Structural shape optimization — a survey
Computer Methods in Applied Mechanics and Engineering
Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Generating optimal topologies in structural design using a homogenization method
Computer Methods in Applied Mechanics and Engineering
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Efficient generalized conjugate gradient algorithms, Part 1: theory
Journal of Optimization Theory and Applications
Semi-Lagrangian methods for level set equations
Journal of Computational Physics
A fast modular semi-Lagrangian method for moving interfaces
Journal of Computational Physics
Structural boundary design via level set and immersed interface methods
Journal of Computational Physics
A Nonlinear Conjugate Gradient Method with a Strong Global Convergence Property
SIAM Journal on Optimization
Structural optimization using sensitivity analysis and a level-set method
Journal of Computational Physics
A semi-Lagrangian contouring method for fluid simulation
ACM Transactions on Graphics (TOG)
A semi-implicit level set method for structural shape and topology optimization
Journal of Computational Physics
On the partial difference equations of mathematical physics
IBM Journal of Research and Development
Efficient and reliable schemes for nonlinear diffusion filtering
IEEE Transactions on Image Processing
Engineering feature design for level set based structural optimization
Computer-Aided Design
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In level set based structural optimization, semi-Lagrange method has an advantage to allow for a large time step without the limitation of Courant---Friedrichs---Lewy (CFL) condition for numerical stability. In this paper, a line search algorithm and a sensitivity modulation scheme are introduced for the semi-Lagrange method. The line search attempts to adaptively determine an appropriate time step in each iteration of optimization. With consideration of some practical characteristics of the topology optimization process, incorporating the line search into semi-Lagrange optimization method can yield fewer design iterations and thus improve the overall computational efficiency. The sensitivity modulation is inspired from the conjugate gradient method in finite-dimensions, and provides an alternative to the standard steepest descent search in level set based optimization. Two benchmark examples are presented to compare the sensitivity modulation and the steepest descent techniques with and without the line search respectively.