Introduction to Modelling of Multiphysics Problems

In the present Winter semester - from October 2017 to February 2018 - the lectures are on Wednesdays at 14:00, seminar room S-3 (on the 3rd floor) in IPPT PAN in Warsaw (ul. Pawinskiego 5B).

The subject of lectures on the 21st of February 2018:
Bulk and Surface Acoustic Waves in Piezoelectric Media

Introductory Course on Multiphysics Modelling (ICMM)

Tomasz G. Zieliński


  • new Lecture Notes & Slides (see 19)
  • new layout & amendments for all Lectures

Lecture Notes & Slides

  1. Course Outline    notes / slides
  2. Mathematical Preliminaries    notes / slides
  3. Introduction to Partial Differential Equations    notes / slides
  4. Exercises on Partial Differential Equations    notes / slides
  5. Weigthed Residual Methods    notes / slides
  6. Ritz Method    notes / slides
  7. Introduction to Finite Element Method    notes / slides
  8. Heat Transfer Problems    notes / slides
  9. Galerkin Finite Element Model for Heat Transfer    notes / slides
  10. Exercises on Heat Transfer using COMSOL Multiphysics
  11. Fundamentals of Linear Elasticity    notes / slides
  12. Exercises on Elasticity, Thermoelasticity, and COMSOL Multiphysics PDE Interfaces    notes / slides
  13. Fundamentals of Piezoelectricity    notes / slides
  14. Exercises on Piezoelectricity using COMSOL Multiphysics
  15. Ideal Flow Theory and Basic Aerodynamics    notes / slides
  16. Elementary Viscous Flow    notes / slides
  17. Waves in Fluids    notes / slides
  18. Fundamentals of Acoustics    notes / slides
  19. Exercises on Acoustics and Vibroacoustics using COMSOL Multiphysics
  20. Bulk and Surface Acoustic Waves in Piezoelectric Media    notes / slides
  21. Exercises on Piezoelectric Surface Acoustic Waves using COMSOL Multiphysics

Thematic Quiz

    Quiz - for the Introductory Course on Multiphysics Modelling (ICMM)

Course Outline

Introductory lectures:

  1. General mathematical preliminaries
  2. Basics of Partial Differential Equations
    • types and classifications
    • a review of solution techniques
    • a review of classic PDEs
  3. Fundamentals of Finite Element Method (FEM)
    • Weighted Residual Methods
    • Ritz-Galerkin method
    • the equivalence of strong and weak formulations
    • various FEM issues (procedures, shape functions, etc.)

Problems to discuss:

  1. Heat transfer
  2. Linear elasticity
  3. Thermo-elasticity (thermo-mechanical coupling)
  4. Fluid dynamics (and the basics of aerodynamics)
  5. Waves in fluids
  6. Fluid-structure interaction
  7. Acoustics and vibroacoustics (acoustic-structure interaction)
  8. Piezoelectricity (electro-mechanical coupling)
  9. Wave propagation in anisotropic media
  10. Surface Acoustic Waves

Each problem discussion should involve (some of) the following topics:

  • the derivation of the governing PDE (fundamental principles and constitutive laws, primary and secondary dependent variables)
  • a discussion of boundary conditions (from the physical and mathematical points of view)
  • the derivation of the weak formulation
  • the Galerkin's approximation (definitions and interpretations of coefficient matrices)
  • a discussion of analogies and possible couplings to other problems