A review of level-set methods and some recent applications. (English) Zbl 1380.65196
Summary: 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 boundaries as well as the extension of level-set methods to adaptive Cartesian grids and parallel architectures. Illustrative applications are taken from the physical and life sciences. Fast sweeping methods are briefly discussed.
MSC:
| 65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
| 65N08 | Finite volume methods for boundary value problems involving PDEs |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
Keywords:
level-set method; ghost-fluid method; Voronoi interface method; jump condition; Robin boundary condition; Dirichlet boundary condition; octrees; adaptive mesh refinement; parallel computingReferences:
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