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A second-order sharp numerical method for solving the linear elasticity equations on irregular domains and adaptive grids – Application to shape optimization

Theillard, Maxime and Fokoua Djodom, Landry and Vié, Jean-Léopold and Gibou, Frédéric (2013) A second-order sharp numerical method for solving the linear elasticity equations on irregular domains and adaptive grids – Application to shape optimization. Journal of Computational Physics, 233 . pp. 430-448. ISSN 0021-9991. http://resolver.caltech.edu/CaltechAUTHORS:20130104-104126388

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Abstract

We present a numerical method for solving the equations of linear elasticity on irregular domains in two and three spatial dimensions. We combine a finite volume and a finite difference approaches to derive discretizations that produce second-order accurate solutions in the L^∞-norm. Our discretization is 'sharp' in the sense that the physical boundary conditions (mixed Dirichlet/Neumann-type) are imposed at the interface and the solution is computed inside the irregular domain only, without the need of smearing the solution across the interface. The irregular domain is represented implicitly using a level-set function so that this approach is applicable to free moving boundary problems; we provide a simple example of shape optimization to illustrate this capability. In addition, we provide an extension of our method to the case of adaptive meshes in both two and three spatial dimensions: we use non-graded quadtree (2D) and octree (3D) data structures to represent the grid that is automatically refined near the irregular domain’s boundary. This extension to quadtree/octree grids produces second-order accurate solutions albeit non-symmetric linear systems, due to the node-based sampling nature of the approach. However, the linear system can be solved with simple linear solvers; in this work we use the BICGSTAB algorithm.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.jcp.2012.09.002DOIArticle
http://www.sciencedirect.com/science/article/pii/S0021999112005207PublisherArticle
Additional Information:© 2012 by Elsevier Inc. Received 23 September 2011. Received in revised form 22 May 2012. Accepted 4 September 2012. Available online 17 September 2012. This research was supported in part by ONR under grant agreement N00014-11-1-0027, by the National Science Foundation under grant agreement CHE 1027817, by the Department of Energy under grant agreement DE-FG02-08ER15991, by the Institute for Collaborative Biotechnologies through contract No. W911NF-09-D-0001 from the U.S. Army Research Office and by the W.M. Keck Foundation
Group:GALCIT
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-11-1-0027
NSFCHE 1027817
Department of Energy (DOE)DE-FG02-08ER15991
Army Research Office (ARO)W911NF-09-D-0001
W. M. Keck FoundationUNSPECIFIED
Subject Keywords:Second-order discretization; Linear elasticity; Hybrid finite volume/finite difference; Level-set; Irregular domains; Octree data structure; Quadtree/octree data structure; Non-graded adaptive grid
Record Number:CaltechAUTHORS:20130104-104126388
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20130104-104126388
Official Citation:Maxime Theillard, Landry Fokoua Djodom, Jean-Léopold Vié, Frédéric Gibou, A second-order sharp numerical method for solving the linear elasticity equations on irregular domains and adaptive grids – Application to shape optimization, Journal of Computational Physics, Volume 233, 15 January 2013, Pages 430-448, ISSN 0021-9991, 10.1016/j.jcp.2012.09.002. (http://www.sciencedirect.com/science/article/pii/S0021999112005207)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:36168
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:04 Jan 2013 19:00
Last Modified:06 Aug 2018 18:20

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