Loading...
 

Numerical Simulation: EE/CS 219A, Fall 2009

Topics in Numerical Simulation and Modelling: EE 298-007, Fall 2009

Note: Berkeley's official catalog page for EE/CS 219A is out of date.

Links:


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 and mechanical systems. This course provides a detailed introduction to the fundamental principles of these technologies. 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 EECS 298-007 (Topics in Numerical Simulation/Modelling), during which discussions, coding demonstrations/practices, additional lectures, project presentations, etc., will be held.

This course is relevant to the BIO, CIR, DES, INC, MEMS, PHY and SCI areas of EECS, and 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 individual project as approved by instructor), and class attendance/participation.
Credits
  • EE/CS 219A (lectures): 3 credits. Course control number: 25757
  • EE 298-007 (discussion): 1 credit. Course control number: 25836
Class location and times
Textbook and Materials
  • Slides from class are available here.
Instructor
More links