A Local Mesh Modification Strategy for Interface Problems with Application to Shape and Topology Optimization

2016/09/20 by Peter Gangl, Ulrich Langer, Gangl, Peter +1
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #FOS: Mathematics #Numerical Analysis (math.NA) #Topology Optimization in Engineering

paper · doi:10.48550/arxiv.1609.06236

openalex publication_date 2016/09/20 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

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.

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