dc.contributor.author Giraldi, Loic dc.contributor.author Nouy, Anthony dc.date.accessioned 2017-12-28T07:32:16Z dc.date.available 2017-12-28T07:32:16Z dc.date.issued 2017-06-30 dc.identifier.uri http://hdl.handle.net/10754/626565 dc.description.abstract This paper presents a weakly intrusive strategy for computing a low-rank approximation of the solution of a system of nonlinear parameter-dependent equations. The proposed strategy relies on a Newton-like iterative solver which only requires evaluations of the residual of the parameter-dependent equation and of a preconditioner (such as the differential of the residual) for instances of the parameters independently. The algorithm provides an approximation of the set of solutions associated with a possibly large number of instances of the parameters, with a computational complexity which can be orders of magnitude lower than when using the same Newton-like solver for all instances of the parameters. The reduction of complexity requires efficient strategies for obtaining low-rank approximations of the residual, of the preconditioner, and of the increment at each iteration of the algorithm. For the approximation of the residual and the preconditioner, weakly intrusive variants of the empirical interpolation method are introduced, which require evaluations of entries of the residual and the preconditioner. Then, an approximation of the increment is obtained by using a greedy algorithm for low-rank approximation, and a low-rank approximation of the iterate is finally obtained by using a truncated singular value decomposition. When the preconditioner is the differential of the residual, the proposed algorithm is interpreted as an inexact Newton solver for which a detailed convergence analysis is provided. Numerical examples illustrate the efficiency of the method. dc.publisher arXiv dc.relation.url http://arxiv.org/abs/1706.10221v1 dc.relation.url http://arxiv.org/pdf/1706.10221v1 dc.rights Archived with thanks to arXiv dc.title Weakly intrusive low-rank approximation method for nonlinear parameter-dependent equations dc.type Preprint dc.contributor.department Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division dc.eprint.version Pre-print dc.contributor.institution Department of Computer Science and Mathematics, Ecole Centrale de Nantes, Nantes, France. dc.identifier.arxivid arXiv:1706.10221 kaust.person Giraldi, Loic refterms.dateFOA 2018-06-14T09:21:14Z
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