Shape optimization

Thursday, September 7, 2017 - 3:30pm - 4:05pm
Yannick Privat (Université de Paris VI (Pierre et Marie Curie))
We investigate the problem of optimizing the shape and location of actuators or sensors for evolution systems driven by a partial differential equation, like for instance a wave equation, a Schrödinger equation, or a parabolic system, on an arbitrary domain Omega, in arbitrary dimension, with boundary conditions if there is a boundary, which can be of Dirichlet, Neumann, mixed or Robin. This kind of problem is frequently encountered in applications where one aims, for instance, at maximizing the quality of reconstruction of the solution, using only a partial observation.
Wednesday, December 14, 2016 - 9:00am - 10:00am
Luca Rondi (Università di Trieste)
The inverse photolithography problem is a key step in the production of integrated circuits. I propose a regularization and computation strategy for this optimization problem, whose key feature is a regularization procedure for a suitable thresholding operation. The validity of the method is shown by a convergence analysis and by numerical experiments. This is a joint work with Fadil Santosa (University of Minnesota) and Zhu Wang (University of South Carolina).
Friday, June 10, 2016 - 11:30am - 12:30pm
Francois Jouve (Université de Paris VII (Denis Diderot))
Shape and topology optimization via the level set method has started attracting the interest of an increasing number of researchers and industrial designers over the past years. A large number of academic problems, using various objective functions and constraints, have been successfully treated with this class of methods, showing its efficiency and flexibility. But real industrial applications may involve more complex and mixed constraints than classical optimal design problems.
Friday, June 10, 2016 - 10:30am - 11:30am
Peter Gangl (Johannes Kepler Universität Linz)
In industry, it is desirable to design electrical equipment such as electric motors in such a way that they are optimal with respect to some given criteria like, e.g., energy efficiency or having little noise and vibration. Therefore, decisions on the layout of such machines are more and more made relying on computational design optimization tools.
Tuesday, June 7, 2016 - 10:35am - 11:50am
Shawn Walker (Louisiana State University)
1. Quick intro of example shape optimization problems.
2. Review differential geometry for curves/surfaces: parametric surfaces, normal vector, curvature, shape operator, etc.
3. Review surface differential operators: surface gradient/Laplacian, shape operator, integration by parts on surfaces, etc.
4. Intro shape perturbations: material and shape derivatives of functions, shape perturbation of shape functionals, perturbation of the identity, etc.
Friday, December 3, 2010 - 2:00pm - 2:45pm
Ronald Hoppe (University of Houston)

The optimal design of structures and systems described by partial differential equations (PDEs) often gives rise to large-scale optimization problems, in particular if the underlying system of PDEs represents a multi-scale, multi-physics problem. Therefore, reduced order modeling techniques such as balanced truncation model reduction, proper orthogonal decomposition, or reduced basis methods are used to significantly decrease the computational complexity while maintaining the desired accuracy of the approximation.

Tuesday, July 16, 2013 - 5:00pm - 6:00pm
Gunay Dogan (National Institute of Standards and Technology)
Many natural phenomena and engineering problems can be modeled as shape optimization problems, in which our goal is to find shapes, such as curves in 2d or surfaces in 3d, minimizing certain shape energies. Examples of such problems are modeling of crystalline interfaces in material science, vesicles in biology, and image segmentation in computer vision. Finding computational solutions for such problems requires performing an optimization over a space of candidate shapes. In this talk, I will introduce a methodology to compute the optimal shapes in such scenarios.
Wednesday, July 16, 2008 - 2:15pm - 2:25pm
Jon Wilkening (University of California, Berkeley)
Shape optimization plays a central role in engineering and
biological design. However, numerical optimization of complex
systems that involve coupling of fluid mechanics to rigid or
flexible bodies can be prohibitively expensive (to implement
and/or run). A great deal of insight can often be gained by
optimizing a reduced model such as Reynolds' lubrication
approximation, but optimization within such a model can
sometimes lead to geometric singularities that drive the
Wednesday, July 16, 2008 - 10:30am - 11:20am
Sidney Nagel (University of Chicago)
No Abstract
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