CAREER: Modeling and Simulating Generalized Diffusion for Computer Graphics and Computational Science

Rutgers University New Brunswick, New Brunswick NJ

Investigators

Abstract

Many problems that arise in computer graphics (such as virtual painting and phase changes like ice formation and dendrite growth) are driven by diffusion as pigment, crystals, or neural branches spread. The predominant model employed to capture diffusion is Fourier's law. However, this formulation prevents the simulation of anomalous diffusive processes, where diffusion occurs either faster (super-diffusion) or slower (sub-diffusion) than the rate predicted by Fourier's law. Currently, there is a need for efficiently simulating and visualizing super-diffusive phenomena, such as the super-spreader events for disease propagation or the melting of the permafrost due to warming. This project will push the frontiers of physics simulation in computer graphics by developing a general framework for efficiently simulating all kinds of diffusive processes in large-scale applications, thereby enabling for example characterization of diffusion parameters that lead to specific experimental observations in the real world or the design of policies for preventing disease outbreaks in moving crowds. Project outcomes will have broad impact by supporting the visualization of such complex physical processes at greatly expanded scales. Additional broad impact will derive from the ability to run high resolution simulations on commodity workstations, which will allow a broad audience, particularly students in STEM, to simulate large-scale problems on their own workstations that previously may have required less-accessible enterprise-grade computational resources. Outreach and educational activities such as workshops will leverage programs at Rutgers University to recruit and support students. This project will advance the state-of-the-art in computer graphics by developing a novel formulation for diffusion using fractional derivatives that can not only simulate sub- and super-diffusive processes but also recover the efficiency of the best-known solvers for traditional Fourier-based diffusion. A hybrid Lagrangian/Eulerian representation will be adopted for modeling both micro- and macroscopic interactions, the two being strongly coupled together while accounting for discontinuities such as cracks that may emerge. To scale to large problem sizes, an adaptive discretization scheme will be developed using spatial polynomial regions that can flexibly represent the diffusion fluxes in any irregular domain of arbitrary shape using polynomial functions. For fast numerical solutions, this project will develop an efficient solver using Multigrid methods that better utilize the hardware memory bandwidth by avoiding construction of the linear system while leading to fast convergence rates on modern workstations. The resulting framework will allow the simulation of diffusive phenomena such as super-diffusion that have either not been explored in computer graphics or are currently beyond the reach of existing methods. Implementations of the proposed methodology will be made available to the community as open-source software packages, along with a lightweight client that supports interactive user feedback from the browser while the computationally intensive simulation runs on a remote server thereby making this research broadly accessible, in particular to undergraduate and K-12 students, to cultivate their early interest in STEM. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.