Dimensional model reduction in non‐linear finite element dynamics of solids and structures

By Petr Krysl, Sanjay Lall, Jerrold E. Marsden. 2001

296 citations recorded by the source corpus.

Subfields: Numerical Analysis, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2af268ef666969f162f220998cf5f966a6815088

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Citations in the corpus

Reduction Method for Finite Element Nonlinear Dynamic Analysis of Shells (2011, methodology): “[4], Meyer andMatthies [5], and Zilian et al.”
On thea priori model reduction: Overview and recent developments (2006, background): “The main drawback of the KL expansion and snapshot POD is that no adaptation of the empirical eigenvectors is possible when a new state evolution has to be considered in order to improve the basis functions or in order to increase the number of basis functions [ 9 ].”
Structure-preserving model reduction for mechanical systems (2003, methodology): “[15,16], and symmetry methods are better understood (see, for example,[36]), these methods will become more practical.”
Proper orthogonal decomposition and modal analysis for acceleration of transient FEM thermal analysis (2005, background): “Reference [2] gives an alternate interpretation of POD for structural problems.”
Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations (2007, background): “The Proper Orthogonal Decomposition (POD) or Karhunen-Loève (KL) [72, 80] approach to sampling [75, 77, 97, 142] is immensely popular in a variety of contexts — turbulent flows [85], fluid-structure interaction [46], non-linear structural mechanics [73], turbo-machinery flows [156] — most notably in”
High-performance model reduction techniques in computational multiscale homogenization (2014, background): “These functions are commonly termed empirical basis functions [41], the qualiﬁer empirical meaning “ derived from computational experiments ” .”
A framework for data-driven analysis of materials under uncertainty: Countering the curse of dimensionality (2017, methodology): “Successful applications of the NTFA [58–60], POD [54,55,61,62] and PGD [63] demonstrate the usefulness of these approaches.”
POD-DEIM model order reduction for strain softening viscoplasticity (2017, methodology): “In the field of solid mechanics, MOR techniques such as POD-G [12,13], Karhunen Loeve Expansion [14,15], and Proper Generalized Decomposition (PGD) [16,17] are employed to reduce the dimension of the system of equations.”
Dimensional reduction of nonlinear finite element dynamic models with finite rotations and energy‐based mesh sampling and weighting for computational efficiency (2014, background): “This is usually expected because, in this case, a projection-based ROM is supposed to filter out the dependence of the stability time-step on the high mesh frequencies of the associated HDM (for example, see [38]).”
Reduced-basis output bound methods for parabolic problems (2006, background): “Usually relevant a priori results establish the approximation properties of these methods (see [8] for a discussion); on the contrary, ways to a posteriori validate the accuracy are scarce.”