2022/01/07 by Kiprian Berbatov, Berbatov, Kiprian, Pieter D. Boom +5 · 3 citations
Computer Science · Engineering · #52B70 #52B99 #65N50 #80A20 #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics #FOS: Physical sciences #Mathematical Physics (math-ph) #Phase Equilibria and Thermodynamics
paper · pdf · doi:10.48550/arxiv.2201.03704
openalex publication_date 2022/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The formulation of combinatorial differential forms, proposed by Forman for analysis of topological properties of discrete complexes, is extended by defining the operators required for analysis of physical processes dependent on scalar variables. The resulting description is intrinsic, different from the approach known as Discrete Exterior Calculus, because it does not assume the existence of smooth vector fields and forms extrinsic to the discrete complex. In addition, the proposed formulation provides a significant new modelling capability: physical processes may be set to operate differently on cells with different dimensions within a complex. An application of the new method to the heat/diffusion equation is presented to demonstrate how it captures the effect of changing properties of microstructural elements on the macroscopic behavior. The proposed method is applicable to a range of physical problems, including heat, mass and charge diffusion, and flow through porous media.