201. fast level set topology optimization using a hierarchical data structure

Department: Structural Engineering
Faculty Advisor(s): Hyunsun Kim

Primary Student
Name: Carolina Miranda Jauregui
Email: cjauregu@ucsd.edu
Phone: 858-442-4913
Grad Year: 2020

Abstract
Using the level set method in topology optimization has several advantages, such as being able to handle complex topological changes and having a crisp definition of the boundary. However, a common criticism is that they tend to be slower in convergence than the traditional density-based approach. One reason for this slowness is attributed to having to search through grid points, such as when updating the level set functions and finding the nearest neighbor of a grid point. For example, a popular method for updating the level set function, the Fast Marching Method, has an algorithm of O(NlogN) because it uses a sorted binary tree as the data structure for storing grid values. This becomes very costly and slow as the number of grid points (N) increases. This paper will show that the efficiency of the level set method can be substantially improved by using a hierarchical data structure designed to take advantage of the level set method?s unique characteristics. The hierarchical data structure is a volumetric dynamic grid that is similar to B+ trees and allows for the efficient storage and manipulation of sparse volumetric data. By arranging blocks of the grid into a hierarchical structure that resembles a B+ tree, it can be shown that the structure can support fast random, sequential, and stencil access (average O(1)) to the grid data. This fast access speeds up the level set update and associated computations such as calculating the normal at the boundary. The presentation will demonstrate the efficiency of the level set topology optimization method with the hierarchical data structure for a range of problem sizes and the convergence will be compared against typical level set topology optimization results.

Industry Application Area(s)
Aerospace, Defense, Security | Civil/Structural Engineering | Software, Analytics

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