MATHICSE Technical Report: Reduced basis methods: from low-rank matrices to low-rank tensor

We propose a novel combination of the reduced basis method with low-rank tensor techniques for the efficient solution of parameter-dependent linear systems in the case of several parameters. This combination, called rb Tensor, consists of three ingredients. First, the underlying parameter-dependent operator is approximated by an explicit affine representation in a low-rank tensor format. Second, a standard greedy strategy is used to construct a problem-dependent reduced basis. Third, the associated reduced parametric system is solved fo all parameter values on a tensor grid simultaneously via a low-rank approach. This allows us to explicitly represent and store an approximate solution for all parameter values at a time. Once this approximation is available, the computation of output functionals and the evaluation of statistics of the solution becomes a cheap online task, without requiring the solution of a linear system.


Year:
2015-10
Publisher:
Écublens, MATHICSE
Note:
MATHICSE Technical Report Nr. 27.2015 October 2015
Laboratories:




 Record created 2019-12-09, last modified 2020-01-06

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