1. The use and application of FEMLAB
S.H.Lee and J.K.Lee
Plasma Application Modeling Lab.
Department of Electronic and Electrical Engineering
Pohang University of Science and Technology
24. Apr. 2006

2. What is FEMLAB?
FEMLAB : a powerful interactive environment for modeling and
solving various kinds of scientific and engineering problems based
on partial differential equations (PDEs).
Overview
Finite element method
GUI based on Java
Unique environments for modeling
(CAD, Physics, Mesh, Solver, Postprocessing)
Modeling based on equations (broad application)
Predefined equations and User-defined equations
No limitation in Multiphysics
MATLAB interface (Simulink)
Mathematical application modes and types of analysis
Mathematical application modes
1. Coefficient form : suitable for linear or nearly linear models.
2. General form : suitable for nonlinear models
3. Weak form : suitable for models with PDEs on boundaries, edges,
and points, or for models using terms with mixed space and time
derivatives.
Various types of analysis
1. Eigenfrequency and modal analysis
2. Stationary and time-dependent analysis
3. Linear and nonlinear analysis
*Reference: Manual of FEMLAB Software
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3. Useful Modules in FEMLAB
Application areas
Microwave engineering
Optics
Photonics
Porous media flow
Quantum mechanics
Radio-frequency components
Semiconductor devices
Structural mechanics
Transport phenomena
Wave propagation
Acoustics
Bioscience
Chemical reactions
Diffusion
Electromagnetics
Fluid dynamics
Fuel cells and electrochemistry
Geophysics
Heat transfer
MEMS
Additional Modules
1. Application of Chemical engineering Module
Momentum balances
- Incompressible Navier-Stokes eqs.
- Dary’s law
- Brinkman eqs.
- Non-Newtonian flow
Mass balances
- Diffusion
- Convection and Conduction
- Electrokinetic flow
- Maxwell-stefan diffusion and convection
Energy balances
- Heat equation
- Heat convection and conduction
2. Application of Electromagnetics Module
- Electrostatics
- Conductive media DC
Magnetostatic
Low-frequency electromagnetics
- In-plane wave propagation
Axisymmetric wave propagation
Full 3D vector wave propagation
Full vector mode analysis in 2D and 3D
3. Application of the Structural Mechanics Module
Plane stress
Plane strain
2D, 3D beams, Euler theory
Shells

4. FEMLAB Environment Model Navigator Pre-defined Equations
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5. User-defined Equations
Classical PDE modes
PDE modes ( General, Coefficient, Weak)
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6. Multiphysics Equations
Different built-in physics models are combined in the
multi-physics mode.
1. Select eqs.
2. Add used eqs. by using ‘add’ button.
3. Multi-eqs. are displayed here.
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7. FEMLAB Modeling Flow
In FEMLAB, use solid modeling or boundary modeling to create objects
in 1D, 2D, and 3D.
Draw menu
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8. Physics and Mesh Menus
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9. Solve and Postprocessing Menus
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10. Magnetic Field of a Helmholtz Coil
Introduction of Helmholtz coil
A Helmholtz coil is a parallel pair of identical circular coils spaced
one radius apart and wound so that the current flows through both
coils in the same direction.
This winding results in a very unifrom magnetic field between the
coils.
Helmholtz field generation can be static, time-varying, DC or AC,
depending on applications.
Domain equations and boundary conditions
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11. Procedure of Simulation (1)
1. Choose 3D, Electromagnetic Module, Quasi-statics mode in
Model Navigator.
2. After Application Mode Properties in Model Navigator is clicked,
the potential and Default element type are set to magnetic and
vector, respectively. Gauge fixing is off.
3. In the Options and setting menu, select the constant dialog box.
Define constant value (J0=1) in the constant dialog box.

12. Procedure of Simulation (2)
4. In the Geometry Modeling menu, open Work Plane Settings dialog
box, and default work plane is selected in x-y plane.
5. In the 2D plane, set axes and grid for drawing our simulation
geometry easily as follows,
6. Draw two rectangles by using Draw menu, then select these
rectangles . Click Revolve menu to revolve them in 3D.
In the 3D, add a sphere with radius of 1 and center of zero position.
It determines a calculation area.
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13. Geometry Modeling 2D plotting 3D plotting Revolve
Addition of a sphere with radius of 1 and center of zero position.
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14. -J0*z/sqrt(x^2+z^2) 0 J0*x/sqrt(x^2+z^2)
Procedure of Simulation (3)
7. In the Physics Settings menu, select boundary conditions, and use
default for boundary conditions.
Select the Subdomain Settings, then fill in conductivity and external
current density in the Subdomain Settings dialog box.
Subdomain 1
2,3  Je
0 0 0
-J0*z/sqrt(x^2+z^2) 0 J0*x/sqrt(x^2+z^2)

