Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Generating optimal topologies in structural design using a homogenization method
Computer Methods in Applied Mechanics and Engineering
On the Topological Derivative in Shape Optimization
SIAM Journal on Control and Optimization
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Structural optimization using sensitivity analysis and a level-set method
Journal of Computational Physics
An element-based displacement preconditioner for linear elasticity problems
Computers and Structures
Incorporating topological derivatives into shape derivatives based level set methods
Journal of Computational Physics
International Journal of Parallel, Emergent and Distributed Systems
Feature sensitivity: A generalization of topological sensitivity
Finite Elements in Analysis and Design
A 199-line Matlab code for Pareto-optimal tracing in topology optimization
Structural and Multidisciplinary Optimization
On reducing computational effort in topology optimization: how far can we go?
Structural and Multidisciplinary Optimization
An isogeometrical approach to structural topology optimization by optimality criteria
Structural and Multidisciplinary Optimization
Structural and Multidisciplinary Optimization
Stress-constrained topology optimization: a topological level-set approach
Structural and Multidisciplinary Optimization
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The objective of this paper is to introduce an efficient algorithm and implementation for large-scale 3-D topology optimization. The proposed algorithm is an extension of a recently proposed 2-D topological-sensitivity based method that can generate numerous pareto-optimal topologies up to a desired volume fraction, in a single pass. In this paper, we show how the computational challenges in 3-D can be overcome. In particular, we consider an arbitrary 3-D domain-space that is discretized via hexahedral/brick finite elements. Exploiting congruence between elements, we propose a matrix-free implementation of the finite element method. The latter exploits modern multi-core architectures to efficiently solve topology optimization problems involving millions of degrees of freedom. The proposed methodology is illustrated through numerical experiments; comparisons are made against previously published results.