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PARALLEL SOLUTION OF THE TOPOLOGY OPTIMIZATION PROBLEM FOR ELASTIC CONTINUA

LAWRENCE, WILLIAM ERIC
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1060894691

Abstract Details

2003, MS, University of Cincinnati, Engineering : Mechanical Engineering.
Topology optimization problems require the repeated solution of finite element problems that are often extremely ill-conditioned. This ill-conditioning is due to the highly heterogenous material properties that result as the topology optimization problem converges. It can make the use of iterative solvers inefficient if proper reconditioning is not applied to the stiffness matrix or if steps are not taken to reduce the solve time of these systems. This problem is addressed by considering the solution of the topology optimization problem for elastic continua using parallel computing and domain decomposition techniques. A parallel algorithm for the SIMP (Solid Isotropic Material with Penalization) formulation of the topology optimization problem is presented. This includes a study of the efficiency of the parallel linear solvers used to solve the equilibrium problem at each step of the iterative optimization problem. The solvers that are studied include two preconditioned conjugate gradient (PCG) methods: one using a diagonal preconditioner and one using an incomplete LU factorization preconditioner with a drop tolerance. A third condensation solver that employs a hybrid of direct and iterative (PCG) techniques is also studied. This condensation solver is shown to be the most effective of the three solvers studied both in terms of parallel e±ciency and in terms of its ability to mitigate the effects of the ill-conditioned systems. In addition to examining the parallel linear solvers, the heuristic design variable update scheme, commonly used in topology optimization problems, is also implemented and parallelized. The parallelization of this update scheme is found to be quite simple and straightforward. More difficult is the parallelization of the mesh-independency filter which is also addressed here. A modified filtering approach is presented that limits the number of "ghost" elements needed to be exchanged across parallel sub-domains.
Dr. Kumar Vemaganti (Advisor)
94 p.
Engineering, Mechanical
topology optimization; parallel computing

Recommended Citations

Citations

  • LAWRENCE, W. E. (2003). PARALLEL SOLUTION OF THE TOPOLOGY OPTIMIZATION PROBLEM FOR ELASTIC CONTINUA [Master's thesis, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1060894691

    APA Style (7th edition)

  • LAWRENCE, WILLIAM. PARALLEL SOLUTION OF THE TOPOLOGY OPTIMIZATION PROBLEM FOR ELASTIC CONTINUA. 2003. University of Cincinnati, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1060894691.

    MLA Style (8th edition)

  • LAWRENCE, WILLIAM. "PARALLEL SOLUTION OF THE TOPOLOGY OPTIMIZATION PROBLEM FOR ELASTIC CONTINUA." Master's thesis, University of Cincinnati, 2003. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1060894691

    Chicago Manual of Style (17th edition)

ucin1060894691
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© 2003, all rights reserved.
This open access ETD is published by University of Cincinnati and OhioLINK.