Computationally efficient standard-cell FEM-based thermal analysis

Abstract

Thermal analysis is a high performance computing problem because the microscale spatial and time discretization of the heat equation translates into repeatedly solving large linear systems of equations. In previous works, compact models of integrated circuits (IC) were introduced to speed up this process. However, such methods are limited in their accuracy as they approximate the underlying physics. The solution methodologies for such models are also ill-suited to simulate the thermal characteristics of an IC at cell-level. The finite element method (FEM) is an appropriate computational technique for providing both fast and accurate thermal analyses. Considering that the number of cells in modern ICs is in the order of millions, thermal analysis at this abstraction level is a formidable task. Consequently, handling the computational meshes and computing thermal profiles of an IC at the cell-level requires intensive computing power. In order to provide accurate cell-level thermal simulations at a lower computational cost, this work introduces an advanced mesh generator for cell-level floorplans. This mesh generator applies a cell-homogenization technique based on the initial cell-level floorplan and the power trace to create reduced order meshes for e cient cell-level thermal simulations. The e↵ects of using di↵erent homogenization algorithms are explored to illustrate the tradeo↵ between the simulation speed and the solution accuracy. Results show that the proposed technique can achieve a 90% reduction in the number of nodes in the mesh with less than 5% error to the temperature of the full scale mesh. In addition, the simulation time is reduced by an order of magnitude.