#ece1254

Marks are in for Winter 2016

I started my formal re-education program back in 2010 after 20 years out of school. The first few courses were particularly tough after such a long break from school (and exam based courses still are), but I’m getting the hang of playing that game again. Here’s my score so far:

Crs Code Title Wgt Mrk Grd CrsAvg PHY356H1 Quantum Mechanics I 0.50 78 B+ C+ PHY450H1 Rel Electrodynamics 0.50 78 B+ *…

[mathjax]

[Click here for a PDF of this post with nicer formatting]

Laplace transforms were used to solve the MNA equations for time dependent systems, and to find the moments used to in MOR.

For the record, the Laplace transform is defined as:

\begin{equation}\label{eqn:laplaceTransformVec:20} \boxed{ \LL( f(t) ) = \int_0^\infty e^{-s t} f(t) dt. } \end{equation}

The only Laplace transform pair…

ECE1254H Modeling of Multiphysics Systems. Lecture 19: Model order reduction (cont).. Taught by Prof. Piero Triverio

[mathjax]

[Click here for a PDF of this post with nicer formatting]

Disclaimer

Peeter’s lecture notes from class. These may be incoherent and rough.

Model order reduction (cont).

An approximation of the following system is sought

\begin{equation}\label{eqn:multiphysicsL19:20} \BG \Bx(t) + C \dot{\Bx}(t) = B \Bu(t) \end{equation} \begin{equation}\label{eqn:multiphysicsL19:40} \By(t) = \BL^\T \Bx(t).

Stability of discretized linear differential equations

[mathjax]

[Click here for a PDF of this post with nicer formatting]

In class today was a highlight of stability methods for linear multistep methods. To motivate the methods used, it is helpful to take a step back and review stability concepts for LDE systems.

By way of example, consider a second order LDE homogeneous system defined by

\begin{equation}\label{eqn:stabilityLDEandDiscreteTime:20} \f…

ECE1254H Modeling of Multiphysics Systems. Lecture 15: Nonlinear differential equations. Taught by Prof. Piero Triverio

[mathjax]

[Click here for a PDF of this post with nicer formatting]

Disclaimer

Peeter’s lecture notes from class. These may be incoherent and rough.

Nonlinear differential equations

Assume that the relationships between the zeroth and first order derivatives has the form

\begin{equation}\label{eqn:multiphysicsL15:20} F\lr{ x(t), \dot{x}(t) } = 0 \end{equation} \begin{equation}\label{eqn:multiphysi…

Current collection of multiphysics modeling notes (ece1254)

I’ve now posted v.1 of my current notes collection for “Modeling of Multiphysics Systems” (ECE1254H1F), a course I’m now taking taught by Prof. Piero Triverio. This includes the following individual lecture or personal notes, which may or may not have been posted as separate blog entries:

October 27, 2014 Struts and Joints, Node branch formulation

October 24, 2014 Conjugate gradient method

Octobe…

ECE1254H Modeling of Multiphysics Systems. Lecture 12: Struts and Joints, Node branch formulation. Taught by Prof. Piero Triverio

[mathjax]

[Click here for a PDF of this post with nicer formatting]

Disclaimer

Peeter’s lecture notes from class. These may be incoherent and rough.

Struts and Joints, Node branch formulation

Let’s consider the simple strut system of fig. 1 again.

fig. 1. Simple strut system

  Our unknowns are

Forces at each of the points we have a force with two components \begin{equation}\label{eqn:multiphysicsL…

ECE1254H Modeling of Multiphysics Systems. Lecture 11: Nonlinear equations. Taught by Prof. Piero Triverio

[mathjax]

[Click here for a PDF of this post with nicer formatting]

ECE1254H Modeling of Multiphysics Systems. Lecture 11: Nonlinear equations. Taught by Prof. Piero Triverio

Disclaimer

Peeter’s lecture notes from class. These may be incoherent and rough.

Solution of N nonlinear equations in N unknowns

We’d now like to move from solutions of nonlinear functions in one variable:

\begin{equation}\l…