An Introductory Course on
Multiphysics Modelling

  • General information:  Advanced one-semester course (ETCS: 4) delivered in English for postgraduate and PhD students
  • Author / Lecturer:  Tomasz G. Zieliński, DSc, PhD, MSc, Eng
  • Location:  Institute of Fundamental Technological Research of the Polish Academy of Sciences (IPPT PAN), Warsaw, Poland
  • Contact:  tzielins@ippt.pan.pl

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. Weighted 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 FEM for Heat Transfer → notes / slides
  10. Tutorials on Heat Transfer using COMSOL Multiphysics
  11. Fundamentals of Linear Elasticity → notes / slides
  12. Tutorials on Elasticity and Thermoelasticity using COMSOL Multiphysics
  13. Tutorials on Weak and Strong Form model implementation using COMSOL Multiphysics PDE Interfaces → notes / slides
  14. Fundamentals of Piezoelectricity → notes / slides
  15. Tutorials on Piezoelectricity using COMSOL Multiphysics
  16. Ideal Flow Theory and the Basics of Aerodynamics → notes / slides
  17. Elementary Viscous Flow → notes / slides
  18. Tutorials on Fluid-Structure Interaction (FSI) using COMSOL Multiphysics
  19. Waves in Fluids → notes / slides
  20. Basics of Multiscale Modelling: Tutorial on Porous Media Flow using COMSOL Multiphysics → slides
  21. Fundamentals of Acoustics → notes / slides
  22. Tutorials on Acoustics and Vibroacoustics using COMSOL Multiphysics
  23. Bulk and Surface Acoustic Waves in Piezoelectric Media → notes / slides
  24. Tutorials on Piezoelectric Surface Acoustic Waves using COMSOL Multiphysics

Thematic Quiz

  • Quiz ← for the Introductory Course on Multiphysics Modelling

Course Outline

Introductory lectures:

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

Main problems to discuss:

  1. Heat transfer
  2. Linear elasticity and elastodynamics
  3. Thermo-elasticity (thermo-mechanical coupling)
  4. Fluid dynamics and the basics of aerodynamics
  5. Waves in fluids (water waves, capillary waves, etc.)
  6. Fluid-structure interaction
  7. Acoustics (sound wave propagation and absorption)
  8. Vibroacoustics (acoustic-structure interaction)
  9. Piezoelectricity (electro-mechanical coupling)
  10. Wave propagation in anisotropic media
  11. Surface acoustic waves (Rayleigh and Lamb waves)
  12. Multi-scale modelling (example: transport in porous media)

The following topics are discussed for physical problems:

  • Derivation of the governing PDE based on fundamental principles and constitutive laws (primary and secondary dependent variables)
  • Discussion of boundary conditions from a physical and mathematical perspective
  • Derivation of the weak formulation
  • The Galerkin approximation (interpretations of the coefficient matrices)
  • Analogies and possible couplings with other problems

Introduction to COMSOL Multiphysics

  • A brief, selective summary of short courses conducted at IPPT PAN on Theoretical and Practical Introduction to COMSOL Multiphysics → notes / slides