Interior point multigrid methods for topology optimization

Authors:
B. Maar;V. Schulz
Affiliations:
Interdisciplinary Center for Scientific Computing (IWR), University of Heidelberg, Im Neuenheimer Feld 368, D-69120 Heidelberg, Germany, DE;Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Mohrenstrasse 39, D-10117 Berlin, Germany
Venue:
Structural and Multidisciplinary Optimization
Year:
2000

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Abstract

In this paper, a new multigrid interior point approach to topology optimization problems in the context of the homogenization method is presented. The key observation is that nonlinear interior point methods lead to linear-quadratic subproblems with structures that can be favourably exploited within multigrid methods. Primal as well as primal-dual formulations are discussed. The multigrid approach is based on the transformed smoother paradigm. Numerical results for an example problem are presented.