Perturbative Analytical Framework for Thermal Wave Diffusion in Non-linear Building Envelopes

Corentin Guigot

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arXiv · 2605.16310

Perturbative Analytical Framework for Thermal Wave Diffusion in Non-linear Building Envelopes

Corentin Guigot

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Abstract

Model Predictive Control (MPC) in building energy management requires transient thermal models balancing thermodynamic accuracy with computational efficiency. Standard spatial discretization triggers state-space inflation, paralyzing real-time solvers, while analytical Transfer Matrix Methods (TMM) suffer from high-frequency numerical overflow and assume material homogeneity. This paper introduces a frequency-domain framework based on the continuous spatial Riccati equation. A recursive admittance mapping strictly bounds exponential growth, preventing numerical instability. Regular perturbation theory analytically resolves continuous spatial property gradients ($\lambda$(x)) and non-linear T 4 radiative boundaries as equivalent harmonic source terms. This meshless approach eliminates spatial truncation errors. It analytically corrects peak heating load deviations of 21.9% in wetted media and mitigates artificial nocturnal cooling fluxes of 12.0 W/m 2 . Preserving an O(N ) spatial complexity, the framework structurally avoids state-space inflation, ensuring the high-speed execution demanded by multi-week MPC optimization.

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Corentin Guigot. 2026-05-04. Perturbative Analytical Framework for Thermal Wave Diffusion in Non-linear Building Envelopes. https://arxiv.org/abs/2605.16310

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