A STATIC PDE APPROACH FOR MULTIDIMENSIONAL EXTRAPOLATION USING FAST SWEEPING METHODS

A static partial differential equation (PDE) approach is presented for multidimensional extrapolation under the assumption that a level set function exists which separates the region of known values from the region to be extrapolated. Arbitrary orders of polynomial extrapolation can be obtained through solutions of a series of static linear PDEs. Fast sweeping methods of first and second orders are presented to solve the PDEs for constant, linear, and quadratic extrapolation. Numerical examples are presented to demonstrate the approach.