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Philip Herbert (University of Sussex)8/14/24, 2:00 PMMS 12: Innovative Methods for Shape OptimizationMinisymposium Contribution
In this talk, we will consider a novel strategy for the approximation of optimal shapes. The approach is to use a phase field to provide a near-optimal shape. When adaptively refining the phase field, one ensure a well resolved interface. Upon meeting a desired stopping criteria, the level set of the phase field, which defines a shape is passed onto a sharp interface shape optimisation...
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Alberto Paganini (University of Leicester)8/14/24, 2:30 PMMS 12: Innovative Methods for Shape OptimizationMinisymposium Contribution
The well-established level-set shape optimisation method is based on the implicit description of domain boundaries as zero-level sets of a level-set function. Within this framework, domains are updated by evolving the level-set function according to a Hamilton-Jacobi equation, which itself comprises shape gradients as velocity terms.
The common approach is to employ standard finite elements...
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Henrik Wyschka (Universität Hamburg)8/14/24, 3:00 PMMS 12: Innovative Methods for Shape OptimizationMinisymposium Contribution
Shape optimization constrained to partial differential equations is a vibrant field of research with high relevance for industrial-grade applications. Recent developments suggest that using a $p$-harmonic approach to determine descent directions is superior to classical Hilbert space methods. This applies in particular to the representation of kinks and corners in occurring shapes. However,...
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Laura Hetzel (University of Duisburg-Essen)8/15/24, 9:00 AMMS 12: Innovative Methods for Shape OptimizationMinisymposium Contribution
A crucial issue in numerically solving PDE-constrained shape optimization problems is avoiding mesh degeneracy. Recently, there were two suggested approaches to tackle this problem: (i) departing from the Hilbert space towards the Lipschitz topology approximated by $W^{1,p^*}$ with $p^*>2$ and (ii) using the symmetric rather than the full gradient to define a norm.
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In this talk we will... -
Dr Peter Marvin Müller (Hamburg University of Technology)8/15/24, 9:30 AMMS 12: Innovative Methods for Shape OptimizationMinisymposium Contribution
The talk discusses the efficiency and robustness aspects of a first-order approach based on ADMM (Alternating Direction Method of Multipliers) for approximating the direction of the steepest descent in $W^{1,\infty}$ with Lipschitz domains. The robustness of an implementation with respect to certain parameters is crucial for the technical application of shape optimization problems. For...
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Maximilian Urmann (Universität Regensburg)8/15/24, 10:00 AMMS 12: Innovative Methods for Shape OptimizationMinisymposium Contribution
One main goal of topology optimization is to find an optimal distribution of multiple materials in a design domain in such away that it can withstand internal and external loads applied on the structure. Additive manufacturing techniques like 3D-printing are able to produce complex structures and topologies. To guarantee constructability overhangs need either support structures or should be...
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Leon Baeck (Fraunhofer Institute for Industrial Mathematics ITWM)8/15/24, 11:00 AMMS 12: Innovative Methods for Shape OptimizationMinisymposium Contribution
Topology Optimization considers the optimization of a domain by changing its geometric properties by either adding or removing material. Typically, topology optimization problems feature multiple local minimizers. In order to guarantee convergence to local minimizers that perform best globally, it is important to identify multiple local minimizers of topology optimization problems. Moreover,...
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Michael Winkler (RICAM)8/15/24, 11:30 AMMS 12: Innovative Methods for Shape OptimizationContributed Talk
We aim to solve a topology optimization problem where the distribution of material in the design domain is represented by a density function. To obtain candidates for local minima, we want to solve the first order optimality system via Newton's method. This requires the initial guess to be sufficiently close to the a priori unknown solution. Introducing a stepsize rule often allows for less...
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Nepomuk Krenn (Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences)8/15/24, 12:00 PMMS 12: Innovative Methods for Shape OptimizationContributed Talk
We consider a PDE-constrained design optimization problem with multiple materials, where some material properties are defined by an additional parameter. For this problem we derive the topological derivative i.e. the pointwise sensitivity of the cost functional subject to material changes and use it to update a vector-valued level set function describing the material distribution within the...
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