The role of PDE-based parameterization techniques in gradient-based IGA shape optimization applications

This paper proposes a shape optimization algorithm based on the principles of Isogeometric Analysis (IGA) in which the parameterization of the geometry enters the problem formulation as an additional PDE-constraint. Inspired by the isoparametric principle of IGA, the parameterization and the governing state equation are treated using the same...

Extension of B-spline Material Point Method for unstructured triangular grids using Powell–Sabin splines

The Material Point Method (MPM) is a numerical technique that combines a fixed Eulerian background grid and Lagrangian point masses to simulate materials which undergo large deformations. Within the original MPM, discontinuous gradients of the piecewise-linear basis functions lead to the so-called grid-crossing errors when particles cross...

Spline-based meshing techniques for industrial applications

Isogeometric Analysis (IgA) has become an accepted framework for the mod-elling, simulation and optimization (MSO) of engineering processes. However, the fully automatized generation of analysis-suitable parameterizations of geometries as they arise in practical workflows is still a challenging task, which often requires application-specific...