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Sharp Interface Limit for a Phase Field Model in Structural Optimization
Luise Blank, Harald Garcke, Claudia Hecht and Christoph Rupprecht SIAM Journal on Control and Optimization 54(3) 1558 (2016) https://doi.org/10.1137/140989066
Topology optimization of a coupled thermal-fluid system under a tangential thermal gradient constraint
Grégoire Allaire, François Jouve and Georgios Michailidis Springer Optimization and Its Applications, Variational Analysis and Aerospace Engineering 116 1 (2016) https://doi.org/10.1007/978-3-319-45680-5_1
An evolutionary topology optimization approach with variationally controlled growth
Large strain phase‐field‐based multi‐material topology optimization
Mathias Wallin, Niklas Ivarsson and Matti Ristinmaa International Journal for Numerical Methods in Engineering 104(9) 887 (2015) https://doi.org/10.1002/nme.4962
Numerical Approximation of Phase Field Based Shape and Topology Optimization for Fluids
Harald Garcke, Claudia Hecht, Michael Hinze and Christian Kahle SIAM Journal on Scientific Computing 37(4) A1846 (2015) https://doi.org/10.1137/140969269
Three-Dimensional Dynamic Topology Optimization with Frequency Constraints Using Composite Exponential Function and ICM Method
PolyTop++: an efficient alternative for serial and parallel topology optimization on CPUs & GPUs
Leonardo S. Duarte, Waldemar Celes, Anderson Pereira, Ivan F. M. Menezes and Glaucio H. Paulino Structural and Multidisciplinary Optimization 52(5) 845 (2015) https://doi.org/10.1007/s00158-015-1252-x
Topology and shape optimization methods using evolutionary algorithms: a review
Optimal fine-scale structures in compliance minimization for a uniaxial load
Robert V. Kohn and Benedikt Wirth Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470(2170) 20140432 (2014) https://doi.org/10.1098/rspa.2014.0432
Multimaterial topology optimization by volume constrained Allen–Cahn system and regularized projected steepest descent method
Luise Blank, M. Hassan Farshbaf-Shaker, Harald Garcke, Christoph Rupprecht and Vanessa Styles International Series of Numerical Mathematics, Trends in PDE Constrained Optimization 165 231 (2014) https://doi.org/10.1007/978-3-319-05083-6_15
Explicit feature control in structural topology optimization via level set method
Relating phase field and sharp interface approaches to structural topology optimization
Luise Blank, Harald Garcke, M. Hassan Farshbaf-Shaker and Vanessa Styles ESAIM: Control, Optimisation and Calculus of Variations 20(4) 1025 (2014) https://doi.org/10.1051/cocv/2014006
Primal‐dual active set methods for Allen–Cahn variational inequalities with nonlocal constraints
Luise Blank, Harald Garcke, Lavinia Sarbu and Vanessa Styles Numerical Methods for Partial Differential Equations 29(3) 999 (2013) https://doi.org/10.1002/num.21742
A critical comparative assessment of differential equation-driven methods for structural topology optimization
Binary Level-Set Shape Optimization Model and Algorithm for Volumetric Modulated Arc Therapy in Radiotherapy Treatment
Li-Tien Cheng, Bin Dong, Chunhua Men, Xun Jia and Steve Jiang SIAM Journal on Scientific Computing 35(6) B1321 (2013) https://doi.org/10.1137/120890430
PolyTop: a Matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes
Cameron Talischi, Glaucio H. Paulino, Anderson Pereira and Ivan F. M. Menezes Structural and Multidisciplinary Optimization 45(3) 329 (2012) https://doi.org/10.1007/s00158-011-0696-x
Phase field method for mean curvature flow with boundary constraints
A phase-field model for compliance shape optimization in nonlinear elasticity
Patrick Penzler, Martin Rumpf and Benedikt Wirth ESAIM: Control, Optimisation and Calculus of Variations 18(1) 229 (2012) https://doi.org/10.1051/cocv/2010045
Structural topology optimization with design-dependent pressure loads
A New Framework of Multiphase Segmentation and Its Application to Partial Volume Segmentation
Fuhua Chen, Yunmei Chen, Hemant D. Tagare and Antonio Di Nola Applied Computational Intelligence and Soft Computing 2011(1) (2011) https://doi.org/10.1155/2011/786369
Topology optimization using a reaction–diffusion equation
Jae Seok Choi, Takayuki Yamada, Kazuhiro Izui, Shinji Nishiwaki and Jeonghoon Yoo Computer Methods in Applied Mechanics and Engineering 200(29-32) 2407 (2011) https://doi.org/10.1016/j.cma.2011.04.013
A variational binary level-set method for elliptic shape optimization problems
Structural Optimization Based on the Phase Field Method and Sensitivity Analysis
Akihiro TAKEZAWA, Shinji NISHIWAKI and Mitsuru KITAMURA Transactions of the Japan Society of Mechanical Engineers Series A 76(761) 1 (2010) https://doi.org/10.1299/kikaia.76.1
Volume preserving nonlinear density filter based on heaviside functions
Structural Optimization Based on the Phase Field Method : Validation of Perimeter Constraint Effect and Extension to Compliant Mechanism Design Problem and Eigen-Frequency Maximization Problem
Akihiro TAKEZAWA, Shinji NISHIWAKI and Mitsuru KITAMURA Transactions of the Japan Society of Mechanical Engineers Series A 75(760) 1784 (2009) https://doi.org/10.1299/kikaia.75.1784
An alternative truly-mixed formulation to solve pressure load problems in topology optimization
Topology optimization of slightly compressible fluids
A. Evgrafov ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 86(1) 46 (2006) https://doi.org/10.1002/zamm.200410223
A binary level set model and some applications to Mumford-Shah image segmentation