Comparative study for several embedded methods, namely: CutFEM [1], AgFEM [2], SBM [3] and WSBM [4]. This repo contains the code required to setup, run and post-process the results. The problem being solved is an interaction problem between rigid objects and a fluid represented by linearized potential flow. The current implementation focuses on floating structures with uniform constant seabed. No mooring systems have been accounted for as of yet. For the 3D simulations there is an implementation that is reliant on the p4est library for adaptive mesh refinement, albeit that the code is crude but functional for AgFEM and CutFEM. For SBM and WSBM the Hessian operator is neglected as this is currently not defined on the reference element within Gridap for this mesh type.
[1]: Burman, Erik, et al. "CutFEM: discretizing geometry and partial differential equations." International Journal for Numerical Methods in Engineering 104.7 (2015): 472-501.
[2]: Badia, Santiago, Francesc Verdugo, and Alberto F. Martín. "The aggregated unfitted finite element method for elliptic problems." Computer Methods in Applied Mechanics and Engineering 336 (2018): 533-553.
[3]: Main, Alex, and Guglielmo Scovazzi. "The shifted boundary method for embedded domain computations. Part I: Poisson and Stokes problems." Journal of Computational Physics 372 (2018): 972-995.
[4]: Colomés, Oriol, et al. "A weighted shifted boundary method for free surface flow problems." Journal of Computational Physics 424 (2021): 109837.