A Successive Constraint Linear Optimization Method for Lower Bounds of Parametric Coercivity and Inf-Sup Stability Constants

By Dinh Bao Phuong Huynh, Gianluigi Rozza, Sugata Sen, Anthony T. Patera. 2007

300 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/07e1f620f68c0be579fb05bf6d231fa06b0db7c3

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

A static condensation reduced basis element method: Complex problems (2013, unknown): “…however, it is possible to improve the current error bound further by simply constructing a better lower bound for the inf-sup parameter, such as by the successive constraint method [24] [25] Figure 3: System configuration for System 1 and the magnitude of pressure field solution for k = 2.”
Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers’ equation (2009, unknown): “Note, however, that for completeness we do include in this paper a summary of some earlier work: a brief description of the Ofﬂine-Online approach to evaluation of the dual norm of the residual [28, 36]; and a short summary of the Successive Constraint Method (SCM) [16, 35].”
Comparison of the reduced-basis and POD a posteriori error estimators for an elliptic linear-quadratic optimal control problem (2011, methodology): “This lower bound can be obtained amongst others by the application of the so-called Successive Constraint Method (SCM, see [14]), which in fact provides both a lower bound and an upper bound to βf , that is, 0 < βLB f ≤ βf ≤ βUB f .”
Shape optimization for viscous flows by reduced basis methods and free‐form deformation (2012, unknown): “where ‖ · ‖Y′ is the dual norm of the residual defined as ‖rN (·;μ)‖Y′ = sup V ∈YN rN (V ;μ) ‖V ‖Y and βLB(μ) is a computable lower bound for the inf-sup constant β(μ) [22].”
Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations (2007, methodology): “In relation to Part II, the key new methodological elements are the development of (i) discretely stable primal-dual RB approximations [89], (ii) an efficient Offline-Online computational procedure [62, 139] for the construction of a lower bound for the general inf-sup constant [9] required by our a”
A natural-norm Successive Constraint Method for inf-sup lower bounds (2010, methodology): “The proof is analogous to the proof of Proposition 1 in [7].”
REDUCED BASIS APPROXIMATION AND A POSTERIORI ERROR ESTIMATION FOR THE PARAMETRIZED UNSTEADY BOUSSINESQ EQUATIONS (2011, methodology): “Second, we must construct our SCM “con-straint sample” — a pre-computed set of ρ N ( t k ; µ ) — by a procedure described in [29,53].”
Certified reduced basis approximation for parametrized partial differential equations and applications (2011, methodology): “An efficient algorithm for the computation of αN LB(μ) is given by the so-called Successive Constraint Method (SCM), widely analyzed in [1, 33, 34].”
Reduced Basis Approximation and a Posteriori Error Estimation for Parametrized Parabolic PDEs: Application to Real‐Time Bayesian Parameter Estimation (2010, methodology): “(readily computed, once, in the Construction phase); the lower bound for the coercivity constants, α N LB ( μ ) and σ N LB ( μ ), computed Oﬄine–Online by the Successive Constraint Method (SCM) as described in detail in Huynh et al .”
Stabilized reduced basis method for parametrized advection-diffusion PDEs (2014, methodology): “2 For a complete presentation of the reduced basis method we refer to [25, 29], now we just recall its main features and we introduce some notations.”
Reduced basis methods for partial differential equations with stochastic influences (2013, methodology): “2 Inf-Sup Constant For the evaluation of the inf-sup constant, we refer to the successive constraint method (SCM) [57] that can almost directly be applied to the stochastic case.”
Survey of multifidelity methods in uncertainty propagation, inference, and optimization (2018, methodology): “Depending on the problem of interest, these reduced-basis models can be equipped with cheap a posteriori error estimators for the reduced-model outputs [107, 86, 92, 182, 206, 215].”