Using Reduced Order Modeling to Solve Nonlocal and Anomalous Diffusion Problems
Anomalous diffusion problems include such applications as flow through a porous media, where the diffusion rate is not necessarily linear with respect to time. Nonlocal approaches have been shown to be prime candidates for solving these types of diffusion problems. These nonlocal methods rely on the concept of a horizon, or radius in which surrounding particles interact with one another. Due to the increase in interactions for a given particle in a defined system, as well as the use of discontinuous basis functions, the computational cost for such problems can balloon significantly.