Dimensional splitting of hyperbolic partial differential equations using the Radon transform
Provides a new theoretical framework for splitting hyperbolic PDEs, potentially benefiting computational PDE solvers, but the abstract lacks empirical validation.
The paper introduces a dimensional splitting method using the Radon transform for hyperbolic PDEs, enabling multi-dimensional extensions of large time-step methods, absorbing boundary conditions, and transport reversal. No concrete numerical results are provided.
We introduce a dimensional splitting method based on the intertwining property of the Radon transform, with a particular focus on its applications related to hyperbolic partial differential equations (PDEs). This dimensional splitting has remarkable properties that makes it useful in a variety of contexts, including multi-dimensional extension of large time-step (LTS) methods, absorbing boundary conditions, displacement interpolation, and multi-dimensional generalization of transport reversal.