An Efficient Reduced Basis Construction for Stochastic Galerkin Matrix Equations Using Deflated Conjugate Gradients

0537200 - ÚGN 2021 RIV CH eng C - Conference Paper (international conference)
Béreš, Michal
An Efficient Reduced Basis Construction for Stochastic Galerkin Matrix Equations Using Deflated Conjugate Gradients.
Lecture Notes in Electrical Engineering. Vol. 554. Cham: Springer Nature Switzerland AG, 2020 - (Zelinka, I.; Brandstetter, P.; Trong Dao, T.; Hoang Duy, V.; Kim, S.), s. 175-184. ISBN 978-3-030-14906-2. ISSN 1876-1100. E-ISSN 1876-1119.
[International Conference on Advanced Engineering Theory and Applications 2018 /5./. Ostrava (CZ), 11.11.2018-13.11.2018]
R&D Projects: GA MŠMT LQ1602
Institutional support: RVO:68145535
Keywords : stochastic Galerkin method * reduced basis method * deflated conjugate gradients method * darcy flow problem
OECD category: Applied mathematics
https://link.springer.com/chapter/10.1007/978-3-030-14907-9_18

In this article, we examine an efficient solution of the stochastic Galerkin (SG) matrix equations coming from the Darcy flow problem with uncertain material parameters on given interfaces. The solution of the SG system of equations, here represented as matrix equations, is usually a very challenging task. A relatively new approach to the solution of the SG matrix equations is the reduced basis (RB) solver, which looks for the low-rank representation of the solution. The construction of the RB is usually done iteratively and consists of multiple solutions of systems of equations. We aim to speed up the process using the deflated conjugate gradients (DCG). Other contributions of this work are a modified specific construction of the RB without the need of Cholesky factor and an adaptive choice of the candidate vectors for the expansion of the RB. The proposed approach allows an efficient parallel implementation
Permanent Link: http://hdl.handle.net/11104/0314977