Chebyshev Radon Transform Methods for Solving Multidimensional Linear Hyperbolic Systems

Abstract

The Radon transform has been shown to have useful applications with reducing computational complexity for multidimensional linear hyperbolic partial differential equations (PDEs). The intertwining property of derivatives possessed by the transform reduces multidimensional problems into a series of one dimensional PDEs. The system can then be evolved to a desired time in Radon space using 1D PDE solvers. Finally, we invert the transform to recover the physical solution at the final time. The goal of this work is to implement a high-order discretization of the Radon transform and its inverse in C++ and demonstrate the method with numerical examples.