8 Reduced-order modeling for applications to the cardiovascular system
DOI10.1515/9783110499001-008zbMath1477.65157OpenAlexW4249698933MaRDI QIDQ4993249
Niccolò Dal Santo, Andrea Manzoni, Stefano Pagani, Alfio M. Quarteroni
Publication date: 15 June 2021
Published in: Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1515/9783110499001-008
proper orthogonal decompositionreduced basis methodhemodynamicscardiac electrophysiologyhyperreduction techniques
PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations for incompressible viscous fluids (76D05) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Physiological flows (76Z05) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Physiological flow (92C35)
Uses Software
Cites Work
- Reduced basis approximation and a posteriori error estimation for Stokes flows in parametrized geometries: roles of the inf-sup stability constants
- Automatic mesh update with the solid-extension mesh moving technique
- Reduced order model in cardiac electrophysiology with approximated Lax pairs
- Fast local reduced basis updates for the efficient reduction of nonlinear systems with hyper-reduction
- Stability analysis of the POD reduced order method for solving the bidomain model in cardiac electrophysiology
- An `empirical interpolation' method: Application to efficient reduced-basis discretization of partial differential equations
- Numerical approximation of parametrized problems in cardiac electrophysiology by a local reduced basis method
- An algebraic least squares reduced basis method for the solution of nonaffinely parametrized Stokes equations
- Machine learning in drug development: characterizing the effect of 30 drugs on the QT interval using Gaussian process regression, sensitivity analysis, and uncertainty quantification
- Machine learning in cardiovascular flows modeling: predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks
- Hyper-reduced order models for parametrized unsteady Navier-Stokes equations on domains with variable shape
- A matrix DEIM technique for model reduction of nonlinear parametrized problems in cardiac mechanics
- Integrated heart -- coupling multiscale and multiphysics models for the simulation of the cardiac function
- Efficient model reduction of parametrized systems by matrix discrete empirical interpolation
- Fast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD-Galerkin method and a vascular shape parametrization
- Mathematical cardiac electrophysiology
- A general multipurpose interpolation procedure: The magic points
- Simulating patterns of excitation, repolarization and action potential duration with cardiac bidomain and monodomain models
- Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty
- Galerkin approximation with proper orthogonal decomposition : new error estimates and illustrative examples
- A Reduced Basis Model with Parametric Coupling for Fluid-Structure Interaction Problems
- Nonlinear model order reduction based on local reduced-order bases
- Supremizer stabilization of POD-Galerkin approximation of parametrized steady incompressible Navier-Stokes equations
- Nonlinear Model Reduction via Discrete Empirical Interpolation
- Computational modeling of cardiac electrophysiology: A novel finite element approach
- Mesh Moving Techniques for Fluid-Structure Interactions With Large Displacements
- Semi-Implicit Time-Discretization Schemes for the Bidomain Model
- The cardiovascular system: Mathematical modelling, numerical algorithms and clinical applications
- Model Reduction and Approximation
- Efficient Reduction of PDEs Defined on Domains with Variable Shape
- A PARALLEL SOLVER FOR REACTION–DIFFUSION SYSTEMS IN COMPUTATIONAL ELECTROCARDIOLOGY
- Shape optimization for viscous flows by reduced basis methods and free‐form deformation
- A Galerkin strategy with Proper Orthogonal Decomposition for parameter-dependent problems – Analysis, assessments and applications to parameter estimation
- Reduced Basis Methods for Partial Differential Equations
