Rigorous domain triangulation for the finite element computation

Abstract

This study introduces a novel algorithm designed to facilitate the accurate generation of domain triangulation for certain n-dimensional simplex domains. Traditional mesh generators employing floating-point arithmetic often encounter rounding errors, leading to a discrepancy between the generated domain triangulation and the intended geometric domain. Our algorithm introduces strategic perturbations to the triangulation nodes. This ensures that boundary nodes are precisely aligned on the domain boundary, thereby preserving the domain’s geometric integrity. Furthermore, this paper highlights the algorithm’s significance in enhancing the precision and reliability of high-precision eigenvalue computations for differential operators through practical mesh generation examples.