Introduction to Modelling of Multiphysics Problems

Dr. Tomasz G. Zieliński

The one-semester course is devoted to mathematical modelling of fundamental problems of physics with an emphasis put on existing or possible multiphysics couplings. It consists of a few introductory lectures concerning relevant mathematical tools and numerical methods, and a series of lectures devoted to single- and multi-physics problems.

Apart from some general mathematical preliminaries useful for the course, the introductory lectures present in a concise form the basics of Partial Differential Equations which are essential for modelling of the problems of physics (including a review of classic PDEs, their types and classifications, and solution techniques), as well as some fundamentals of the Finite Element Method which is one of the most important numerical techniques applied to solve a lot of practical problems (the FEM lectures will involve a discussion of Weighted Residual Methods, the equivalence of strong and weak forms, the Ritz-Galerkin method, some general topics concerning the shape functions and relevant procedures, etc.). The main problems and couplings addressed during the course are: the heat transfer, linear elasticity, thermo-elasticity (the thermo-mechanical coupling), fluid dynamics, acoustics, fluid-structure and acoustics-structure interactions, piezoelectricity (the electro-mechanical coupling).

The course will also provide the lecturers with a practical introduction to COMSOL Multiphysics envi-ronment, which is a powerful numerical tool for solving boundary-value and initial-boundary-value problems describing different coupled phenomena of physics, and moreover, allowing scientists and engineers to implement and test completely new models, in a modern and very effective manner involving symbolic expressions. This latter, non-standard approach will be especially treated during the lectures.

Lecture notes for the course (printable documents for reading as well as slides) are available on Internet at: