Efficient Pre-conditional Single-Node SOR Method of Statistical 3D Thermal Analysis for Hot Spots*

This paper proposes an efficient statistical method to analyze temperature variations for few hot spots in a 3D thermal analysis. The new method, called EPSN-SOR (and its non-preconditioned version SNSOR), is based on a novel localized relaxation and iterative scheme. The new method can perform statistical analysis on single spot at a time. EPSN-SOR employs evolution and pre-condition techniques for speedup by exploiting topological similarity of two nearby spots. The method further considers spatial correlation in energy and conductance disturbances. Experiments show that EPSN-SOR is about three orders of magnitude faster than the Monte-Carlo method with small errors and is about 80X faster than general global SOR (successive over relaxation) method in statistical analysis of 450 hot spots for a test case with 1.3 million nodes (average 0.0553 second per spot) under spatially correlated energy and thermal conductance disturbances on a normal desktop PC.