Application of the isogeometric shifted boundary method to the Poisson problem

This paper describes a novel use of the Shifted Boundary Method (SBM) within the Isogeometric Analysis (IGA) framework to solve 2D and 3D Poisson problems. Numerical tests demonstrate that combining SBM with higher-order Taylor expansions consistently results in optimal convergence rates. Furthermore, we show that SBM, within the IGA framework, eliminates the so-called small cut-cell instability, a common issue in many embedded methods that try to integrate the cut cells. We provide two main findings: a comparison with the Isogeometric Boundary Representation Analysis (IBRA) approach in 2D, and validation of our SBM-IGA framework in 3D, demonstrating its robustness through a variety of scenarios.

Duke Scholars

Author Guglielmo Scovazzi Civil and Environmental Engineering