Journal Article10.1002/NME.2785
A finite element-based level set method for structural optimization
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TL;DR: In this paper, a finite element-based level set method is implemented for structural optimization and a Dirichlet boundary condition is enforced during the reinitialization to prevent the boundary from drifting.
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Abstract: A finite element-based level set method is implemented for structural optimization. The streamline diffusion finite element method is used for solving both the level set equation and the reinitialization equation. The lumped scheme is addressed and the accuracy is compared with the conventional finite difference-based level set method. A Dirichlet boundary condition is enforced during the reinitialization to prevent the boundary from drifting. Numerical examples of minimum mean compliance design illustrate the reliability of the proposed optimization method. Copyright © 2009 John Wiley & Sons, Ltd.
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Citations
Topology optimization of steady Navier–Stokes flow with body force
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A finite element-based level set method for structural optimization
TL;DR: In this paper, a finite element-based level set method is implemented for structural optimization and a Dirichlet boundary condition is enforced during the reinitialization to prevent the boundary from drifting.
41
Isogeometric analysis for phase-field models of geometric PDEs and high-order PDEs on stationary and evolving surfaces
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TL;DR: An isogeometric analysis (IGA) for phase-field models of three different yet closely related classes of partial differential equations (PDEs): geometric PDEs, high-order P DEs on stationary surfaces, and high-orders on evolving surfaces; the latter can be a coupling of the former two classes.
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A Study on Basis Functions of the Parameterized Level Set Method for Topology Optimization of Continuums
TL;DR: The effects of different basis functions in the PLSM are examined by analyzing and comparing the required storage, convergence speed, computational efficiency, and optimization results, with the benchmark minimum compliance problems subject to a volume constraint.
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References
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Stanley Osher,James A. Sethian +1 more
TL;DR: The PSC algorithm as mentioned in this paper approximates the Hamilton-Jacobi equations with parabolic right-hand-sides by using techniques from the hyperbolic conservation laws, which can be used also for more general surface motion problems.
14K
•Book
Level Set Methods and Dynamic Implicit Surfaces
Stanley Osher,Ronald Fedkiw +1 more
- 31 Oct 2002
TL;DR: A student or researcher working in mathematics, computer graphics, science, or engineering interested in any dynamic moving front, which might change its topology or develop singularities, will find this book interesting and useful.
6.1K
Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
A. N. Brooks,Thomas J. R. Hughes +1 more
TL;DR: In this article, a new finite element formulation for convection dominated flows is developed, based on the streamline upwind concept, which provides an accurate multidimensional generalization of optimal one-dimensional upwind schemes.
5.6K
A level set approach for computing solutions to incompressible two-phase flow
TL;DR: A level set method for capturing the interface between two fluids is combined with a variable density projection method to allow for computation of two-phase flow where the interface can merge/break and the flow can have a high Reynolds number.
4.7K