RT Conference Proceedings
T1 Towards large scale unfitted adaptive finite element simulations
A1 Badia Rodríguez, Santiago
K1 Ecuaciones en derivadas parciales
AB The use of unfitted finite element methods (FEMs) is an appealingapproach for different reasons. They are interesting in coupled problemsor to avoid the generation of body-fitted meshes. One of the bottlenecksof the simulation pipeline is the body-fitted mesh generation step andthe unstructured mesh partition. The use of unfitted methods onbackground octree Cartesian meshes avoids the need to define body-fittedmeshes, and can exploit efficient and scalable space-filling curvealgorithms. In turn, such schemes complicate the numerical integration,imposition of Dirichlet boundary conditions, and the linear solverphase. The condition number of the resulting linear system does dependon the characteristic size of the cut elements, the so-called small cutcell problem.In this work, we will present an parallel unfitted framework that relieson adaptive octree background meshes and space-filling curvepartitioners. In order to solve the small cut cell problem, we willpursue two different lines. The first one is a re-definition of thefinite element spaces that solves this issue, leading to conditionnumber bounds as the ones for body-fitted schemes without any kind ofperturbation/stabilization of the Galerkin formulation. Another approachwill be to define appropriate iterative linear solvers based on domaindecomposition preconditioning that are robust with respect to the smallcut cell problem. Finally, we will apply the resulting framework to thenumerical simulation of metal additive manufacturing.
YR 2018
FD 2018-04-23
LK https://hdl.handle.net/10630/15578
UL https://hdl.handle.net/10630/15578
LA eng
NO Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech.
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 3 mar 2026