Finite Element Modeling of Distributed Software Systems: Bridging Functional and Non-Functional Resilience via Computational Complexity

We present a formal framework for modeling distributed software systems using Finite Element Analysis (FEA). Each microservice is treated as a discrete element whose stiffness. is influenced by both structural coupling and computational complexity. We derive the stiffness formulation, prove its monotonic behavior, and show how eigenvalue analysis of the global stiffness matrix reveals system resilience. A pseudo-code example illustrates the bridging of functional logic with non- functional metrics. Validation with public benchmarks supports the hypothesis and opens new research directions.