57 citations · 164 across the 14 of their papers we have counts for
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Gap-SBM: A New Conceptualization of the Shifted Boundary Method with Optimal Convergence for the Neumann and Dirichlet Problems
J. Haydel Collins, Kangan Li, Alexei Lozinski +1
We propose and mathematically analyze a new Shifted Boundary Method for the treatment of Dirichlet and Neumann boundary conditions, with provable optimal accuracy in the - and…
A High-Order Shifted Interface Method for Lagrangian Shock Hydrodynamics
Nabil M. Atallah, Ketan Mittal, Guglielmo Scovazzi +1
We present a new method for two-material Lagrangian hydrodynamics, which combines the Shifted Interface Method (SIM) with a high-order Finite Element Method. Our approach relies on…
Weak Boundary Conditions for Lagrangian Shock Hydrodynamics: A High-Order Finite Element Implementation on Curved Boundaries
Nabil M. Atallah, Vladimir Z. Tomov, Guglielmo Scovazzi
We propose a new Nitsche-type approach for weak enforcement of normal velocity boundary conditions for a Lagrangian discretization of the compressible shock-hydrodynamics equations…
Optimal Surrogate Boundary Selection and Scalability Studies for the Shifted Boundary Method on Octree Meshes
Cheng-Hau Yang, Kumar Saurabh, Guglielmo Scovazzi +3
The accurate and efficient simulation of Partial Differential Equations (PDEs) in and around arbitrarily defined geometries is critical for many application domains. Immersed bound…
A penalty-free Shifted Boundary Method of arbitrary order
J. Haydel Collins, Alexei Lozinski, Guglielmo Scovazzi
We introduce and analyze a penalty-free formulation of the Shifted Boundary Method (SBM), inspired by the asymmetric version of the Nitsche method. We prove its stability and conve…
Embedded domain Reduced Basis Models for the shallow water hyperbolic equations with the Shifted Boundary Method
Xianyi Zeng, Giovanni Stabile, Efthymios N. Karatzas +2
We consider fully discrete embedded finite element approximations for a shallow water hyperbolic problem and its reduced-order model. Our approach is based on a fixed background me…
Analysis of the Shifted Boundary Method for the Poisson Problem in General Domains
Nabil M. Atallah, Claudio Canuto, Guglielmo Scovazzi
The shifted boundary method (SBM) is an approximate domain method for boundary value problems, in the broader class of unfitted/embedded/immersed methods. It has proven to be quite…
The Second-Generation Shifted Boundary Method and Its Numerical Analysis
Nabil M. Atallah, Claudio Canuto, Guglielmo Scovazzi
Recently, the Shifted Boundary Method (SBM) was proposed within the class of unfitted (or immersed, or embedded) finite element methods. By reformulating the original boundary valu…
A Reduced-Order Shifted Boundary Method for Parametrized incompressible Navier-Stokes equations
Efthymios N. Karatzas, Giovanni Stabile, Leo Nouveau +2
We investigate a projection-based reduced-order model of the steady incompressible Navier-Stokes equations for moderate Reynolds numbers. In particular, we construct an "embedded"…
A Reduced Basis approach for PDEs on parametrized geometries based on the Shifted Boundary Finite Element Method and application to a Stokes Flow
Efthymios N. Karatzas, Giovanni Stabile, Leo Nouveau +2
We propose a model order reduction technique integrating the Shifted Boundary Method (SBM) with a POD-Galerkin strategy. This approach allows to treat more complex parametrized dom…
A Reduced Order Approach for the Embedded Shifted Boundary FEM and a Heat Exchange System on Parametrized Geometries
E. N. Karatzas, G. Stabile, N. Atallah +2
A model order reduction technique is combined with an embedded boundary finite element method with a POD-Galerkin strategy. The proposed methodology is applied to parametrized heat…