Author

Michel Duprez

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Preprint Sep 2026

phi-FD, a second order finite difference scheme for geometries defined by a level-set function: the Neumann case

We extend the phi-FD finite-difference scheme, which handles domains described by a level-set function on a Cartesian grid, to Neumann boundary conditions. The condition is relaxed near the boundary through the level-set and an auxiliary field, which is eliminated by writing the relaxed condition at a boundary node and...

Michel Duprez, V. Lleras, Alexei Lozinski et al. · 0 citations

Preprint Sep 2026

A {\phi}-FEM approach for time-dependent domains with unfitted meshes

In this work, we propose an unfitted finite element scheme to approximate the solution of the heat equation on moving domains. We use the {\phi}-FEM paradigm in which the computational domain is described implicitly by a level-set function {\phi}. This function is incorporated into the variational formulation in order...

Michel Duprez, Johan Marguet, Alexei Lozinski et al. · 0 citations