The generation of tetrahedral meshes for NURBS-enhanced FEM

Abstract

This work presents the first method for generating tetrahedral-based volume meshes dedicated to the NURBS-enhanced finite element method (NEFEM). Built upon the developed method of generating feature-independent surface meshes tailored for NEFEM, the proposed mesh generation scheme is able to grow volume elements that inherit the feature-independence by using the surface mesh as the initial boundary discretisation. Therefore, the generated tetrahedral elements may contain triangular faces that span across multiple NURBS surfaces whilst maintaining the exact boundary description. The proposed strategy completely eliminates the need for de-featuring complex watertight CAD models. At the same time, it eliminates the uncertainty originated from the simplification of CAD models adopted in industrial practice and the error introduced by traditional isoparametric mesh generators that produce polynomial approximations of the true boundary representation. Thanks to the capability of having element faces traversing multiple geometric surfaces, small geometric features in the CAD model no longer restrict the minimum element size, and the user-required mesh spacing in the generated mesh is better satisfied than in traditional meshes that require local refinement. To demonstrate the ability of the proposed approach, a variety of CAD geometries are meshed with the proposed strategy, including examples relevant to the fluid dynamics, wave propagation and solid mechanics communities.