An Alternative to IGA: Level Set based Finite Element Analysis Directly from CAD: Finite Elements on Implicit Domains

http://orbilu.uni.lu/handle/10993/12915 http://orbilu.uni.lu/bitstream/10993/12915/1/2011implicitDomainFEM_CMAME...

In this paper, we present some novel results and ideas for robust and
accurate implicit representation of geometric surfaces in finite element
analysis. The novel contributions of this paper are threefold: (1)
describe and validate a method to represent arbitrary parametric
surfaces implicitly; (2) represent arbitrary solids implicitly,
including sharp features using level sets and boolean operations; (3)
impose arbitrary Dirichlet and Neumann boundary conditions on the
resulting implicitly defined boundaries. The methods proposed do not
require local refinement of the finite element mesh in regions of high
curvature, ensure the independence of the domain's volume on the mesh,
do not rely on boundary regularization, and are well suited to methods
based on fixed grids such as the extended finite element method (XFEM).
Numerical examples are presented to demonstrate the robustness and
effectiveness of the proposed approach and show that it is possible to
achieve optimal convergence rates using a fully implicit representation
of object boundaries. This approach is one step in the desired direction
of tying numerical simulations to computer aided design (CAD),
similarly to the isogeometric analysis paradigm.