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)
NEW:
new Lecture Notes & Slides (see 19)
new layout & amendments for all Lectures
Lecture Notes & Slides
Course Outline
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Mathematical Preliminaries
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Introduction to Partial Differential Equations
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Exercises on Partial Differential Equations
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Weigthed Residual Methods
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Ritz Method
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Introduction to Finite Element Method
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Heat Transfer Problems
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Galerkin Finite Element Model for Heat Transfer
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Exercises on Heat Transfer using COMSOL Multiphysics
Fundamentals of Linear Elasticity
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Exercises on Elasticity, Thermoelasticity, and COMSOL Multiphysics PDE Interfaces
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Fundamentals of Piezoelectricity
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Exercises on Piezoelectricity using COMSOL Multiphysics
Ideal Flow Theory and Basic Aerodynamics
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Elementary Viscous Flow
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Waves in Fluids
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Fundamentals of Acoustics
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Exercises on Acoustics and Vibroacoustics using COMSOL Multiphysics
Bulk and Surface Acoustic Waves in Piezoelectric Media
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Exercises on Piezoelectric Surface Acoustic Waves using COMSOL Multiphysics
Thematic Quiz
Quiz
- for the Introductory Course on Multiphysics Modelling (ICMM)
Course Outline
Introductory lectures:
General mathematical preliminaries
Basics of Partial Differential Equations
types and classifications
a review of solution techniques
a review of classic PDEs
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:
Heat transfer
Linear elasticity
Thermo-elasticity (thermo-mechanical coupling)
Fluid dynamics (and the basics of aerodynamics)
Waves in fluids
Fluid-structure interaction
Acoustics and vibroacoustics (acoustic-structure interaction)
Piezoelectricity (electro-mechanical coupling)
Wave propagation in anisotropic media
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