Reduced Basis Methods for Parameterized Partial Differential Equations with Stochastic Influences Using the Karhunen--Loève Expansion

2013 ◽  
Vol 1 (1) ◽  
pp. 79-105 ◽  
Author(s):  
Bernard Haasdonk ◽  
Karsten Urban ◽  
Bernhard Wieland
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Reduced Basis ◽  
Partial Differential ◽  
Reduced Basis Methods

scholarly journals RBniCS - reduced order modelling in FEniCS

2015 ◽  
Author(s):  
Francesco Ballarin ◽  
Alberto Sartori ◽  
Gianluigi Rozza
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
High Performance ◽  
Theoretical Physics ◽  
Reduced Order Models ◽  
Reduced Basis ◽  
Partial Differential ◽  
Reduced Order ◽  
Reduced Order Modelling ◽  
Reduced Basis Methods

RBniCS (freely available under the GNU LGPL, version 3, at http://mathlab.sissa.it/rbnics) is a python-based library, developed on top of FEniCS (http://fenicsproject.org), aimed at the developement of reduced order models in the FEniCS environment. In particular, reduced order techniques such as the certified reduced basis method and proper orthogonal decomposition-Galerkin methods are implemented. The FEniCS project allows RBniCS to take advantage of the high-level (e.g., human readable) code used for the automated solution of partial differential equations. Thanks to the features of FEniCS the final user needs to prepare a short code (around 100 lines) to carry out a reduced order simulation. It is ideally suited for novice users willing to learn reduced basis methods and reduced order modelling, thanks to an object-oriented approach and an intuitive and versatile python interface. Indeed, it is a companion of the introductory reduced basis handbook [Hesthaven, Rozza, Stamm. Certified Reduced Basis Methods for Parametrized Partial Differential Equations. SpringerBriefs in Mathematics, Springer International Publishing, 2015], and has been already used in doctoral classes within the "Mathematical Analysis, Modelling, and Applications" PhD course at SISSA, as well as for courses within the "Master in High Performance Computing" held by SISSA and International Centre for Theoretical Physics (ICTP). RBniCS can also be used as a basis for more advanced projects that would like to assess the capability of reduced order models in their existing FEniCS-based software, thanks to the availability of several reduced order methods and algorithms in the library.

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