Sponsor: NSF
The purpose of this training and research project is to develop innovative computational methods and software for problems in electromagnetics arising in VLSI design. This work is to be conducted by the post-doctoral research associate in close cooperation with Professors Ahmed Sameh and Ananth Grama; who have active research groups pursuing related interests. The project focuses on developing robust, effective, and parallelizable solvers and preconditioners for linear systems arising from finite element and boundary element modeling of inductive and capacitive effects in high speed integrated circuits. Techniques based on a hierarchy of representations using multipoles and block low-rank approximations of the coefficient matrix are investigated. The implications of these techniques for approximate inverse preconditioners and multilevel schemes for sparse solvers are also addressed. Portable parallel formulations of the techniques along with theoretical estimates for convergence and parallel performance are targeted. In addition to development of innovative techniques and training of the post-doctoral research associate, this project serves to strengthen the recent initiative in computational electromagnetics at Purdue University. The presence of a post-doctoral researcher in electromagnetics also complements the PIs' areas of expertise. This is critical because of the interdisciplinary nature of the project.