Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Total-variation-diminishing time discretizations
SIAM Journal on Scientific and Statistical Computing
Generating textures on arbitrary surfaces using reaction-diffusion
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Fast tree-based redistancing for level set computations
Journal of Computational Physics
A new Eulerian method for the computation of propagating short acoustic and electromagnetic pulses
Journal of Computational Physics
A fixed grid method for capturing the motion of self-intersecting wavefronts and related PDEs
Journal of Computational Physics
Variational problems and partial differential equations on implicit surfaces
Journal of Computational Physics
Motion of curves constrained on surfaces using a level-set approach
Journal of Computational Physics
Anisotropic Diffusion in Vector Field Visualization on Euclidean Domains and Surfaces
IEEE Transactions on Visualization and Computer Graphics
An Eulerian Formulation for Solving Partial Differential Equations Along a Moving Interface
Journal of Scientific Computing
Efficient algorithms for solving static hamilton-jacobi equations
Efficient algorithms for solving static hamilton-jacobi equations
Fourth order partial differential equations on general geometries
Journal of Computational Physics
An Improvement of a Recent Eulerian Method for Solving PDEs on General Geometries
Journal of Scientific Computing
Diffusion generated motion of curves on surfaces
Journal of Computational Physics
Level Set Equations on Surfaces via the Closest Point Method
Journal of Scientific Computing
Segmentation on surfaces with the closest point method
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
A Finite Volume Method for Solving Parabolic Equations on Logically Cartesian Curved Surface Meshes
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Modeling Cell Movement and Chemotaxis Using Pseudopod-Based Feedback
SIAM Journal on Scientific Computing
Journal of Computational Physics
Articulated motion segmentation of point clouds by group-valued regularization
EG 3DOR'12 Proceedings of the 5th Eurographics conference on 3D Object Retrieval
Real-Time Fluid Effects on Surfaces using the Closest Point Method
Computer Graphics Forum
Closest point turbulence for liquid surfaces
ACM Transactions on Graphics (TOG)
Journal of Computational Physics
A level-set method for two-phase flows with moving contact line and insoluble surfactant
Journal of Computational Physics
Hi-index | 31.47 |
It is increasingly common to encounter partial differential equations (PDEs) posed on surfaces, and standard numerical methods are not available for such novel situations. Herein, we develop a simple method for the numerical solution of such equations which embeds the problem within a Cartesian analog of the original equation, posed on the entire space containing the surface. This allows the immediate use of familiar finite difference methods for the discretization and numerical solution. The particular simplicity of our approach results from using the closest point operator to extend the problem from the surface to the surrounding space. The resulting method is quite general in scope, and in particular allows for boundary conditions at surface boundaries, and immediately generalizes beyond surfaces embedded in R^3, to objects of any dimension embedded in any R^n. The procedure is also computationally efficient, since the computation is naturally only carried out on a grid near the surface of interest. We present the motivation and the details of the method, illustrate its numerical convergence properties for model problems and also illustrate its application to several complex model equations.