SUMMARYThe importance of thermal effects on the reliability and performance of VLSI circuits has grown in recent years. The heat conduction problem is commonly described as a second-order partial differential equation (PDE), and several numerical methods, including simple explicit, simple implicit and Crank-Nicolson methods, all having at most second-order spatial accuracy, have been applied to solve the problem. This paper reviews these methods and further proposes a fourth-order spatial-accurate finite difference scheme to better approximate the PDE solution. Moreover, we devise a fourth-order accurate approximation of the convection boundary condition, and apply it to the proposed finite difference scheme. We use a block cyclic reduction and a recently developed numerically stable algorithm for inversion of block-tridiagonal and banded matrices to solve the PDE-based system efficiently. Despite their higher computation complexity than direct computation in a sequential processor, we make it possible for the very first time to employ a divide-and-conquer algorithm, viable for parallel computation, in heat conduction analysis. Experimental results prove such possibility, suggesting that applying divide-and-conquer algorithms, higher-order finite difference schemes can achieve better simulation accuracy with even faster speed and less memory requirement than conventional methods.