skip to main content

Title: Accelerated fixed-point formulation of topology optimization: Application to compliance minimization problems
We present a simple, effective, and scalable approach for significantly accelerating the convergence in Topology Optimization simulations. Specifically, treating the design process as a fixed-point iteration, we propose employing a recently developed acceleration technique in which Anderson extrapolation is applied periodically, with simple weighted relaxation used for the remaining steps. Through selected examples in compliance minimization, we show that the proposed approach is able to accelerate the overall simulation several fold, while maintaining the quality of the solution.  more » « less
Award ID(s):
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Mechanics research communications
Page Range / eLocation ID:
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. We propose a novel system for creating data plugs and sockets for plug-and-play database web services. We adopt a plug-and-play approach to couple an application to a database. In our approach a designer constructs a “plug,” which is a simple specification of the output produced by the service. If the plug can be “played” on the database “socket” then the web service is generated. Our plug-and-play approach has three advantages. First, a plug is portable. A plug can be played on any data source to generate a web service. Second, a plug is reliable. The database is checked to ensure that the service can be safely and correctly generated. Third, plug-and-play web services are easier to code for complex data since a service designer can write a simple plug, abstracting away the data’s real complexity. We describe a system for plug-and-play web services and experimentally evaluate the system. 
    more » « less
  2. null (Ed.)
    We consider recognition and reconfiguration of lattice-based cellular structures by very simple robots with only basic functionality. The underlying motivation is the construction and modification of space facilities of enormous dimensions, where the combination of new materials with extremely simple robots promises structures of previously unthinkable size and flexibility; this is also closely related to the newly emerging field of programmable matter. Aiming for large-scale scalability, both in terms of the number of the cellular components of a structure, as well as the number of robots that are being deployed for construction requires simple yet robust robots and mechanisms, while also dealing with various basic constraints, such as connectivity of a structure during reconfiguration. To this end, we propose an approach that combines ultra-light, cellular building materials with extremely simple robots. We develop basic algorithmic methods that are able to detect and reconfigure arbitrary cellular structures, based on robots that have only constant-sized memory. As a proof of concept, we demonstrate the feasibility of this approach for specific cellular materials and robots that have been developed at NASA. 
    more » « less
  3. We study the problem of detecting talking activities in collaborative learning videos. Our approach uses head detection and projections of the log-magnitude of optical flow vectors to reduce the problem to a simple classification of small projection images without the need for training complex, 3-D activity classification systems. The small projection images are then easily classified using a simple majority vote of standard classifiers. For talking detection, our proposed approach is shown to significantly outperform single activity systems. We have an overall accuracy of 59% compared to 42% for Temporal Segment Network (TSN) and 45% for Convolutional 3D (C3D). In addition, our method is able to detect multiple talking instances from multiple speakers, while also detecting the speakers themselves. 
    more » « less
  4. Summary

    Structural learning of Gaussian graphical models in the presence of latent variables has long been a challenging problem. Chandrasekaran et al. (2012) proposed a convex program for estimating a sparse graph plus a low-rank term that adjusts for latent variables; however, this approach poses challenges from both computational and statistical perspectives. We propose an alternative, simple solution: apply a hard-thresholding operator to existing graph selection methods. Conceptually simple and computationally attractive, the approach of thresholding the graphical lasso is shown to be graph selection consistent in the presence of latent variables under a simpler minimum edge strength condition and at an improved statistical rate. The results are extended to estimators for thresholded neighbourhood selection and constrained $\ell_{1}$-minimization for inverse matrix estimation as well. We show that our simple thresholded graph estimators yield stronger empirical results than existing methods for the latent variable graphical model problem, and we apply them to a neuroscience case study on estimating functional neural connections.

    more » « less
  5. Abstract

    Plate tectonics is a tectonic style thought to be the hallmark of habitable planets, and yet the inherent complexities of plate tectonic convection have clouded the establishment of simple scaling laws with which to model convective behavior and thermal evolution. We have recently developed a scaling approach for mixed heated convection, based upon several simple physical principles. Here, we generalize our scaling approach to mixed heated convection with pseudoplastic rheology, which gives rise to the plate tectonic mode of convection. We then apply our scaling results to the so‐called bistability of tectonic mode. By illustrating common pitfalls regarding heating mode and nondimensionalization, we demonstrate that tectonic mode is unique with respect to key planetary properties, and that a convective regime diagram for terrestrial planets is within reach.

    more » « less