Embedded domain Reduced Basis Models for the shallow water hyperbolic equations with the Shifted Boundary Method

  title={Embedded domain Reduced Basis Models for the shallow water hyperbolic equations with the Shifted Boundary Method},
  author={Xianyi Zeng and Giovanni Stabile and Efthymios N. Karatzas and Guglielmo Scovazzi and Gianluigi Rozza},


Galerkin finite element methods for the Shallow Water equations over variable bottom
A symmetric formulation for computing transient shallow water flows
The shifted boundary method for embedded domain computations. Part I: Poisson and Stokes problems
A Reduced Order Approach for the Embedded Shifted Boundary FEM and a Heat Exchange System on Parametrized Geometries
A model order reduction technique is combined with an embedded boundary finite element method with a POD-Galerkin strategy and the Shifted Boundary Method, recently proposed, is applied to parametrized heat transfer problems and it relies on a sufficiently refined shape-regular background mesh to account for parametRIzed geometries.
Efficient geometrical parametrization for finite‐volume‐based reduced order methods
This work presents an approach for the efficient treatment of parametrized geometries in the context of POD-Galerkin reduced order methods based on Finite Volume full order approximations, which relies on basis functions defined on an average deformed configuration and makes use of the Discrete Empirical Interpolation Method (D-EIM).
A Reduced Order Model for a stable embedded boundary parametrized Cahn-Hilliard phase-field system based on cut finite elements
This work investigates for the first time with a cut finite element method, a parameterized fourth-order nonlinear geometrical PDE, namely the Cahn-Hilliard system, and manages to find an efficient global, concerning the geometric manifold, and independent of geometric changes, reduced-order basis.
An Extended Finite Element Method for Two-Phase Fluids
The finite element approximation can capture the discontinuities at the interface without requiring the mesh to conform to the interface, eliminating the need for remeshing.