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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 and Guglielmo Scovazzi Computer Methods in Applied Mechanics and Engineering 453 118793 (2026) https://doi.org/10.1016/j.cma.2026.118793
φ-FEM-FNO: A new approach to train a Neural Operator as a fast PDE solver for variable geometries
Michel Duprez, Vanessa Lleras, Alexei Lozinski, Vincent Vigon and Killian Vuillemot Communications in Nonlinear Science and Numerical Simulation 152 109131 (2026) https://doi.org/10.1016/j.cnsns.2025.109131
$$\varphi -$$FD: A Well-conditioned Finite Difference Method Inspired by $$\varphi -$$FEM for General Geometries on Elliptic PDEs
Low-order fictitious domain method with enhanced mass conservation for an interface stokes problem
Daniele C. Corti, Guillaume Delay, Miguel A. Fernández, Fabien Vergnet and Marina Vidrascu ESAIM: Mathematical Modelling and Numerical Analysis 58(1) 303 (2024) https://doi.org/10.1051/m2an/2023103
A penalty-free Shifted Boundary Method of arbitrary order
J. Haydel Collins, Alexei Lozinski and Guglielmo Scovazzi Computer Methods in Applied Mechanics and Engineering 417 116301 (2023) https://doi.org/10.1016/j.cma.2023.116301
ϕ-FEM for the heat equation: optimal convergence on unfitted meshes in space
Michel Duprez, Vanessa Lleras, Alexei Lozinski and Killian Vuillemot Comptes Rendus. Mathématique 361(G11) 1699 (2023) https://doi.org/10.5802/crmath.497