Goal-oriented model reduction for parametrized time-dependent nonlinear partial differential equations
From MaRDI portal
Publication:2060100
DOI10.1016/j.cma.2021.114206OpenAlexW3207282223WikidataQ114196871 ScholiaQ114196871MaRDI QIDQ2060100
Michael K. Sleeman, Masayuki Yano
Publication date: 13 December 2021
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cma.2021.114206
compressible flowreduced basis methodhyperreductiontime-dependent PDEsempirical quadratureparametrized nonlinear PDEs
Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)
Related Items (8)
Sparse data-driven quadrature rules via \(\ell^p\)-quasi-norm minimization ⋮ Registration-based model reduction of parameterized two-dimensional conservation laws ⋮ Efficient hyperreduction of high-order discontinuous Galerkin methods: element-wise and point-wise reduced quadrature formulations ⋮ A multi-fidelity ensemble Kalman filter with hyperreduced reduced-order models ⋮ An MP-DWR method for \(h\)-adaptive finite element methods ⋮ Linearization errors in discrete goal-oriented error estimation ⋮ Model order reduction for deforming domain problems in a time‐continuous space‐time setting ⋮ Registration-based model reduction of parameterized PDEs with spatio-parameter adaptivity
Cites Work
- Unnamed Item
- Unnamed Item
- The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows
- Output-based space-time mesh adaptation for the compressible Navier-Stokes equations
- Proper orthogonal decomposition closure models for turbulent flows: a numerical comparison
- A priori hyperreduction method: an adaptive approach
- Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Application to transport and continuum mechanics.
- A new finite element formulation for computational fluid dynamics. I: Symmetric forms of the compressible Euler and Navier-Stokes equations and the second law of thermodynamics
- Approximate Riemann solvers, parameter vectors, and difference schemes
- Efficient model reduction in nonlinear dynamics using the Karhunen-Loève expansion and dual-weighted-residual methods
- An LP empirical quadrature procedure for parametrized functions
- Galerkin v. least-squares Petrov-Galerkin projection in nonlinear model reduction
- An `empirical interpolation' method: Application to efficient reduced-basis discretization of partial differential equations
- An LP empirical quadrature procedure for reduced basis treatment of parametrized nonlinear PDEs
- Entropy stable reduced order modeling of nonlinear conservation laws
- Dimensional hyper-reduction of nonlinear finite element models via empirical cubature
- Reduced basis methods with adaptive snapshot computations
- A stabilized POD model for turbulent flows over a range of Reynolds numbers: optimal parameter sampling and constrained projection
- A minimum-residual mixed reduced basis method: Exact residual certification and simultaneous finite-element reduced-basis refinement
- A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
- A Posteriori Error Estimation for DEIM Reduced Nonlinear Dynamical Systems
- Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations
- CERTIFIED REDUCED BASIS METHODS FOR NONAFFINE LINEAR TIME-VARYING AND NONLINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS
- Reduced Basis Approximation for Nonlinear Parametrized Evolution Equations based on Empirical Operator Interpolation
- Space-Time Error Representation and Estimation in Navier-Stokes Calculations
- Certified Reduced Basis Methods for Parametrized Partial Differential Equations
- Dimensional reduction of nonlinear finite element dynamic models with finite rotations and energy-based mesh sampling and weighting for computational efficiency
- Structure-preserving, stability, and accuracy properties of the energy-conserving sampling and weighting method for the hyper reduction of nonlinear finite element dynamic models
- Adaptiveh-refinement for reduced-order models
- REDUCED BASIS APPROXIMATION ANDA POSTERIORIERROR ESTIMATION FOR THE PARAMETRIZED UNSTEADY BOUSSINESQ EQUATIONS
- An optimal control approach to a posteriori error estimation in finite element methods
- Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations
- Adaptivity with Dynamic Meshes for Space-Time Finite Element Discretizations of Parabolic Equations
- Newton-GMRES Preconditioning for Discontinuous Galerkin Discretizations of the Navier–Stokes Equations
- GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
- Turbulence and the dynamics of coherent structures. I. Coherent structures
- Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E.’s
- Discontinuous Galerkin methods
- Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
- Space--Time Least-Squares Petrov--Galerkin Projection for Nonlinear Model Reduction
- Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics
- Model Order Reduction in Fluid Dynamics: Challenges and Perspectives
- A space-time hp-interpolation-based certified reduced basis method for Burgers' equation
- Convergence Rates of the POD–Greedy Method
- A posteriorierror bounds for reduced-basis approximations of parametrized parabolic partial differential equations
- Variational multiscale proper orthogonal decomposition: Navier‐stokes equations
- A Space-Time Petrov--Galerkin Certified Reduced Basis Method: Application to the Boussinesq Equations
- An improved error bound for reduced basis approximation of linear parabolic problems
- Reduced basis method for finite volume approximations of parametrized linear evolution equations
- Reduced-basis output bound methods for parabolic problems
- Galerkin proper orthogonal decomposition methods for parabolic problems
- Simultaneous empirical interpolation and reduced basis method for non-linear problems
This page was built for publication: Goal-oriented model reduction for parametrized time-dependent nonlinear partial differential equations
