Incorporating topological derivatives into level set methods

Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations

Stanley Osher, James A. Sethian · Journal of Computational Physics · 1988 · 13.7K citations

Numerical Analysis, Geometric Modeling, Machine Vision +12

Structural Boundary Design via Level Set and Immersed Interface Methods

James A. Sethian, Andreas Wiegmann · Journal of Computational Physics · 2000 · 1.2K citations

Geometric Modeling, Engineering, Fluid-structure Interaction +14

Weighted ENO Schemes for Hamilton--Jacobi Equations

Guang-Shan Jiang, Danping Peng · SIAM Journal on Scientific Computing · 2000 · 1.1K citations

Numerical Analysis, Hamiltonian Theory, Numerical Computation +14

On the Topological Derivative in Shape Optimization

Antoni Żochowski · SIAM Journal on Control and Optimization · 1999 · 886 citations

Geometric Modeling, Arbitrary Shape Functional, Engineering +13

Modelling crack growth by level sets in the extended finite element method

Magdalena Stolarska, David L. Chopp, Nicolas Moës et al. · International Journal for Numerical Methods in Engineering · 2001 · 771 citations

Engineering, Fracture Optimization, Mechanical Engineering +22