Space-Time Reduced Basis Methods for Parametrized Unsteady Stokes Equations
DOI10.1137/22m1509114arXiv2206.12198MaRDI QIDQ6194969
Simone Deparis, Riccardo Tenderini, Unnamed Author
Publication date: 12 March 2024
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2206.12198
reduced basis methodtwofold saddle point problemsleast-squares Petrov-Galerkin projectionhæmodynamicsspace-time model order reductionsupremizers enrichment
Numerical optimization and variational techniques (65K10) PDEs in connection with fluid mechanics (35Q35) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Medical applications (general) (92C50) Stokes and related (Oseen, etc.) flows (76D07) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) 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) Physiological flows (76Z05) Finite difference and finite volume methods for ordinary differential equations (65L12) Physiological flow (92C35) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)
Cites Work
- Unnamed Item
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- Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
- Reduced basis approximation and a posteriori error estimation for Stokes flows in parametrized geometries: roles of the inf-sup stability constants
- Reduced basis approximation of parametrized optimal flow control problems for the Stokes equations
- Inf-sup conditions for twofold saddle point problems
- A parareal in time procedure for the control of partial differential equations
- A new error bound for reduced basis approximation of parabolic partial differential equations
- A coupled momentum method for modeling blood flow in three-dimensional deformable arteries
- Reduced basis method for multi-parameter-dependent steady Navier-Stokes equations: applications to natural convection in a cavity
- Computational vascular fluid dynamics: problems, models and methods
- Galerkin v. least-squares Petrov-Galerkin projection in nonlinear model reduction
- Decreasing the temporal complexity for nonlinear, implicit reduced-order models by forecasting
- An algebraic least squares reduced basis method for the solution of nonaffinely parametrized Stokes equations
- Space-time reduced order model for large-scale linear dynamical systems with application to Boltzmann transport problems
- Model order reduction of flow based on a modular geometrical approximation of blood vessels
- Windowed space-time least-squares Petrov-Galerkin model order reduction for nonlinear dynamical systems
- Hyper-reduced order models for parametrized unsteady Navier-Stokes equations on domains with variable shape
- A Petrov-Galerkin reduced basis approximation of the Stokes equation in parameterized geometries
- Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries
- Characterizing the inf-sup condition on product spaces
- Comparisons between reduced order models and full 3D models for fluid-structure interaction problems in haemodynamics
- Supremizer stabilization of POD-Galerkin approximation of parametrized steady incompressible Navier-Stokes equations
- Nonlinear Model Reduction via Discrete Empirical Interpolation
- Reduced Basis Error Bound Computation of Parameter-Dependent Navier–Stokes Equations by the Natural Norm Approach
- Time-decomposed parallel time-integrators: theory and feasibility studies for fluid, structure, and fluid-structure applications
- Space--Time Least-Squares Petrov--Galerkin Projection for Nonlinear Model Reduction
- On optimization, control and shape design of an arterial bypass
- Mixed Finite Element Methods and Applications
- Model Order Reduction in Fluid Dynamics: Challenges and Perspectives
- A space-time hp-interpolation-based certified reduced basis method for Burgers' equation
- Parallel Time Integration with Multigrid
- 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 Methods for Partial Differential Equations
- PDE-Aware Deep Learning for Inverse Problems in Cardiac Electrophysiology