Skip to main content
Open Access Publications from the University of California


UCLA Previously Published Works bannerUCLA

Numerical methods for high dimensional Hamilton-Jacobi equations using radial basis functions

  • Author(s): Cecil, T;
  • Qian, J L;
  • Osher, S
  • et al.

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. (C) 2003 Elsevier Inc. All rights reserved.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
For improved accessibility of PDF content, download the file to your device.
Current View