2014 American Control Conference 2014
DOI: 10.1109/acc.2014.6859104
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Nonlinear model reduction using Space Vectors Clustering POD with application to the Burgers' equation

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Cited by 4 publications
(3 citation statements)
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“…As a result, model order reduction techniques have been applied to dramatically reduce the dimension and the complexity of the resulting system of ODEs, see e.g., [9,53,26,44,25,27,30]. In particular, the common approach is to form a lexicographic ordering of the spatial nodes, unrolling the arrays (i.e., matrices or tensors when d = 2 and d = 3 respectively) of nodal values into long vectors in R N , i.e., the unknown vectors u i (t) ∈ R N .…”
mentioning
confidence: 99%
“…As a result, model order reduction techniques have been applied to dramatically reduce the dimension and the complexity of the resulting system of ODEs, see e.g., [9,53,26,44,25,27,30]. In particular, the common approach is to form a lexicographic ordering of the spatial nodes, unrolling the arrays (i.e., matrices or tensors when d = 2 and d = 3 respectively) of nodal values into long vectors in R N , i.e., the unknown vectors u i (t) ∈ R N .…”
mentioning
confidence: 99%
“…When the one-dimensional Burgers equation is considered, the corresponding POD/DEIM ROM has been developed, and the control problem involved was also discussed. It has been shown in [40][41][42][43] that good results are achieved. Yet to the best of our knowledge, there are very few results reporting the POD/DEIM-reduced order modeling issues for 2D Burgers equation, particularly in the case where the Reynolds number becomes large, and it is an open question if the use of a proper number of DEIM points is really beneficial for POD/DEIM CPU cost.…”
Section: In Stefanescu Et Almentioning
confidence: 99%
“…As a result, model order reduction techniques have been applied to dramatically reduce the dimension and the complexity of the resulting system of ODEs, see e.g., [8,44,21,37,20,22,25]. In particular, the common approach is to form a lexicographic ordering of the spatial nodes, unrolling the arrays (i.e., matrices or tensors when d = 2 and d = 3 respectively) of nodal values into long vectors in R N , i.e., the unknown vectors u i (t) ∈ R N .…”
mentioning
confidence: 99%