High Order Numerical Discretization for Hamilton–Jacobi Equations on Triangular Meshes
Journal of Scientific Computing
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Animation and rendering of complex water surfaces
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
A technique of treating negative weights in WENO schemes
Journal of Computational Physics
Journal of Computational Physics
Motion of curves constrained on surfaces using a level-set approach
Journal of Computational Physics
Geometric optics in a phase-space-based level set and Eulerian framework
Journal of Computational Physics
A level set approach for computing discontinuous solutions of Hamilton-Jacobi equations
Mathematics of Computation
A hybrid particle level set method for improved interface capturing
Journal of Computational Physics
Journal of Computational Physics
A local piecewise parabolic method for Hamilton--Jacobi equations
Applied Numerical Mathematics
Journal of Computational Physics
Journal of Scientific Computing
An Introduction to Eulerian Geometrical Optics (1992–2002)
Journal of Scientific Computing
Construction of Shapes Arising from the Minkowski Problem Using a Level Set Approach
Journal of Scientific Computing
A Level Set Approach for the Numerical Simulation of Dendritic Growth
Journal of Scientific Computing
Overapproximating Reachable Sets by Hamilton-Jacobi Projections
Journal of Scientific Computing
Multidomain WENO Finite Difference Method with Interpolation at Subdomain Interfaces
Journal of Scientific Computing
A Slowness Matching Eulerian Method for Multivalued Solutions of Eikonal Equations
Journal of Scientific Computing
An Eulerian Formulation for Solving Partial Differential Equations Along a Moving Interface
Journal of Scientific Computing
High-order semi-discrete central-upwind schemes for multi-dimensional Hamilton--Jacobi equations
Journal of Computational Physics
Identification of contact regions in semiconductor transistors by level-set methods
Journal of Computational and Applied Mathematics
Incorporating topological derivatives into level set methods
Journal of Computational Physics
Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations
Journal of Computational Physics
High-order schemes for Hamilton-Jacobi equations on triangular meshes
Journal of Computational and Applied Mathematics
A level set based Eulerian method for paraxial multivalued traveltimes
Journal of Computational Physics
Journal of Computational Physics
A Eulerian level set/vortex sheet method for two-phase interface dynamics
Journal of Computational Physics
Hermite WENO schemes for Hamilton-Jacobi equations
Journal of Computational Physics
ACM SIGGRAPH 2005 Papers
Journal of Computational Physics
A quadrature-free discontinuous Galerkin method for the level set equation
Journal of Computational Physics
A level-set method for interfacial flows with surfactant
Journal of Computational Physics
Stochastic Motion and the Level Set Method in Computer Vision: Stochastic Active Contours
International Journal of Computer Vision
Adaptive Central-Upwind Schemes for Hamilton---Jacobi Equations with Nonconvex Hamiltonians
Journal of Scientific Computing
Fourth order partial differential equations on general geometries
Journal of Computational Physics
A TVD-type method for 2D scalar Hamilton-Jacobi equations on unstructured meshes
Journal of Computational and Applied Mathematics - Special issue: The international symposium on computing and information (ISCI2004)
Applied Numerical Mathematics - Numerical methods for viscosity solutions and applications
Journal of Computational Physics
Maintaining the point correspondence in the level set framework
Journal of Computational Physics
An extended level set method for shape and topology optimization
Journal of Computational Physics
WENO schemes with Lax-Wendroff type time discretizations for Hamilton-Jacobi equations
Journal of Computational and Applied Mathematics
Parallelization of a level set method for simulating dendritic growth
Journal of Parallel and Distributed Computing
Journal of Computational Physics
Flux-based level set method: A finite volume method for evolving interfaces
Applied Numerical Mathematics
Geometric curve flows on parametric manifolds
Journal of Computational Physics
A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations
Journal of Computational Physics
Proceedings of the 2007 ACM symposium on Solid and physical modeling
An active contour model for image segmentation based on elastic interaction
Journal of Computational Physics
A Fast Sweeping Method for Static Convex Hamilton-Jacobi Equations
Journal of Scientific Computing
Convex ENO Schemes for Hamilton-Jacobi Equations
Journal of Scientific Computing
A study of numerical methods for the level set approach
Applied Numerical Mathematics
Journal of Computational Physics
High-fidelity interface tracking in compressible flows: Unlimited anchored adaptive level set
Journal of Computational Physics
Data-dependent MLS for faithful surface approximation
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Fast Global Minimization of the Active Contour/Snake Model
Journal of Mathematical Imaging and Vision
Shape and topology optimization of compliant mechanisms using a parameterization level set method
Journal of Computational Physics
A balanced force refined level set grid method for two-phase flows on unstructured flow solver grids
Journal of Computational Physics
Redistancing by flow of time dependent eikonal equation
Journal of Computational Physics
Journal of Computational Physics
A semi-implicit level set method for structural shape and topology optimization
Journal of Computational Physics
On stability condition for bifluid flows with surface tension: Application to microfluidics
Journal of Computational Physics
Differential equation based constrained reinitialization for level set methods
