A novel Shifted Boundary Method (SBM) for embedded domains based on Multi-Point Constraints.

This project presents a recent finite element approach for embedded domains that belongs to the category of approximate boundary methods: the Shifted Boundary Method (SBM). This is an unfitted approach used to represent embedded boundaries. SBM suggests shifting the location of boundary conditions from the true boundary to a surrogate boundary and adjusting the Dirichlet boundary conditions appropriately to preserve the optimal convergence rate. The theory and implementation details of the developed formulations in the open-source Kratos Multiphysics software have been comprehensively covered for Poisson and convection-diffusion problems. In addition, we introduced a novel approach based on Multi-Point constraints. The new technique allows the method to impose the new Dirichlet boundary conditions, which depend on the gradient of the solution, without introducing any nonlinear loop. The new shifted boundary method was validated by performing convergence studies on stationary and transient convection-diffusion problems, also testing embedded complex inner and outer boundaries.