The triple dexel model as a basis for numerical analysis on time-dependent domains

In this paper, we introduce an efficient and straightforward coupling between a Triple Dexel Model (TDM) and the Finite Element Method (FEM) via an Immersed Boundary Method (IBM) approach, enabling numerical process analysis directly on the Cartesian background grid used for geometrical verification in Computer Aided Manufacturing (CAM) workflows. This avoids costly remeshing on time-dependent domains and establishes a direct link between geometry verification and physics-based simulation within a single framework. Our method integrates the numerical analysis of process-governing physics, such as temperature fields, within the CAM framework, laying the groundwork for future process planning, optimization loops, and extensions towards additional physics such as stress analysis. By combining geometrical verification with numerical analysis, we aim to improve quality assurance and manufacturing workflows, allowing the wealth of advanced techniques developed in both fields to be utilized jointly. We demonstrate the approach on a heat flow analysis, first on a simple case to illustrate the coupling, and then on a more complex repair scenario with irregular geometry to show the method’s applicability beyond trivial cases. The results are validated against a boundary-fitted FEM solution, showing good agreement. These findings highlight the potential of this integration for developing more adaptive and autonomous CAM systems in the future.