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Discrete Exterior Calculus
Building Modeling and Simulation Tools on Discrete Exterior Calculus Foundations
James Fairbanks, University of Florida
Friday, September 5, 2025
Abstract: Discrete Exterior Calculus (DEC) has proven to be an effective modeling framework for computational physics on discrete spaces, particularly for complex multiphysics systems. This talk will present Decapodes.jl, a software package developed to facilitate the modeling and simulation of such systems using DEC. Decapodes provides a flexible framework for representing multiphysics systems on manifold-like discrete spaces in up to three dimensions, enabling researchers to encode, manipulate, and analyze complex models algorithmically.
We will discuss how the DEC plays a role in the automatic assembly of multiphysics implementations from high-level physics specifications. Recent developments support advanced fluid mechanical models, including pressure projection techniques for Euler’s equations, and vorticity formulations of the incompressible Navier-Stokes equations. Capabilities of the software package are demonstrated through illustrative examples and highlight its applications in mathematical physics, systems theory, and scientific computing. The talk will highlight open opportunities to bring the DEC to more practitioners through software development.