Transcript 슬라이드 1 - Pohang University of Science and Technology

FEMLAB and its applications
S.S. Yang and J.K. Lee
Oct. 25, 2005
Plasma Application Modeling Lab.
POSTEC
H
Contents
Introduction
of
FEMLAB
How to run FEMLAB
How to draw geometry (2D and
3D)
How to generate meshes
Examples (Electro-static cases)
Parallel capacitor with dielectric circle
Plasma display panel structure
Spherical capacitor
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FEMLAB (COMSOL Multiphysics)
COMSOL
Multiphysics
Ver. 3.2
(Package name is changed)
1995
1999
2000 2001
2002 2003 2004
2005
COMputer SOLutions (COMSOL) is a Swedish-based software company in partnership
with Mathworks. They developed the PDE Toolbox for use with MATLAB, and more
recently the FEMLAB computing environment, also MATLAB based. Now, FEMLAB
is upgraded and program name is changed to “COMSOL Multiphysics”
FEMLAB has a powerful interactive environment for modeling and solving various
kinds of scientific and engineering problems using finite element method (FEM) based
on partial differential equations (PDEs).
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FEMLAB - Key features
 Fast, interactive and user-friendly Java-based graphical user interface for all steps of the modeling process
 Powerful direct and iterative solvers based on state-of-the-art C++ technology
 Linear and nonlinear stationary, time-dependent and eigen-value analyses of large and complex models
 Total freedom in the specification of physical properties, whether as analytical expressions or functions
 Unlimited multi-physics capabilities for coupling of all types of physics
 General formulations for quick and easy modeling of arbitrary systems of PDEs
 Built in CAD tools for solid modeling in 1, 2, and 3D
 CAD import and geometry repair of DXF (vector data format) and IGES (neutral data format) files
 Fully automatic and adaptive mesh generation with explicit and interactive control of mesh size
 Extensive model libraries that document and demonstrate more than 100 solved examples
 Parametric solver for parametric studies and efficient solution of highly nonlinear models
 Interactive post-processing and visualization using high performance graphics
 Smooth interface to MATLAB
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FEMLAB – modeling flow
Application areas
FEMLAB modeling flow
• Acoustics
• Bioscience
• Chemical reactions
• Diffusion
• Electromagnetics
• Fluid dynamics
• Fuel cells and electrochemistry
• Geophysics
• Heat transfer
• MEMS
• Microwave engineering
• Optics
• Photonics
• Porous media flow
• Quantum mechanics
• Radio-frequency components
• Semiconductor devices
• Structural mechanics
• Transport phenomena
• Wave propagation
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Running of FEMLAB - Model Navigator
When you run FEMLAB program, you
meet Model Navigator from which
you can choose Space dimension and
pre-defined equations and modules.
Model Navigator
You can combine several modules
using Multiphysics function. Click OK,
then you can meet the interface to
design the structures.
Pre-defined equations
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FEMLAB geometry and CAD environment
2-D
Mesh Solver
generation
Zoom
View mode
Draw
toolbar
In [Draw] menu, you also has the same toolbar buttons!
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FEMLAB geometry and CAD environment
3-D
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FEMLAB geometry and CAD environment
2-D draw
toolbar
3-D draw
toolbar
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2-D geometry drawing (1)
Open the Model Navigator
and select 2D in the Space
dimension list, then click OK
Draw rectangle
Draw triangle
Create Composite Object
Or
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2-D geometry drawing (2)


In [Option] menu

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2-D geometry drawing (3)
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3-D geometry drawing (1)
Open the Model Navigator
and select 3D in the Space
dimension list, then click OK.
Go to the Draw menu and open the Work Plane
Settings dialog box. Proceed to the Quick tab,
select the x-y button, and then click OK.
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3-D geometry drawing (2)



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3-D geometry drawing (3)
In [Draw] menu
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3-D geometry drawing (4)
Go to the Draw menu and choose Extrude.
Select CO2 and enter 0.2 in the Distance
field. Click OK.
Click the Zoom Extents button to optimize
your view of the new geometry object.
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Generating mesh (1)



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Generating mesh (2)

Domain 1

Domain 2
 Then, using mesh buttons (
),
we can generate initial meshes and control
the mesh density.
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Generating mesh (3)
Initialize Mesh
Refine Mesh
1299 elements
5196 elements
Refine Mesh (again)
20784 elements
By default, the maximum element size
used is 1/15 (in 2D) of the maximum
axis parallel distance in the geometry.
However, we can control element size
and mesh density.
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Generating mesh (4)
Element number :15
Maximum element size scaling factor : 1
Element growth rate : 1.3
Element number :8
Maximum element size scaling factor : 2
Element growth rate : 1.3
Maximum element size scaling factor : 2
Element growth rate : 2
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Generating mesh (5)
The Mesh curvature factor determines the
size of boundary elements compared to the
curvature of the geometric boundary
Mesh curvature factor : 0.3
Mesh curvature cut off : 0.001
The Mesh curvature cut off prevents the
generation of many elements around small
curved parts of the geometry
Mesh curvature factor : 1
Mesh curvature cut off : 0.001
Mesh curvature factor : 0.3
Mesh curvature cut off : 0.1
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Generating mesh (6)
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Example 1 – model & structure
Choose 2D, Electromagnetics,
Electrostatics mode in Model
Navigator
At first, draw a rectangle and a
small circle in the rectangle.
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Example 1 – subdomain setting
In Physics, Subdomain Setting menu,
define the characteristics of each domain.
To set the material properties, you can use
Library material. In this example, let’s
assume that subdomain 1 is air(=1) and
subdomain 2 is silicon (~12).
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Example 1 – boundary setting
100V
0V
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Example 1 – mesh and solver
Running
solver
Generating mesh
Postprocess - potential
Postprocess - potential
Postprocess – electric field
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Example 2 – 2D PDP model & structure
200V
0V
 = 12
=1
 = 12
100V
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Example 2 – 2D PDP mesh and postprocess
Running
solver
Generating mesh
Postprocess - potential
Postprocess - potential
Postprocess – electric field
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Example 2 – 3D PDP
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Example 3 – Spherical Capacitor (1)


Axial symmetry (2D)
Electromagnetics
Electrostatics

Axes/Grid setting in [Options]

Define variables and expressions or values
Draw the structure using circles,
rectangle, and composite object
function
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Example 3 – Spherical Capacitor (2)
 Set boundary conditions

Set subdomain 1 to Glass
(quartz) material in
Subdomain Setting.

Running
solver
Generating mesh
Postprocess – electric potential
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Example 3 – Spherical Capacitor
Calculation of capacitance
Postprocess – 3D plot
Ri
V   E  e r dR 
R0
C 
Q 1
1 
  
4  Ri R0 
1 1 
Q
 4   
V
 Ri R0 
Q2
C
, We   D  E dV
2 We

C = 3.171097e-11
C = 3.170985e-11
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