15. Procedure of Simulation (4)
8. Element growth rate is set to 1.8 in Mesh Parameters dialog box
in Mesh Generation menu, and initialize it.
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16. Result of a Helmholtz Coil
9. By using Postprocessing and Visualization menu, optimize your results.
by using the Suppress Boundaries dialog box in the Options menu,
suppress sphere boundaries (1, 2, 3, 4, 21, 22, 31, 32).
select Slice, Boundary, Arrow in the Plot Parameter.
In the Slice tab, use magnetic flux density, norm for default slice data.
In the boundary tab, set boundary data to 1.
In the Arrow tab, select arrow data magnetic field.
for giving lighting effect, open Visualization/Selection Settings dialog
box, and select Scenelight, and cancel 1 and 3.
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17. Heated Rod in Cross Flow
Introduction of Heated Rod in Cross Flow
Heat analysis of 2D cylindrical heated rod is supplied.
A rectangular region indicates the part of air flow.
A flow velocity is 0.5m/s in an inlet and pressure is 0 in an outlet.
The cross flow of rod is calculated by Incompressible Navier-Stokes
application mode.
The velocity is calculated by Convection and Conduction application
mode.
Procedure of simulation
1. Select 2D Fluid Dynamic, Incompressible Navier-Stokes, steady-state
analysis in the Model Navigator.
2. By using Draw menu, rectangle and half circle.
3. In the Subdomain Settings of Physics settings, enter v(t0)=0.5 in init tab.
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18. Subdomain Settings Subdomain settings (physics tab)
Subdomain settings (init tab)
4. In the Boundary Settings dialog box, all boundaries are set to
Slip/Symmetry. Boundaries of 7 and 8 are no-slip.
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19. Boundary Settings and Mesh Generation
Inflow boundary
outflow boundary
5. Generate Mesh, and click Solve button.
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20. Result of Velocity Flow
6. Add the Convection and Conduction mode in the Model Navigator.
7. In the Subdomain Settings, enter T(t0)=23 in the init tab of subdomain
of 1, 2.
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21. Solving Convection and Conduction Eq.
8. In the Boundary Settings dialog box, all boundary conditions are thermal
insulation. 2 and 5 have the following boundary conditions.
9. In the Solver Manager, click Solver for tab, and select convection and
conduction. Click a Solve button.
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22. Temperature Result of Heated Rod in Cross Flow
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23. Steady-State 2D Axisymmetric Heat Transfer with Conduction#3
Boundary conditions
#1,2 : Thermal insulation
#3,4,5 : Temperature
#6 : Heat flux #2 #4 #6 #1 #5
k=52W/mK
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24. Boundary condition variations - General Heat Transfer
Boundary conditions variation
At #1,2 boundaries,
Thermal insulation  Temperature
Boundary conditions variation
At #3 boundaries,
heat transfer coefficient is changed from 0 to 1e5.
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25. Permanent Magnet #1 Relative permeability At #1 subdomain : 1,#3 #2 #4
Magnetization
At #3 subdomain : 7.5e5 A/m,
#4 subdomain : -7.5e5 A/m
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26. Electrostatic Potential Between Two Cylinder
This 3D model computes the potential field in vacuum around two cylinders, one with a potential of +1 V and the other with a potential of -1 V.
zero charge
grounded
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27. Porous Reactor with Injection Needle
Inlet species A
Inlet species C
Inlet species B
A + B  C
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28. D: diffusion coefficient(5e-5) R: reaction rate(0) C: concentration(5)
Thin Layer Diffusion
D: diffusion coefficient(5e-5)
R: reaction rate(0)
C: concentration(5)
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29. Electromagnetic module(II) – Copper Plate
Introduction of copper plate
Imagine a copper plate measuring 1 x 1 m that also contains a small hole and suppose that you subject the plate to electric potential difference across two opposite sides.
Conductive Media DC application mode.
The potential difference induces a current.
Boundary conditions
B.1
B.4
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30. Electromagnetic module – Copper Plate
simulation Result
The plot shows the electric potential in copper plate.
The arrows show the current density.
The hole in the middle of geometry affects the potential and the current leading to a higher current density above and below the hole.
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31. 2D Steady-State Heat Transfer with Convection
Introduction of 2D Steady-State Heat Transfer with Convection
This example shows a 2D steady-state thermal analysis
including convection to a prescribed external (ambient) temperature.
2D in the Space dimension
the Conduction node & Steady-state analysis
Domain equations and boundary conditions
-Domain equation
-Boundary condition
material properties
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32. Heat Transfer - 2D Steady-State Heat Transfer with Convection
simulation Result( boundary : 100 ℃)
556 elements is used as mesh.
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33. 2D symmetric Transient Heat Transfer
Introduction of 2D Transient Heat Transfer with Convection
This example shows an symmetric transient thermal analysis with a step change to 1000 ℃ at time 0.
Domain equations and boundary conditions
-Domain equation
-Boundary condition
material properties
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34. Heat Transfer - 2D symmetric Transient Heat Transfer
simulation Result( T : 1000 time= 190s)
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35. Semiconductor Diode Model
Introduction of Semiconductor Diode Model
A semiconductor diode consists of two regions with different doping: a p-type region with a dominant concentration of holes, and an n-type region with a dominant concentration of electrons.
It is possible to derive a semiconductor model from Maxwell’s equations and Boltzmann transport theory by using simplifications such as the absence of magnetic fields and the constant density of states.
Domain equations and boundary conditions
-Domain equation
Where,
RSRH:
-Boundary condition
: symmetric boundary conditions
neumann boundary conditions
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36. Semiconductor Diode Model
Input parameter of Semiconductor Diode Model
Simulation result ( Vapply : 0.5V)
hole concentration
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37. Introduction of Pressure Recovery in a Diverging Duct
Momentum Transport
Introduction of Pressure Recovery in a Diverging Duct
When the diameter of a pipe suddenly increases, as shown in the figure below, the area available for flow increases. Fluid with relatively high velocity will decelerate into a relatively slow moving fluid.
Water is a Newtonian fluid and its density is constant at isothermal conditions.
Domain equations and boundary conditions
-Domain equation
: Navier-Stokes equation
continuity equation
0.135m
0.01m
0.005m
-Boundary condition
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38. Momentum Transport Input parameter of Semiconductor Diode Model
Simulation result ( Vmax : 0.02 )
velocity distribution
It is clear and intuitive that the magnitude of the velocity vector decreases as the cross-sectional area for the flow increases.
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