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NONLINEAR PRECONDITIONING: HOW TO USE A NONLINEAR SCHWARZ METHOD TO PRECONDITION NEWTON'S METHOD

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Fig. 2.1: Illustration of the residual when RAS is used as a nonlinear solver (left), or as a preconditioner for Newton’s method (right).
Fig. 3.1: Error as function of non-linear iteration numbers in the top row, and as number of subdomain solves in the bottom row, for ASPIN (left), and RASPEN (right).
Fig. 4.1: Permeability field (left), source term (middle), initial guess and solution (right).
Fig. 4.3: Error obtained with two-level ASPIN (left) and two-level FAS RASPEN (right) obtained with 20 subdomains, h = 0.003, and decreasing overlap 15h, 9h, 3h, h
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