A Local Mesh Modification Strategy for Interface Problems with Application to Shape and Topology Optimization
For engineers solving interface problems in shape and topology optimization, this method provides a robust and accurate discretization approach.
The paper presents a finite element method that locally modifies triangular grids to resolve interfaces while maintaining the maximal angle condition, achieving optimal convergence and stiffness matrix conditioning. It is applied to shape optimization of an electric motor, demonstrating effectiveness as interfaces evolve.
We present and analyze a new finite element method for solving interface problems on a triangular grid. The method locally modifies a given triangulation such that the interfaces are accurately resolved and the maximal angle condition holds. Therefore, optimal order of convergence can be shown. Moreover, an appropriate scaling of the basis functions yields an optimal condition number of the stiffness matrix. The method is applied to an optimal design problem for an electric motor where the interface between different materials is evolving in the course of the optimization procedure.