Abstract Recently, the Shifted Boundary Method (SBM) was proposed within the class of
unfitted (or immersed, or embedded) finite element methods. By reformulating the original …

In this article we first review various approaches developed to date for the weak imposition
of Dirichlet boundary conditions in fictitious domain analysis for elasticity problems. The …

This paper presents an overview of a unified framework for finite element and spectral
element methods in 1D, 2D and 3D in C++ called Feel++. The article is divided in two parts …

This work introduces a distributed memory machine and octree-based Finite Element (FE)
framework for modeling metal Additive Manufacturing (AM) processes. In this sense, an …

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 …

We consider formulations of the Shifted Boundary Method based on extrapolation operators
other than the Taylor expansion. In the specific case of the Poisson equation, we prove that …

Numerical simulations of a complete laser powder bed fusion (LPBF) additive manufacturing
(AM) process are extremely challenging, or even impossible, to achieve without a radical …

The analysis of stability and accuracy of the shifted boundary method is developed for the
Stokes flow equations. The key feature of the shifted boundary method, an embedded finite …

We propose a formulation of the Shifted Boundary Method, an immersed/embedded/unfitted
boundary method, for transient thermo-elasticity problems characterized by very complex …

The fictitious domain, finite cell and fat boundary method, which are commonly adopted for
fluid–structure interaction (FSI) problems, have been considered and implemented in a …