Détermination d’une opérateur de précondinionnement pour la résolution itérative du problème de Stoke dans la formulation d’Helmholtz. (A preconditioning operator for the iterative solution of the Stokes problem via the Helmholtz formulation). (French) Zbl 0637.65123
We use Fourier analysis to construct analytically, in the case of a simple geometry, the symbol of a pseudo-differential operator which plays a fundamental role in the solution of the Stokes problem via the Helmholtz formulation. We then use this information to construct a preconditioning operator which appears to be quite efficient, even for complicated geometries, in order to speed up conjugate gradient algorithms for solving the Stokes problem; these properties will be illustrated by results of numerical experiments.
MSC:
65Z05 | Applications to the sciences |
65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |
65F10 | Iterative numerical methods for linear systems |
76D07 | Stokes and related (Oseen, etc.) flows |
35Q99 | Partial differential equations of mathematical physics and other areas of application |
35A22 | Transform methods (e.g., integral transforms) applied to PDEs |
65F35 | Numerical computation of matrix norms, conditioning, scaling |