ECCE 753 Computational Prototyping of Dynamical Systems
This course covers the theory, algorithms, and best programming practices for the numerical simulation of dynamical systems. The course will draw examples from a variety of engineering disciplines, including electrical, mechanical, chemical, and aerospace engineering. Methods for the automatic generation of large-scale, state-space descriptions are presented. Direct and iterative techniques from numerical linear algebra are used to compute steady state solutions of linear systems. Numerical issues such as stability, pivoting, conditioning, and accuracy are discussed in depth. Special attention is given to sparse matrix techniques. Newton’s algorithm for finding the equilibrium points of non-linear systems is presented next along with the automatic generation of the companion models of nonlinear elements. For transient analysis, the course covers the numerical algorithms for the solution of non-linear ordinary differential equations using first-order and higher-order methods with emphasis on linear multistep methods. The stability and error theories of such methods are also covered. State-of-the-art topics related to the macromodeling of dynamical systems using model-order reduction methods will wrap up the course. One distinguishing feature of this course is a semester-long project that will result in the implementation of a full, working dynamical system simulator and its application to solve a computational problem in the student’s area of PhD research.