Multi Space Reduced Basis Preconditioners for Large-Scale Parametrized PDEs

Authors:
  • NSNiccolò Dal Santo
    Niccolò Dal Santo
  • SDSimone Deparis
    Simone Deparis
  • AMAndrea Manzoni
    Andrea Manzoni
  • AQAlfio Quarteroni
    Alfio Quarteroni
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Abstract
In this work we introduce a new two-level preconditioner for the efficient solution of large-scale linear systems arising from the discretization of parametrized PDEs. The proposed preconditioner combines in a multiplicative way a reduced basis solver, which plays the role of coarse component, and a “traditional” fine-grid preconditioner, such as one-level additive Schwarz, block Gauss--Seidel, or block Jacobi preconditioners. The coarse component is built upon a new multi space reduced basis (MSRB) method that we introduce for the first time in this paper, where a reduced basis space is built through the proper orthogonal decomposition algorithm at each step of the iterative method at hand, like the flexible GMRES method. MSRB strategy consists in building reduced basis spaces that are well suited to perform a single iteration, by addressing the error components which have not been treated yet. The Krylov iterations employed to solve the resulting preconditioned system target small tolerances with a very...
Funding Information
  • Swiss State Secretariat for Education, Research and Innovation (C14 0068)
  • Swiss National Supercomputing Centre (s635)

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