Parametric analytical preconditioning and its applications to the reduced collocation methods |
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| Affiliation: | 1. Department of Mathematics, University of Massachusetts Dartmouth, 285 Old Westport Road, North Dartmouth, MA 02747, USA;2. Sorbonne Universités, Université Paris-6 (UPMC), UMR 7598, Laboratoire Jacques-Louis-Lions & Institut universitaire de France, 75005 Paris, France;3. Division of Applied Mathematics, Brown University, 182 George St., Providence, RI 02912, USA |
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| Abstract: | In this paper, we extend the recently developed reduced collocation method [3] to the nonlinear case, and propose two analytical preconditioning strategies. One is parameter independent and easy to implement, the other one has the traditional affinity with respect to the parameters, which allows an efficient implementation through an offline–online decomposition. Overall, preconditioning improves the quality of the error estimation uniformly on the parameter domain, and speeds up the convergence of the reduced solution to the truth approximation. |
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