## Optimization strategy for parameter sampling in the reduced basis method

2015
Preprint
##### Abstract
The reduced basis (RB) method is an efficient technique to solve parametric partial differential equations in a multi-query context, where the solution has to be computed for many different parameter values. The RB method drastically reduces the computational time for any additional solution (during the so-called online stage) once an initial set of basis functions has been computed (during the so-called offline stage) still retaining a certified level of accuracy. The greedy algorithm is the classical sampling strategy to select parameter values that define the set of basis functions. Here, an alternative and competitive approach for choosing the parameter values is presented. The new approach is based on an optimization problem for the parameters that allows to reduce the computational complexity of the offline stage of the RB method and improve its effectiveness.
510 Mathematics
##### Cite This
ISO 690IAPICHINO, Laura, Stefan VOLKWEIN, 2015. Optimization strategy for parameter sampling in the reduced basis method
BibTex
@unpublished{Iapichino2015Optim-30107,
year={2015},
title={Optimization strategy for parameter sampling in the reduced basis method},
author={Iapichino, Laura and Volkwein, Stefan},
note={Konferenzbeitrag zu: MATHMOD 2015, 8th Vienna Conference on Mathematical Modeling, February 18-20, 2015}
}

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<dcterms:abstract xml:lang="eng">The reduced basis (RB) method is an efficient technique to solve parametric partial differential equations in a multi-query context, where the solution has to be computed for many different parameter values. The RB method drastically reduces the computational time for any additional solution (during the so-called online stage) once an initial set of basis functions has been computed (during the so-called offline stage) still retaining a certified level of accuracy. The greedy algorithm is the classical sampling strategy to select parameter values that define the set of basis functions. Here, an alternative and competitive approach for choosing the parameter values is presented. The new approach is based on an optimization problem for the parameters that allows to reduce the computational complexity of the offline stage of the RB method and improve its effectiveness.</dcterms:abstract>
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##### Comment on publication
Konferenzbeitrag zu: MATHMOD 2015, 8th Vienna Conference on Mathematical Modeling, February 18-20, 2015
Yes