, pp.28. ⟨inria-00161891v2⟩

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