Numerical Simulation: EE/CS 219A, Spring 2009

Topics in Numerical Simulation and Modelling: EE 298-003, Spring 2009

Note: Berkeley's official catalog page for EE/CS 219A is out of date.

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Links:

• Lecture materials | Homeworks | Midterm | Final Exam

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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, biochemical systems, mechanical systems, etc.. This course provides a detailed introduction to the fundamental principles of these technologies.

The Spring 2009 offering of EE/CS 219A has been restructured and contains new material, including canonical DAE formulations, illustrative applications in several different domains (e.g., electronic circuits, biology, chemistry, nanoscale devices, mechanics and optoelectronics), and significant focus on uncertainty, randomness, variability and stochastic modelling/simulation techniques. It will emphasize hands-on programming and application to examples as an important means to understand and benefit from the material. Pre-requisites will be reviewed in class in order to make the course as self-contained as possible. Students are strongly encouraged to co-register in EE 298-003 (Topics in Numerical Simulation/Modelling), during which discussions, coding demonstrations/practices, additional lectures, etc., will be held.

This course is a part of Berkeley's Designated Emphasis in Computational Science and Engineering (CSE).

Syllabus

1. Introduction: Computational modelling/simulation for analog, RF and digital circuits, biology, mechanics, nanotechnology, optoelectronics and other domains.
2. Electronic device models: Constitutive relationships of common circuit elements. Linear and nonlinear resistors, capacitors, inductors, memristors. Simple semiconductor device models: diodes, BJTs, MOSFETs. Continuity, differentiability, smoothing.
3. Equation systems for electronics: Setting up circuit equations using KVL, KCL and branch constitutive relations. Sparse tableau, nodal, and modified nodal circuit equation formulations. Canonical DAE and ODE formulations.
4. Quiescent steady state simulation: Numerical solution of nonlinear algebraic equations. The ))Newton-Raphson(( method. DC analysis. NR initialization and limiting. Damped Newton.
5. Sparse matrix solution concepts: Jacobian matrices. The importance of sparsity. Gaussian Elimination. LU factorization. Pivoting for sparsity. Error buildup and stability. Iterative linear methods.
6. Equation systems from other domains: Biochemical rate equations. Circadian system and bursting neuron equations. Nanodevice equations. Optoelectronic and mechanical system examples.
7. Time-domain ODE/DAE simulation: Existence and uniqueness issues; initial conditions. Forward Euler, Backward Euler and Trapezoidal methods. Transient analysis. Stability and accuracy. Linear multi-step (LMS) methods. Stiff differential equations, stiffly stable methods.
8. Linear(ized) systems, frequency-domain simulation: Linear ODEs and DAEs. Relevance in applications. Linearization around quiescent steady state. Periodic steady states. AC analysis.
9. Basic noise simulation: Review of random variables and stochastic processes — probability distributions, autocorrelation functions, power spectral density. Types of noise sources. Noise in linear time-invariant systems. Stationary noise analysis for DAE/ODE systems. Connections with AC analysis.
10. Basic variability and sensitivity analysis: Linearization of parameter dependence. Propagation of Gaussian statistics. Principal components. Direct and adjoint DC sensitivity analysis. Basics of ))Monte-Carlo(( methods.
11. Stochastic modelling and simulation: Well-stirred systems. Master equations. Gillespie's stochastic simulation algorithm (SSA). Tau leaping. Langevin equations. Deterministic rate equations.
12. Basic model order reduction (MOR): The interconnect delay problem. Delay models, Elmore delay. Moments and moment matching. Padé approximation. Companion form realizations. Asymptotic Waveform Evaluation (AWE). Introduction to Krylov-subspace based MOR methods.

Course format

• The grade for the course will be based on assigned homeworks, a midterm exam, a final examination (or projects, TBD), and class attendance/participation.

Credits

• EE/CS 219A (lectures): 3 credits. Course control number: 25776
• EE 298-003 (discussion): 1 credit. Course control number: 25868

Class location and times

• Lectures (EE/CS 219A): M W 1-2:30pm
  • from Feb 18th: in 299 Cory Hall.
  • through Feb 16th: in 212 Cory Hall.
• Discussion (EE 298-003): W 3-4pm
  • from Feb 18th: in 299 Cory Hall.
  • through Feb 16th: in 45 Evans Hall 212 Cory Hall.

Textbook and Materials

• Slides/notes are available at the lecture materials page.

Instructor

• Prof. Jaijeet Roychowdhury.

More links

• UCB's online schedule of classes:
  • [http://osoc.berkeley.edu/OSOC/osoc?p_term=SP&p_classif=+Choose+a+Course+Classification+&p_deptname=+Choose+a+Department+Name+&p_presuf=+Choose+a+Course+Prefix%2FSuffix+&p_dept=EECS&p_course=219A&p_title=&p_instr=&p_exam=&p_ccn=&p_day=&p_hour=&p_bldg=&p_units=&p_restr=&p_info=&p_updt=&x=77&y=5|entry for EE/CS 219A]
  • [http://osoc.berkeley.edu/OSOC/osoc?p_term=SP&p_classif=+Choose+a+Course+Classification+&p_deptname=+Choose+a+Department+Name+&p_presuf=+Choose+a+Course+Prefix%2fSuffix+&p_dept=&p_course=&p_title=&p_instr=&p_exam=&p_ccn=25868&p_day=&p_hour=&p_bldg=&p_units=&p_restr=&p_info=&p_updt=&x=60&y=6|entry for EE 298-003]
• TeleBears registration website (information about registration)
• Other web pages for EE/CS 219A: EECS Dept. Courses page for 219A, cse.berkeley.edu page for 219A, bSpace page for 219A, inst.eecs.berkeley.edu page (out of date), official catalog page for EECS 219A (out of date)
• Previous offerings of EE/CS 219A: Spring 2006