Thermal Analysis with Considering Interactions among Temperature/Power/Heat Conductance and Its Fast Precondition-Solving Algorithm FPSCG

In nanometer regime, the temperature´s influences on the leakage power and heat conductance become significant and thus, should be taken into account in the full-chip 3D thermal analysis. In order to analyze and assess the interactions among the temperature, power and heat conductance, for the first time, this work proposes an iterative thermal analysis method TPG. TPG uses initial values of nodal power density vector P and heat conductance matrix G to solve the nodal temperature vector T. Then it refreshes P and G with the obtained T and further solves T with the refreshed P and G. Although the CG and ICCG algorithm are widely used to solve T with P and G, both converge slowly and need hundreds of iterations. As G needs refreshed and changes per iteration, this work proposes a fast precondition-solving algorithm FPSCG which uses the Double-Nested Fast Fourier Transformation as CG´s precondition. Based on the GPU parallel computing, this work further proposes an efficient algorithm FPSCG_GPU. A large amount of experiments show: (1) FPSCG only needs 4-6 iterations to solve T each time. (2) Without any precision lose, FPSCG_GPU can achieve 8X and 14X speed-up over CG and ICCG. (3) Compared with present methods which partially consider T´s influence on G or P, our TPG method considers all T/P/G interactions and obtains higher simulation results about the maximum temperature and chip power consumption.