Reduced-order modeling of time-dependent PDEs with multiple parameters in the boundary data

By Max D. Gunzburger, J. Peterson, John N. Shadid. 2007

208 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/a6f4f71370d881f634073f9c54ea75e2a01df768

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Citations in the corpus

Reduced Basis Approximation and a Posteriori Error Estimation for Affinely Parametrized Elliptic Coercive Partial Differential Equations (2007, methodology): “Thus, combination of “parameter + time” approaches — essentially the marriage of ROM in time with RB in parameter, sometimes referred to as PROM (Parametric ROM) — is quite natural [31,40,42, 59 ,46, 83,143].”
Supremizer stabilization of POD–Galerkin approximation of parametrized steady incompressible Navier–Stokes equations (2015, background): “In this paper, we consider the latter [11, 26, 35, 36].”
Alleviating mesh constraints : Model reduction, parallel time integration and high resolution homogenization (2008, background): “Some recent advances in such approaches can be found in [16,15,18,5,7,12] and the references therein.”
Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers’ equation (2009, unknown): “Although there are many examples of reduced order models for the unsteady incompressible Navier-Stokes equations [5, 7, 9, 13, 14, 17–21], none is endowed with rigorous a posteriori error bounds.”
A priori model reduction through Proper Generalized Decomposition for solving time-dependent partial differential equations (2010, methodology): “…classically used as an a posteriori model reduction technique for long-time simulations or parametric analyses of evolution problems [5] [4] [19] [20] [16] [36] [24] [10] [15] [3] In this paper, we focus on the more challenging problem of the a priori construction of such separated representations.”
Nonintrusive reduced‐order modeling of parametrized time‐dependent partial differential equations (2013, background): “[11], studied this problem for a special class of parametrized PDE models, where only the boundary conditions are parametrize d.”
Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations (2007, methodology): “However, POD economization techniques can be and have successfully been applied within the parametric RB context [31, 40, 43, 59, 86].”
An efficient reduced‐order modeling approach for non‐linear parametrized partial differential equations (2008, background): “Nevertheless, its success and thus applications remain very much limited to linear and quadratically non-linear problems such as linearized Euler and parabolic equations [12, 13, 23], Burgers equation [10, 24], and incompressible Navier– Stokes equations [11, 25, 26].”
Model Reduction for Large-Scale Systems with High-Dimensional Parametric Input Space (2008, methodology): “We are interested in large-scale systems of the form (2.1), typically with state order n > 10 5 , which might arise from spatial discretization of a set of PDEs or from a naturally discrete large-scale simulation, such as in molecular dynamics or circuit simulation.”
Computational Reduction for Parametrized PDEs: Strategies and Applications (2012, background): “The first applications of POD were concerned with the analysis of turbulent flows and date back to the early ’90s [1, 2]; more recent applications can be found, for instance, in [22, 25, 27, 30], as well as in [9, 12,20] for parametrized flows.”
PGD-Based Computational Vademecum for Efficient Design, Optimization and Control (2013, background): “The interested readers can reefer to [2, 5, 15, 20, 36, 58, 60–63, 67, 74] and the numerous references therein.”