Abstract
We propose two algorithms for elliptic boundary value problems in shape optimization. With the finite element method, the optimization problem is replaced by a discrete variational problem. We give rules and use them to decide which elements are to be reserved. Those rules are determined by the optimization; as a result, we get the optimal design in shape. Numerical examples are provided to show the effectiveness of our algorithms.
Highlights
With numerous applications in structural engineering and fluid mechanics, shape optimization has received much more attention in recent years [1,2,3,4,5]
Level set methods are popular for solving shape optimization problems
Based on the greedy idea, we have presented two interesting and promising algorithms for solving the linear elliptic problems in shape optimization
Summary
With numerous applications in structural engineering and fluid mechanics, shape optimization has received much more attention in recent years [1,2,3,4,5]. The method is very promising in that it is nearly independent on the initial guess for design It has a rigorous mathematical result of the existence of the solution. This method can be applied to limited areas and particular objective functions. Level set methods are popular for solving shape optimization problems (see [5, 9,10,11,12,13]). Level set methods can naturally be applied to solve shape and topology optimization problems. By its nature, the obtained level set function decreases the number of connected components of resulting geometrical domains during the optimization process. We propose a novel method for a class of linear elliptic problems in shape optimization.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
