Summary
Various reduced basis element methods are compared for performing transient thermal simulations of integrated circuits. The reduced basis element method is a type of reduced order modeling that takes advantage of repeated geometrical features. It uses a reduced set of basis functions to approximate the solution of a PDE on subdomains (blocks); then these blocks are coupled together to perform a simulation on an entire domain. As the simulations are transient, a proper orthogonal decomposition basis is used, and the proper orthogonal decomposition eigenvalues from each block are used to derive error bounds for the entire simulation. These bounds are used to examine choices of block decompositions for a simplified integrated circuit structure. A decomposition that uses a single block for each transistor device is compared with a decomposition that uses one block for multiple devices. It was found that larger blocks are more computationally efficient; however, the advantage decreases if the devices within a block receive independent signals. Continuous and discontinuous methods of coupling the blocks were also compared. The coupling methods lend themselves to different solution approaches such as static condensation (continuous coupling) and block‐based inversion (discontinuous). Static condensation yielded the best convergence rate, accuracy, and operation count. Copyright © 2017 John Wiley & Sons, Ltd.