We review some of the recent advances in level-set methods and their applications. In
particular, we discuss how to impose boundary conditions at irregular domains and free …

We present a level set method on non-graded adaptive Cartesian grids, ie grids for which
the ratio between adjacent cells is not constrained. We use quadtree and octree data …

We present scalable algorithms for the level-set method on dynamic, adaptive Quadtree and
Octree Cartesian grids. The algorithms are fully parallelized and implemented using the MPI …

A partial differential equation based reinitialization method is presented in the framework of
a localized level set method. Two formulations of the new reinitialization scheme are …

Level set methods [Osher and Sethian. Fronts propagating with curvature-dependent speed:
algorithms based on Hamilton–Jacobi formulations. J. Comput. Phys. 79 (1988) 12] have …

Level set methods are a popular and powerful class of numerical algorithms for dynamic
implicit surfaces and solution of Hamilton-Jacobi PDEs. While the advanced level set …

A method is introduced to decrease the computational labor of the standard level set method
for propagating interfaces. The fast approach uses only points close to the curve at every …

We propose a method that significantly improves the accuracy of the level set method and
could be of value for numerical solutions of differential equations in general. Level set …

Level set methods for moving interface problems require efficient techniques for
transforming an interface to a globally defined function whose zero set is the interface, such …

We present a high-order accurate scheme for the reinitialization equation of Sussman et
al.(J. Comput. Phys. 114: 146–159,[1994]) that guarantees accurate computation of the …