A two-year Postdoc position is available at Cerfacs, Toulouse. The project aims to develop concepts and a toolchain based on artificial intelligence to automatically generate a performant preconditioner for a Krylov subspace iterative solver for the solution of linear systems arising from a discretized Stokes problem. We will focus in particular on a geometric multigrid preconditioner for the (1,1)-block, here, the Laplace operator, to ensure the scalability of the solver when passing to large-scale problems. The solver will be broken down into components, which are then recombined in an optimal manner for predefined criteria, using evolutionary algorithm design techniques. The particular difficulty to develop such a toolchain for saddle point systems is the large number of possible combinations of solution techniques, e.g., preconditioned Krylov subspace solvers, Schur complement approaches, deflation and augmentation techniques, or also monolithic multigrid solvers on the whole block system. As final step, we envisage to obtain executable code applying the best guess solver through automatic code generation.
Required profile: PhD with experience in one or several of the following domains: applied mathematics, computer science, iterative solvers, numerical linear algebra, artificial intelligence, high performance computing.
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