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Numerical Simulation and Modeling II: EECS 290A, Spring 2013


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Numerical simulation and computational modelling are technologies that pervade science and engineering, from electronics (e.g., analog/RF/mixed-signal circuits, high-speed digital circuits, interconnect, etc.) to optics, nanotechnology, chemistry, biology and mechanics.

This is a second course on these technologies, covering subjects beyond those in the first course 219A. Topics covered include continuation techniques for solving nonlinear equations, periodic steady state methods in the time and frequency domains, linearization around "large-signal" time-varying waveforms, Floquet analysis, analytical and numerical techniques for nonlinear oscillators (including oscillator phase macromodels) and Krylov-subspace concepts (including applications to linear system solution, periodic steady state computation and model order reduction of linear time-invariant systems). The impact of good modelling and equation setup practice on the effectiveness of simulation algorithms, i.e., the importance of a holistic approach to modelling and simulation, is an underlying theme in this course.

This course is relevant to the BIO, CIR, DMA, INC, MEMS, PHY and SCI areas of EECS.

Numerical Simulation and Modeling (219A) is a pre-requisite for taking this course.

Syllabus
  1. Introduction: Review of basic simulation algorithms from 219A.
  2. Numerical continuation: Continuation (homotopy) methods for solving "difficult" systems of nonlinear equations numerically.
  3. Shooting: Computing periodic steady state responses of non-autonomous systems in the time domain using "shooting" methods.
  4. Harmonic Balance: Harmonic balance (frequency domain) methods for computing periodic steady states of non-autonomous systems.
  5. Time-varying linearization: Linearizing nonlinear systems around large-signal waveforms. Numerical techniques for frequency- and time-domain solution of LPTV systems.
  6. Floquet theory: Eigenanalysis for linear periodically time varying (LPTV) systems.
  7. (Semi)-analytical techniques for LC and ring oscillators: Nonlinear feedback analysis techniques for estimating the amplitude and frequency of "negative-resistance" LC oscillators. Analytical expressions for the oscillatory waveforms of idealized ring oscillators.
  8. Periodic steady state analysis of oscillators: Applying shooting and harmonic balance to nonlinear oscillators.
  9. Phase macromodels of nonlinear oscillators: Theory and numerical methods for nonlinear phase macromodels of "amplitude-stable" oscillators. Analysing injection locking using phase macromodels.
  10. Linear solution using Krylov-subspace-based iterative methods: Krylov subspaces and their uses for solving Ax=b. GMRES and QMR.
  11. "Fast" computation of periodic steady states: Using iterative linear methods to make HB/shooting computationally scalable.
  12. Krylov-based LTI model reduction: Krylov subspace methods for model reduction of LTI systems.
Course format
  • The grade for the course will be based on assigned homeworks, a midterm exam, a final examination, and class attendance/participation.
Credits
  • 3 credits. Course control number: 25665
Class location and times
Textbook and Materials
  • Slides/notes will be made available to the students.
Instructor
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