Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Improvements on Delaunay-based three-dimensional automatic mesh generator
Finite Elements in Analysis and Design - Special issue: adaptive meshing part 2
Three-Dimensional Front Tracking
SIAM Journal on Scientific Computing
Semi-Lagrangian methods for level set equations
Journal of Computational Physics
Directional adaptive surface triangulation
Computer Aided Geometric Design
I3D '01 Proceedings of the 2001 symposium on Interactive 3D graphics
Level set methods: an overview and some recent results
Journal of Computational Physics
A front-tracking method for the computations of multiphase flow
Journal of Computational Physics
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
SMI '03 Proceedings of the Shape Modeling International 2003
Structural optimization using sensitivity analysis and a level-set method
Journal of Computational Physics
Velocity Extension for the Level-set Method and Multiple Eigenvalues in Shape Optimization
SIAM Journal on Control and Optimization
A mesh evolution algorithm based on the level set method for geometry and topology optimization
Structural and Multidisciplinary Optimization
| Hi-index | 31.45 |
The aim of this paper is to propose a method for dealing with the problem of mesh deformation (or mesh evolution) in the context of free and moving boundary problems, in three space dimensions. The method consists in combining two different numerical parameterizations of domains: on the one hand, domains are equipped with a computational tetrahedral mesh, and on the other hand, they are represented as the negative subdomains of 'level set' functions. We then consistently switch from one description to the other, depending on their respective convenience with respect to the operations to be performed. Among other things, doing so implies to be able to get a computational mesh from an implicitly-defined domain. This in turns relies on an algorithm for handling three-dimensional domain remeshing (that is, remeshing at the same time both surface and volume parts of a given tetrahedral mesh). Applications are considered in the fields of mesh generation, shape optimization, and computational fluid dynamics.