Automated Geometrically Accurate Mesh Generation

Develop an automated procedure to generate geometrically accurate meshes that conform to domain boundaries and multimaterial interfaces for finite element and spectral element simulations, thereby addressing the lack of a general automatic method for constructing body-fitted meshes with high geometric fidelity.

Background

The paper distinguishes two major requirements for computational meshes: geometric accuracy at boundaries and interfaces, and good element quality for numerical solution accuracy. While numerous techniques exist for improving mesh quality via r- and h-adaptivity, the authors note that automatically generating a geometrically accurate, body-fitted mesh remains unresolved and has motivated the development of unfitted or embedded approaches.

Their work proposes an rp-adaptivity framework tailored to implicit geometries described by level-set functions, aiming to improve geometric accuracy near interfaces while controlling computational cost through mixed-order meshes. The open question highlights the broader need for general automated mesh generation methods that achieve high geometric fidelity without extensive manual intervention or reliance on nonconforming strategies.