Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Convergence of spectral methods for nonlinear conservation laws
SIAM Journal on Numerical Analysis
Shock capturing by the spectral viscosity method
ICOSAHOM '89 Proceedings of the conference on Spectral and high order methods for partial differential equations
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations
SIAM Journal on Numerical Analysis
A viscosity solutions approach to shape-from-shading
SIAM Journal on Numerical Analysis
Family of spectral filters for discontinuous problems
Journal of Scientific Computing
Journal of Computational and Applied Mathematics - Orthogonal polynomials and numerical methods
Legendre pseudospectral viscosity method for nonlinear conservation laws
SIAM Journal on Numerical Analysis
A level set formulation for the solution of the Dirichlet problem for Hamilton-Jacobi equations
SIAM Journal on Mathematical Analysis
The spectral viscosity method applied to simulation of waves in a stratified atmosphere
Journal of Computational Physics
A fast level set method for propagating interfaces
Journal of Computational Physics
Skeletonization via distance maps and level sets
Computer Vision and Image Understanding
A Legendre pseudospectral viscosity method
Journal of Computational Physics
Multi-phase computations in geometrical optics
Journal of Computational and Applied Mathematics - Special issue on TICAM symposium
On the Gibbs Phenomenon and Its Resolution
SIAM Review
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
A PDE-based fast local level set method
Journal of Computational Physics
A Discontinuous Galerkin Finite Element Method for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
A spectral vanishing viscosity method for large-eddy simulations
Journal of Computational Physics
Weighted ENO Schemes for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Optimal Algorithm for Shape from Shading and Path Planning
Journal of Mathematical Imaging and Vision
SIAM Journal on Numerical Analysis
A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods
SIAM Journal on Numerical Analysis
Spectral Viscosity Approximations to Hamilton--Jacobi Solutions
SIAM Journal on Numerical Analysis
High-Order WENO Schemes for Hamilton-Jacobi Equations on Triangular Meshes
SIAM Journal on Scientific Computing
Geometric optics in a phase-space-based level set and Eulerian framework
Journal of Computational Physics
Chebyshev super spectral viscosity method for a fluidized bed model
Journal of Computational Physics
Fast Extraction of Tubular and Tree 3D Surfaces with Front Propagation Methods
ICPR '02 Proceedings of the 16 th International Conference on Pattern Recognition (ICPR'02) Volume 1 - Volume 1
A level set approach for computing solutions to incompressible two-phase flow
A level set approach for computing solutions to incompressible two-phase flow
High-Order Central WENO Schemes for Multidimensional Hamilton--Jacobi Equations
SIAM Journal on Numerical Analysis
A spectral viscosity method for correcting the long-term behavior of POD models
Journal of Computational Physics
Numerical methods for high dimensional Hamilton-Jacobi equations using radial basis functions
Journal of Computational Physics
Efficient techniques for the second-order parabolic equation subject to nonlocal specifications
Applied Numerical Mathematics
Fast Sweeping Methods for Static Hamilton--Jacobi Equations
SIAM Journal on Numerical Analysis
Robust Centerline Extraction Framework Using Level Sets
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Journal of Computational Physics
Mathematics and Computers in Simulation
High Order Fast Sweeping Methods for Static Hamilton---Jacobi Equations
Journal of Scientific Computing
Idempotent filtering in spectral and spectral element methods
Journal of Computational Physics
A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations
Journal of Computational Physics
Fast Sweeping Methods for Eikonal Equations on Triangular Meshes
SIAM Journal on Numerical Analysis
Redistancing by flow of time dependent eikonal equation
Journal of Computational Physics
A second order discontinuous Galerkin fast sweeping method for Eikonal equations
Journal of Computational Physics
A Fast Iterative Method for Eikonal Equations
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Parameter determination in a partial differential equation from the overspecified data
Mathematical and Computer Modelling: An International Journal
IEEE Transactions on Image Processing
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A wide range of applications requires an accurate solution of a particular Hamilton-Jacobi (H-J) equation known as the Eikonal equation. In this paper, we employ the Chebyshev pseudospectral viscosity method to solve this equation. This method essentially consists of adding a spectral viscosity to the equation for high wave numbers of the numerical solution. This spectral viscosity, which is sufficiently small to retain the formal spectral accuracy is large enough to stabilize the numerical scheme. Here the method is described in detail and the numerical results for several examples are provided which reveals the efficiency of the proposed method.