Tentative Schedule of Lectures: EECS 219A, Fall 2012
August 2012
2012/08/27 (Mon):
- 1-2:30: Syllabus and logistics. Introduction. Modelling basic circuit elements: linear resistor, capacitor, inductor, controlled sources, independent sources.
2012/08/29 (Wed):
- 1-2:30 and 4-5: Modelling basic circuit elements (contd.): Linearity and memorylessness. Nonlinear devices: diode, BJT, MOS (Schichman-Hodges) models. Glimpse of BSIM model. Nonlinear capacitors and inductors. Derivatives, continuity concepts.
September 2012
2012/09/03 (Mon): NO CLASS (academic holiday - Memorial Day).
2012/09/05 (Wed):
- 1-2:30 and 4-5: Modelling ckt elements (contd.): Smoothing nonsmooth functions. Domain and finite-precision issues. Memristors. Circuit equation formulations: sparse tableau by example.
- 1-2:30: Circuit equation formulations: nodal analysis and modified nodal analysis by example. Standard DAE form. KVL and KCL using incidence matrices. Formulating Sparse Tableau, NA in general.
2012/09/12 (Wed):
- 1-2:30 and 4-5: Formulating MNA in general. DAEAPI introduction and demo. SPICE netlist syntax; parsing and equation setup. Mechanical equation system example. Quiescent steady state and NR: introduction.
- 1-2:30: NR contd: graphical interpretation, failure of NR, quadratic and linear convergence properties.
2012/09/19 (Wed):
- 1-2:30 and 4-5: NR contd: convergence criteria — deltax and residual, reltol-abstol. NR failure: ))Vsrc-R-diode(( example. Initialization and limiting for NR. Tradeoffs between init/limiting algorithms, equation formulations and code modularity.
- 1-2:30: Jacobian sparsity. Numerical solution of linear equation systems. Gaussian Elimination.
2012/09/26 (Wed):
- 1-2:30 and 4-5: LU factorization; forward and backward substitution. Matrix ordering for sparsity. Algebra of GE and LU. Matrix conditioning; error amplification in Ax=b solution.
October 2012
2012/10/01 (Mon):
- 1-2:30: Ax=b error growth in LU factorization. Pivoting for controlling error growth. Simple iterative techniques for linear solution.
2012/10/03 (Wed):
- 1-2:30 and 4-5: Basic data structures for sparse matrices; sparse matrix packages. Biochemical reaction pathways. Rate equations, conservation, equilibrium for unimolecular reactions. Eigenanalysis of unimolecular reactions. Bimolecular reactions. Rate equations for multi-molecular reactions.
- 1-2:30: Stoichiometry. Enzyme-catalyzed reactions and their ))Michaelis-Menten(( approximations.
2012/10/10 (Wed):
- 1-2:30 and 4-5: Using SVDs to identify conservation laws of reaction chains. Numerical solution of ODEs. Existence and uniqueness conditions. FE, BE and TRAP methods.
- 1-2:30: FE, BE and TRAP methods (contd.). LMS methods. Adapting LMS methods for solving DAEs.
2012/10/17 (Wed):
- 1-2:30 and 4-5: Adapting LMS methods for solving DAEs (contd.). Stability. Stiff systems and the need for "large" timesteps. Stability regions of FE, BE and TRAP. Small-timestep errors of FE, BE and TRAP. Accuracy and truncation error. Starting higher-order LMS methods. Exactness constraints for LMS methods.
- 1-2:30: Highest-accuracy p=2 LMS method. Stability of general LMS methods. The stability polynomial. Best p=2 method unstable for any h>0. Large-sigma behaviour of the trapezoidal method; TRAP and DAEs. Notions of timestep control. Periodic steady state analysis of LTI systems.
2012/10/24 (Wed): MIDTERM EXAM
- 1-2:30 and 4-5: MIDTERM exam. Midterm solution/discussion.
- 1-2:30: LTI DAEs. Linearization of nonlinear systems about quiescent steady states. Small-signal sinusoidal (SSS, aka "AC") analysis. Connection with Laplace-domain analysis.
2012/10/31 (Wed):
- 1-2:30 and 4-5: AC sweeps. Transfer function eigenanalysis. Parameter sensitivity analysis of QSS/DC operating points. Linearization of parameter dependence. Direct and adjoint methods for computing sensitivities. Introduction to noise analysis. Intuitive notions of noise.
November 2012
2012/11/05 (Mon):
- 1-2:30: Probability and random variables primer: Sampling a random variable. Histograms. From histograms to probability density functions. Gaussian and uniform distributions. Mean and variance derived from PDFs. PDFs of functions of RVs. Simultaneous sampling of several RVs - joint probabilities. Independence and correlation. Jointly Gaussian PDF.
2012/11/07 (Wed):
- 1-2:30 and 4-5: Stochastic processes primer: random variables as functions of time. Point-by-point and waveform ensemble views. Stationarity. Ergodicity. Stationary variance as average noise power. Autocorrelation function of a stationary stochastic process. Power spectral density. White noise. Thermal, shot and flicker noise. Propagation of stationary noise through LTI systems.
2012/11/14 (Wed):
- 1-2:30 and 4-5: Vector stochastic processes. Stationary noise computation for LTI systems: direct and adjoint methods. Stochastic modelling of biochemical systems. Well stirred systems. The concept of propensity. Basic reactions and their propensities.
- 1-2:30: State probabilities. The Chemical Master Equation. Example: CME for enzyme-catalyzed reaction system.
2012/11/21 (Wed):
- 1-2:30 and 4-5: Infeasibility of the CME for realistic problems. Waiting time probability to the next reaction. Propensity of the jth reaction after time tau. Next Reaction Index (NRI) and Time to Next Reaction (TtNR) as independent random variables, and their distributions. Gillespie's Stochastic Simulation Algorithm (SSA). Sampling NRI and TtNR. Example: SSA on enzyme-catalyzed reaction system.
- 1-2:30: Computational macromodelling. The model reduction problem. Algorithmic macromodelling. Model reduction for LTI systems. The concept of moments and its importance. LTI MOR via moment matching. Efficient moment computation using a single LU factorization of G. Pade approximants.
2012/11/28 (Wed):
- 1-2:30 and 4-5: Pade approximation. Computing the coefficients of the denominator and the numerator of the Pade rational function. Numerical conditioning issues. Why Pade approximants are better suited to DAE transfer functions than power series. From rational functions to companion form ODEs. Asymptotic Waveform Evaluation. Preview of Krylov subspace MOR methods.
2012/12/10 (Monday): FINAL EXAM 12pm-3pm; 293 Cory.