Some results on uniformly high-order accurate essentially nonoscillatory schemes
Applied Numerical Mathematics - Special issue in honor of Milt Rose's sixtieth birthday
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations
SIAM Journal on Numerical Analysis
On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation
Journal of Computational Physics
Journal of Computational Physics
Numerical schemes for the Hamilton-Jacobi and level set equations on triangulated domains
Journal of Computational Physics
On Families of Pointwise Optimal Finite Volume ENO Approximations
SIAM Journal on Numerical Analysis
Weighted essentially non-oscillatory schemes on triangular meshes
Journal of Computational Physics
Tree methods for moving interfaces
Journal of Computational Physics
High Order Numerical Discretization for Hamilton–Jacobi Equations on Triangular Meshes
Journal of Scientific Computing
Motion of curves in three spatial dimensions using a level set approach
Journal of Computational Physics
High-Order WENO Schemes for Hamilton-Jacobi Equations on Triangular Meshes
SIAM Journal on Scientific Computing
WENO schemes with Lax-Wendroff type time discretizations for Hamilton-Jacobi equations
Journal of Computational and Applied Mathematics
Numerical solution to the optimal feedback control of continuous casting process
Journal of Global Optimization
Shape and topology optimization of compliant mechanisms using a parameterization level set method
Journal of Computational Physics
A semi-implicit level set method for structural shape and topology optimization
Journal of Computational Physics
A second order discontinuous Galerkin fast sweeping method for Eikonal equations
Journal of Computational Physics
The use of PDE centres in the local RBF Hermitian method for 3D convective-diffusion problems
Journal of Computational Physics
Classification Using Geometric Level Sets
The Journal of Machine Learning Research
RBF-FD formulas and convergence properties
Journal of Computational Physics
Adaptive meshless centres and RBF stencils for Poisson equation
Journal of Computational Physics
Radial basis function based level set interpolation and evolution for deformable modelling
Image and Vision Computing
Applied Numerical Mathematics
A boundary-only meshless method for numerical solution of the Eikonal equation
Computational Mechanics
Computers & Mathematics with Applications
Journal of Computational Physics
The Chebyshev spectral viscosity method for the time dependent Eikonal equation
Mathematical and Computer Modelling: An International Journal
Solution to PDEs using radial basis function finite-differences (RBF-FD) on multiple GPUs
Journal of Computational Physics
Level-set methods for structural topology optimization: a review
Structural and Multidisciplinary Optimization
Hi-index | 31.49 |
We utilize radial basis functions (RBFs) to construct numerical schemes for Hamilton-Jacobi (HJ) equations on unstructured data sets in arbitrary dimensions. The computational setup is a meshless discretization of the physical domain. We derive monotone schemes on unstructured data sets to compute the viscosity solutions. The essentially nonoscillatory (ENO) mechanism is combined with radial basis function reconstruction to obtain high order schemes in the presence of gradient discontinuities. Numerical examples of time dependent HJ equations in 2, 3 and 4 dimensions illustrate the accuracy of the new methods.