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Galerkin lumped parameter methods for transient problems
Author(s) -
Bermúdez A.,
Pena F.
Publication year - 2011
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.3140
Subject(s) - galerkin method , finite element method , mathematics , basis (linear algebra) , transient (computer programming) , partial differential equation , basis function , parameter space , domain (mathematical analysis) , space (punctuation) , discontinuous galerkin method , mathematical analysis , computer science , geometry , physics , thermodynamics , operating system
In this paper we propose a general methodology to obtain lumped parameter models for systems governed by parabolic partial differential equations which we call Galerkin lumped parameter methods. The idea consists of decomposing the computational domain into several subdomains connected through so‐called ports. Then a time‐independent adapted reduced basis is introduced by numerically solving several elliptic problems in each subdomain. The proposed lumped parameter model is the Galerkin approximation of the original problem in the space spanned by this basis. The relationship of these methods with classical lumped parameter models is analyzed. Numerical results are shown as well as a comparison of the solution obtained with the lumped model and the ‘exact’ one computed by standard finite element procedures. Copyright © 2011 John Wiley & Sons, Ltd.