2014/11/27 by Stephan Schmidt, Schmidt, Stephan · 1 citation
Computer Science · Engineering · #49Q10 #65DXX #65N50 #Advanced Numerical Methods in Computational Mathematics #Computer Graphics and Visualization Techniques #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1411.7663
openalex publication_date 2014/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A two step mesh deformation approach for large nodal deformations, typically arising from non-parametric shape optimization, fluid-structure interaction or computer graphics, is considered. Two major difficulties, collapsed cells and an undesirable parameterization, are overcome by considering a special form of ray tracing paired with a centroid Voronoi reparameterization. The ray direction is computed by solving an Eikonal equation. With respect to the Hadamard form of the shape derivative, both steps are within the kernel of the objective and have no negative impact on the minimizer. The paper concludes with applications in 2D and 3D fluid dynamics and automatic code generation and manages to solve these problems without any remeshing. The methodology is available as a FEniCS shape optimization add-on at http://www.mathematik.uni-wuerzburg.de/~schmidt/femorph.