Incorporating topological derivatives into level set methods

[1]  Jean-Paul Zolésio,et al.  The Material Derivative (or Speed) Method for Shape Optimization , 1981 .

[2]  M. Delfour,et al.  Shapes and Geometries: Analysis, Differential Calculus, and Optimization , 1987 .

[3]  S. Osher,et al.  Algorithms Based on Hamilton-Jacobi Formulations , 1988 .

[4]  Jan Sokolowski,et al.  Introduction to shape optimization , 1992 .

[5]  Mariano Giaquinta,et al.  Introduction to Regularity Theory for Nonlinear Elliptic Systems , 1993 .

[6]  F. Santosa.  A Level-set Approach Inverse Problems Involving Obstacles , 1995 .

[7]  W. Rundell,et al.  Iterative methods for the reconstruction of an inverse potential problem , 1996 .

[8]  G. Allaire,et al.  Shape optimization by the homogenization method , 1997 .

[9]  F. Santosa,et al.  Reconstruction of a two-dimensional binary obstacle by controlled evolution of a level-set , 1998 .

[10]  James A. Sethian,et al.  The Fast Construction of Extension Velocities in Level Set Methods , 1999 .

[11]  Jan Sokołowski,et al.  Topological derivatives for elliptic problems , 1999 .

[12]  Jan Sokolowski,et al.  On the Topological Derivative in Shape Optimization , 1999 .

[13]  J. Sethian,et al.  Structural Boundary Design via Level Set and Immersed Interface Methods , 2000 .

[14]  E. Miller,et al.  A shape reconstruction method for electromagnetic tomography using adjoint fields and level sets , 2000 .

[15]  Danping Peng,et al.  Weighted ENO Schemes for Hamilton-Jacobi Equations , 1999, SIAM J. Sci. Comput..

[16]  S. Osher,et al.  Level Set Methods for Optimization Problems Involving Geometry and Constraints I. Frequencies of a T , 2001 .

[17]  M. Burger.  A level set method for inverse problems , 2001 .

[18]  Ted Belytschko,et al.  Modelling crack growth by level sets in the extended finite element method , 2001 .

[19]  Philippe Guillaume,et al.  The Topological Asymptotic for PDE Systems: The Elasticity Case , 2000, SIAM J. Control. Optim..

[20]  K. Kunisch,et al.  Level-set function approach to an inverse interface problem , 2001 .

[21]  Arian Novruzi,et al.  Structure of shape derivatives , 2002 .

[22]  Ph. Guillaume,et al.  The Topological Asymptotic Expansion for the Dirichlet Problem , 2002, SIAM J. Control. Optim..

[23]  G. Allaire,et al.  A level-set method for shape optimization , 2002 .

[24]  A. Chambolle,et al.  Design-dependent loads in topology optimization , 2003 .

[25]  Ronald Fedkiw,et al.  Level set methods and dynamic implicit surfaces , 2002, Applied mathematical sciences.

[26]  M. Burger.  A framework for the construction of level set methods for shape optimization and reconstruction , 2003 .

[27]  J. Sethian,et al.  FRONTS PROPAGATING WITH CURVATURE DEPENDENT SPEED: ALGORITHMS BASED ON HAMILTON-JACOB1 FORMULATIONS , 2003 .

[28]  Michael Hintermüller,et al.  An Inexact Newton-CG-Type Active Contour Approach for the Minimization of the Mumford-Shah Functional , 2004, Journal of Mathematical Imaging and Vision.

[29]  M. Burger,et al.  Level set methods for geometric inverse problems in linear elasticity , 2004 .

[30]  G. Allaire,et al.  Structural optimization using sensitivity analysis and a level-set method , 2004 .

[31]  Michael Hintermüller,et al.  A Second Order Shape Optimization Approach for Image Segmentation , 2004, SIAM J. Appl. Math..