Journal of Computational Physics
Essentially Non-Oscillatory Adaptive Tree Methods
Journal of Scientific Computing
A second order discontinuous Galerkin fast sweeping method for Eikonal equations
Journal of Computational Physics
An Unconditionally Stable MacCormack Method
Journal of Scientific Computing
A New Ghost Cell/Level Set Method for Moving Boundary Problems: Application to Tumor Growth
Journal of Scientific Computing
Journal of Scientific Computing
A Local Semi-Implicit Level-Set Method for Interface Motion
Journal of Scientific Computing
Level Set Equations on Surfaces via the Closest Point Method
Journal of Scientific Computing
The Flexible, Extensible and Efficient Toolbox of Level Set Methods
Journal of Scientific Computing
A Second Order Central Scheme for Hamilton-Jacobi Equations on Triangular Grids
Numerical Analysis and Its Applications
A front-tracking/ghost-fluid method for fluid interfaces in compressible flows
Journal of Computational Physics
An improved particle correction procedure for the particle level set method
Journal of Computational Physics
Sharp interface immersed-boundary/level-set method for wave-body interactions
Journal of Computational Physics
POD-based feedback control of the burgers equation by solving the evolutionary HJB equation
Computers & Mathematics with Applications
A fast and accurate semi-Lagrangian particle level set method
Computers and Structures
The constrained reinitialization equation for level set methods
Journal of Computational Physics
An Efficient Data Structure and Accurate Scheme to Solve Front Propagation Problems
Journal of Scientific Computing
Computing multivalued physical observables for the semiclassical limit of the Schrödinger equation
Journal of Computational Physics
Phase-field versus level set method for 2D dendritic growth
NMA'06 Proceedings of the 6th international conference on Numerical methods and applications
Journal of Computational Physics
Variational piecewise constant level set methods for shape optimization of a two-density drum
Journal of Computational Physics
An Eulerian method for multi-component problems in non-linear elasticity with sliding interfaces
Journal of Computational Physics
A Central Discontinuous Galerkin Method for Hamilton-Jacobi Equations
Journal of Scientific Computing
Journal of Scientific Computing
A local discontinuous Galerkin method for directly solving Hamilton-Jacobi equations
Journal of Computational Physics
Journal of Computational Physics
Level set based multi-scale methods for large deformation contact problems
Applied Numerical Mathematics
A Speed-Up Strategy for Finite Volume WENO Schemes for Hyperbolic Conservation Laws
Journal of Scientific Computing
Marker Redistancing/Level Set Method for High-Fidelity Implicit Interface Tracking
SIAM Journal on Scientific Computing
Computational Modeling of Solid Tumor Growth: The Avascular Stage
SIAM Journal on Scientific Computing
An Eulerian approach for computing the finite time Lyapunov exponent
Journal of Computational Physics
A boundary-only meshless method for numerical solution of the Eikonal equation
Computational Mechanics
Finite Elements in Analysis and Design
PhysBAM: physically based simulation
ACM SIGGRAPH 2011 Courses
A Discontinuous Galerkin Solver for Front Propagation
SIAM Journal on Scientific Computing
Uniformly Accurate Discontinuous Galerkin Fast Sweeping Methods for Eikonal Equations
SIAM Journal on Scientific Computing
A level set method for vapor bubble dynamics
Journal of Computational Physics
Computers & Mathematics with Applications
Out-of-Core Computations of High-Resolution Level Sets by Means of Code Transformation
Journal of Scientific Computing
A new volume-of-fluid method with a constructed distance function on general structured grids
Journal of Computational Physics
Elastic interaction models for active contours and surfaces
CVBIA'05 Proceedings of the First international conference on Computer Vision for Biomedical Image Applications
The Chebyshev spectral viscosity method for the time dependent Eikonal equation
Mathematical and Computer Modelling: An International Journal
A level-set continuum method for two-phase flows with insoluble surfactant
Journal of Computational Physics
Journal of Scientific Computing
A uniformly second order fast sweeping method for eikonal equations
Journal of Computational Physics
A two-continua approach to Eulerian simulation of water spray
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Adaptive mesh refinement techniques for the immersed interface method applied to flow problems
Computers and Structures
Hybrid particle---grid fluid animation with enhanced details
The Visual Computer: International Journal of Computer Graphics
Geodesics in heat: A new approach to computing distance based on heat flow
ACM Transactions on Graphics (TOG)
Hermite WENO schemes for Hamilton-Jacobi equations on unstructured meshes
Journal of Computational Physics
A balanced-force algorithm for two-phase flows
Journal of Computational Physics
Alternating evolution discontinuous Galerkin methods for Hamilton-Jacobi equations
Journal of Computational Physics
A level-set method for two-phase flows with moving contact line and insoluble surfactant
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 0.27 |
In this paper, we present a weighted ENO (essentially nonoscillatory) scheme to approximate the viscosity solution of the Hamilton--Jacobi equation: $$ \phi_t + H(x_1,\ldots,x_d,t,\phi,\phi_{x_1},\ldots,\phi_{x_d}) = 0. $$ This weighted ENO scheme is constructed upon and has the same stencil nodes as the third order ENO scheme but can be as high as fifth order accurate in the smooth part of the solution. In addition to the accuracy improvement, numerical comparisons between the two schemes also demonstrate that the weighted ENO scheme is more robust than the ENO scheme.