Hierarchical Methods for Shape Optimization in Aerodynamics: Multilevel parametric shape algorithms and additive preconditioners

This lecture is devoted to the presentation of two particular "hierarchical" approaches to numerical shape optimization in aerodynamics design: 1) multilevel parametric shape optimization algorithms; 2) additive preconditioners. The first approach is inspired from the classical geometrical multigrid method, except that here the geometrical...

Preconditioners for Linearized Discrete Compressible Euler Equations

We consider a Newton-Krylov approach for discretized compressible Euler equations. A good preconditioner in the Krylov subspace method is essential for obtaining an efficient solver in such an approach. In this paper we compare point-block-Gauss-Seidel, point-block-ILU and point-block-SPAI preconditioners. It turns out that the SPAI method is...