Perturbative Analytical Framework for Thermal Wave Diffusion in Non-linear Building Envelopes
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913133438697472 |
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| author | Guigot, Corentin |
| author_facet | Guigot, Corentin |
| contents | 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 ($λ$(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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_16310 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Perturbative Analytical Framework for Thermal Wave Diffusion in Non-linear Building Envelopes Guigot, Corentin Computational Engineering, Finance, and Science 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 ($λ$(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. |
| title | Perturbative Analytical Framework for Thermal Wave Diffusion in Non-linear Building Envelopes |
| topic | Computational Engineering, Finance, and Science |
| url | https://arxiv.org/abs/2605.16310 |