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 exper...
Creator:
Rondi, Luca (Università di Trieste)
Created:
2016-12-14
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Shape optimization plays a central role in engineering andbiological design. However, numerical optimization of complexsystems that involve coupling of fluid mechanics to rigid orflexible bodies can be prohibitively expensive (to implementand/or run). A great deal of insight can often be gained byoptimizing a reduced model such as Reynolds' lubr...
Creator:
Wilkening, Jon (University of California, Berkeley)
Created:
2008-07-16
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
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 ca...
Creator:
Privat, Yannick (Universite de Paris VI (Pierre et Marie Curie))
Created:
2017-09-07
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
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 ort...
Creator:
Hoppe, Ronald H.W. (University of Houston)
Created:
2010-12-03
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
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...
Creator:
Jouve, Francois (Université de Paris VII (Denis Diderot))
Created:
2016-06-10
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
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 too...
Creator:
Gangl, Peter (Johannes Kepler Universität Linz)
Created:
2016-06-10
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
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 compute...
Creator:
Dogan, Gunay (National Institute of Standards and Technology)
Created:
2013-07-16
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
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 ...
Creator:
Walker, Shawn W. (Louisiana State University)
Created:
2016-06-07
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
