Work

FAStSim: A Fast Analytical Stochastic Full-Chip Thermal Simulator via Polynomial Chaos

Year: 2026

Type: article

Abstract: Manufacturing process variations in advanced VLSI nodes introduce stochastic variations in thermal behavior, imposing a prohibitive computational burden on rigorous fullchip risk assessment. To address this challenge, this paper proposes FAStSim, a novel fast spectral-stochastic thermal solver. Unlike traditional generalized polynomial chaos methods that rely on computationally expensive numerical quadrature for coefficient evaluation, we derive a closed-form iterative algebraic formula by exploiting the frequency-domain characteristics of the steady-state heat conduction equation. This allows for the direct analytical computation of the coefficients of polynomial chaos expansion for the stochastic transfer function. By integrating this iterative solver with the spatial discrete cosine transform, we reduce the computational complexity of full-chip stochastic thermal analysis for ans×sgrid resolution toO(s2logs), which is asymptotically equivalent to deterministic solver. Experimental results show that the proposed method achieves a speedup of 600× compared to 10000 Monte Carlo runs while maintaining negligible error (mean and variance deviations < 0.02 K).

Source: IEEE Transactions on Components Packaging and Manufacturing Technology

DOI: 10.1109/tcpmt.2026.3725275

Authors: Hao Ai, Hengyi Chang, Liang Chen, Jianhua Zhang, Wenxing Zhu

Institutions: Fuzhou University, Shanghai University

Language: English

Topic: Probabilistic and Robust Engineering Design

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,645

Funder: National Natural Science Foundation of China