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How to avoid mass matrix for linear hyperbolic problems


Abgrall, Rémi; Bacigaluppi, Paola; Tokareva, Svetlana (2016). How to avoid mass matrix for linear hyperbolic problems. In: Karasözen, B; Manguoglu, M; Tezer-Sezgin, M; Göktepe, S; Ugur, Ö. Numerical Mathematics and Advanced Applications ENUMATH 2015. Cham: Springer, 75-86.

Abstract

We are interested in the numerical solution of linear hyperbolic problems using continuous finite elements of arbitrary order. It is well known that this kind of methods, once the weak formulation has been written, leads to a system of ordinary differential equations in RN, where N is the number of degrees of freedom. The solution of the resulting ODE system involves the inversion of a sparse mass matrix that is not block diagonal. Here we show how to avoid this step, and what are the consequences of the choice of the finite element space. Numerical examples show the correctness of our approach.

Abstract

We are interested in the numerical solution of linear hyperbolic problems using continuous finite elements of arbitrary order. It is well known that this kind of methods, once the weak formulation has been written, leads to a system of ordinary differential equations in RN, where N is the number of degrees of freedom. The solution of the resulting ODE system involves the inversion of a sparse mass matrix that is not block diagonal. Here we show how to avoid this step, and what are the consequences of the choice of the finite element space. Numerical examples show the correctness of our approach.

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Additional indexing

Item Type:Book Section, not_refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Modeling and Simulation
Physical Sciences > General Engineering
Physical Sciences > Discrete Mathematics and Combinatorics
Physical Sciences > Control and Optimization
Physical Sciences > Computational Mathematics
Language:English
Date:2016
Deposited On:01 Mar 2018 15:20
Last Modified:15 Apr 2021 14:44
Publisher:Springer
Number:112
ISBN:978-3-319-39927-0
OA Status:Green
Publisher DOI:https://doi.org/10.1007/978-3-319-39929-4_8

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