ECE1254H - Modeling of multiphysics systems

Blood flow visualization 

Blood flow simulation (Argonne National Labs)

Course description

The course deals with the modeling and simulation of physical systems. It introduces the fundamental techniques to generate and solve the equations of a static or dynamic system. Special attention is devoted to complexity issues and to model order reduction methods, presented as a systematic way to simulate highly-complex systems with acceptable computational cost. Examples from multiple disciplines are considered, including electrical/electromagnetic engineering, structural mechanics, fluid-dynamics. Students are encouraged to work on a project related to their own research interests.


  • Automatic generation of system equations

    • Tableau method

    • modified nodal analysis

  • Solution of linear and nonlinear systems

    • LU decomposition

    • conjugate gradient method

    • sparse systems

    • Newton-Raphson method

  • Solution of dynamical systems

    • Euler and trapezoidal rule

    • accuracy, stability

  • Model order reduction of linear systems

    • proper orthogonal decomposition

    • Krylov methods

    • truncated balanced realization

    • stability/dissipativity enforcement

  • Modeling from experimental data

    • system identification

    • the Vector Fitting algorithm

    • enforcement of stability and dissipativity

  • If time permits, an overview of numerical methods to solve partial differential equations

    • Boundary element method

    • finite elements

    • FDTD

Lecture times

Tuesday 3:30-5 PT473 (Pratt Building)
Wednesday 4:30-6 PT473 (Pratt Building)
First class: January 15