Discretization methods such as finite differences or finite elements were usually employed to provide high fidelity solution approximations for reduced order modeling of parameterized partial differential equations. In this paper, a novel discretization technique-Isogeometric Analysis (IGA) is used in combination with proper orthogonal decomposition (POD) for model order reduction of the time parameterized acoustic wave equations. We propose a new fully discrete IGA-Newmark-POD approximation and we analyze the associated numerical error, which features three components due to spatial discretization by IGA, time discretization with the Newmark scheme, and modes truncation by POD. We prove stability and convergence. Numerical examples are presented to show the effectiveness and accuracy of IGA-based POD techniques for the model order reduction of the acoustic wave equation.
Mots-clés : Isogeometric analysis, proper orthogonal decomposition, reduced order modeling, acoustic wave equation
@article{M2AN_2017__51_4_1197_0, author = {Zhu, Shengfeng and Ded\`e, Luca and Quarteroni, Alfio}, title = {Isogeometric analysis and proper orthogonal decomposition for the acoustic wave equation}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {1197--1221}, publisher = {EDP-Sciences}, volume = {51}, number = {4}, year = {2017}, doi = {10.1051/m2an/2016056}, mrnumber = {3702410}, zbl = {1381.65086}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/m2an/2016056/} }
TY - JOUR AU - Zhu, Shengfeng AU - Dedè, Luca AU - Quarteroni, Alfio TI - Isogeometric analysis and proper orthogonal decomposition for the acoustic wave equation JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 1197 EP - 1221 VL - 51 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2016056/ DO - 10.1051/m2an/2016056 LA - en ID - M2AN_2017__51_4_1197_0 ER -
%0 Journal Article %A Zhu, Shengfeng %A Dedè, Luca %A Quarteroni, Alfio %T Isogeometric analysis and proper orthogonal decomposition for the acoustic wave equation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 1197-1221 %V 51 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2016056/ %R 10.1051/m2an/2016056 %G en %F M2AN_2017__51_4_1197_0
Zhu, Shengfeng; Dedè, Luca; Quarteroni, Alfio. Isogeometric analysis and proper orthogonal decomposition for the acoustic wave equation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 4, pp. 1197-1221. doi : 10.1051/m2an/2016056. http://archive.numdam.org/articles/10.1051/m2an/2016056/
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