A MONTE CARLO METHODOLOGY FOR THE SOLUTION OF MAXWELL'S EQUATIONS: APPLICATIONS TO ELECTROMAGNETIC ANALYSIS OF IC-INTERCONNECT STRUCTURES

This monograph represents the first meaningful attempt to obtain a Monte Carlo solution of Maxwell's equations at sub- and multiple- wavelength length scales. The application area of interest is in the electromagnetic analysis of IC-interconnect structures at multi-GHz frequencies. The methodologies developed in this monograph have laid the foundation for the development of a new Monte Carlo methodology for the solution of nonlinear partial differential equations and for the solution of Neumann and mixed boundary condition problems without 'reflections' at domain boundaries. The target audience of this monograph is engineers, physicists and computational scientists from all disciplines. In general, the Monte Carlo method is less developed compared to other deterministic numerical methods. The author believes that significant progress has been made in applying the Monte Carlo method to problems, where it has not been applied in the past. It is his hope that this monograph, along with its ¿spin-off¿ research will excite interest in the application of the Monte Carlo method to wave problems, to nonlinear problems and to problems with Neumann and mixed boundary conditions.