This course is an introduction to computational techniques for the simulation of electrical circuits and systems with various applications being drawn from aerospace, mechanical, chemical and biological engineering, and materials science. Topics include: mathematical formulations; network problems; sparse direct and iterative matrix solution techniques; Newton methods for nonlinear problems; discretization methods for ordinary, time-periodic and partial differential equations, fast methods for partial differential and integral equations, techniques for dynamical system model reduction, approaches for molecular dynamics, and random simulation of digital systems under constraints and target objectives.
Although the title is verification, the specific focus is on verification through numerical simulation and in particular on the special numerical methods which allow efficient computation. This course covers the underlying methods used in the electrical simulation program SPICE. About 90% of the course deals with analog simulation, while the remainder is about recent methods used in the simulation of discrete systems.