finite element method (fem) & comsol multiphysics part i: quasi … · 2018-06-08 · 1 a....

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1 A. Rennings Finite Element Method (FEM) & Comsol Multiphysics Part I: Quasi-static Fields Nächste Veranstaltungen… 2 CoFT-1 Vorlesung Fr. 06.11.2009, 12:00 - 13:30, BA 349 COMSOL-Demo, drei einfache quasi-statische Beispiele mögliche Termine für CoFT-Lab (ca. 90 min, BA 328) Mo. AM PM Di. AM PM Do. AM PM Fr. leider nicht möglich, wegen GET-Praktikum „Kennenlernen“ der COMSOL-Software durch selbstständiges Durcharbeiten von Tutorials (unter Anleitung!)

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Page 1: Finite Element Method (FEM) & Comsol Multiphysics Part I: Quasi … · 2018-06-08 · 1 A. Rennings Finite Element Method (FEM) & Comsol Multiphysics Part I: Quasi-static Fields Nächste

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A. Rennings

Finite Element Method (FEM) & Comsol Multiphysics

Part I: Quasi-static Fields

Nächste Veranstaltungen…

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CoFT-1 Vorlesung

Fr. 06.11.2009, 12:00 - 13:30, BA 349

COMSOL-Demo, drei einfache quasi-statische Beispiel e

mögliche Termine für CoFT-Lab (ca. 90 min, BA 328)

Mo. AM PM

Di. AM PM

Do. AM PM

Fr. leider nicht möglich, wegen GET-Praktikum

„Kennenlernen“ der COMSOL-Software durch selbststän diges

Durcharbeiten von Tutorials (unter Anleitung!)

Page 2: Finite Element Method (FEM) & Comsol Multiphysics Part I: Quasi … · 2018-06-08 · 1 A. Rennings Finite Element Method (FEM) & Comsol Multiphysics Part I: Quasi-static Fields Nächste

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Outline

Objectives and additional Material

Page 3: Finite Element Method (FEM) & Comsol Multiphysics Part I: Quasi … · 2018-06-08 · 1 A. Rennings Finite Element Method (FEM) & Comsol Multiphysics Part I: Quasi-static Fields Nächste

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What can be solved using FEM?

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Static Fields I

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Page 4: Finite Element Method (FEM) & Comsol Multiphysics Part I: Quasi … · 2018-06-08 · 1 A. Rennings Finite Element Method (FEM) & Comsol Multiphysics Part I: Quasi-static Fields Nächste

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Static Fields II

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Electrodynamics

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What can be simulated using Comsol?

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What is FEM good for?

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Page 6: Finite Element Method (FEM) & Comsol Multiphysics Part I: Quasi … · 2018-06-08 · 1 A. Rennings Finite Element Method (FEM) & Comsol Multiphysics Part I: Quasi-static Fields Nächste

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The Finite Element Method

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Electrostatic model problem

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Page 7: Finite Element Method (FEM) & Comsol Multiphysics Part I: Quasi … · 2018-06-08 · 1 A. Rennings Finite Element Method (FEM) & Comsol Multiphysics Part I: Quasi-static Fields Nächste

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Trivial example: ideal homogeneous 2D plate capacit or

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Matrix equation: 1 st we neglect the essential BCs

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Page 8: Finite Element Method (FEM) & Comsol Multiphysics Part I: Quasi … · 2018-06-08 · 1 A. Rennings Finite Element Method (FEM) & Comsol Multiphysics Part I: Quasi-static Fields Nächste

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Matrix equation: natural BC on all boundaries,

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Matrix equation: Forcing the essential BC,

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Page 9: Finite Element Method (FEM) & Comsol Multiphysics Part I: Quasi … · 2018-06-08 · 1 A. Rennings Finite Element Method (FEM) & Comsol Multiphysics Part I: Quasi-static Fields Nächste

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Matrix equation: Forcing the essential BC,

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Matrix equation… only 3 unknowns left

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Page 10: Finite Element Method (FEM) & Comsol Multiphysics Part I: Quasi … · 2018-06-08 · 1 A. Rennings Finite Element Method (FEM) & Comsol Multiphysics Part I: Quasi-static Fields Nächste

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Demo 1: Surface charge of a metal cylinder

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Potential and total charge

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Value of surface integral: 3.109324e-10 [C], Expres sion: nD_emes, Boundaries: 2, 4, 5

Page 11: Finite Element Method (FEM) & Comsol Multiphysics Part I: Quasi … · 2018-06-08 · 1 A. Rennings Finite Element Method (FEM) & Comsol Multiphysics Part I: Quasi-static Fields Nächste

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TEM transmission lines (TLs) with homog. material

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Demo 2: Square coaxial cable

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Page 12: Finite Element Method (FEM) & Comsol Multiphysics Part I: Quasi … · 2018-06-08 · 1 A. Rennings Finite Element Method (FEM) & Comsol Multiphysics Part I: Quasi-static Fields Nächste

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Demo 2: Characteristic impedance

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Quasi-TEM TLs with inhomogeneous material

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Page 13: Finite Element Method (FEM) & Comsol Multiphysics Part I: Quasi … · 2018-06-08 · 1 A. Rennings Finite Element Method (FEM) & Comsol Multiphysics Part I: Quasi-static Fields Nächste

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Quasi-TEM TLs: alternative approach, if µ = const

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Demo 3: Microstrip line

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Page 14: Finite Element Method (FEM) & Comsol Multiphysics Part I: Quasi … · 2018-06-08 · 1 A. Rennings Finite Element Method (FEM) & Comsol Multiphysics Part I: Quasi-static Fields Nächste

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Demo 3: Microstrip line

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Lecture on 13.11.2009…

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Page 15: Finite Element Method (FEM) & Comsol Multiphysics Part I: Quasi … · 2018-06-08 · 1 A. Rennings Finite Element Method (FEM) & Comsol Multiphysics Part I: Quasi-static Fields Nächste

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1st CoFT-Lab on COMSOL

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