Two Level Correction Algorithms for Model Problems

Jichao Zhao (1) , Jean-Antoine Desideri (1) , Badr Abou El Majd (1)

1 OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE

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.

Mots clés: Shape optimization; Bézier parameterization; multilevel algorithms; discrete Fourier analysis

Domaines: Analyse numérique [math.NA]; Optimisation et contrôle [math.OC]

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