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					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

                                                Plasma Application
                                                Modeling @ POSTECH
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).

                                                                           Plasma Application
                                                                           Modeling @ POSTECH
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


                                                                                          Plasma Application
                                                                                          Modeling @ POSTECH
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

                                                            Plasma Application
                                                            Modeling @ POSTECH
Running of FEMLAB - Model Navigator
  When you run FEMLAB program, you     You can combine several modules
  meet Model Navigator from which      using Multiphysics function. Click OK,
  you can choose Space dimension and   then you can meet the interface to
  pre-defined equations and modules.   design the structures.


        Model Navigator                             Pre-defined equations




                                                                    Plasma Application
                                                                    Modeling @ POSTECH
FEMLAB geometry and CAD environment
   2-D
                                     Mesh Solver         Zoom   View mode
                                   generation




     Draw
    toolbar




In [Draw] menu, you also has the same toolbar buttons!                      Plasma Application
                                                                            Modeling @ POSTECH
FEMLAB geometry and CAD environment
 3-D




                                Plasma Application
                                Modeling @ POSTECH
FEMLAB geometry and CAD environment


 2-D draw
 toolbar




 3-D draw
 toolbar




                                Plasma Application
                                Modeling @ POSTECH
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




                                                           Plasma Application
                                                           Modeling @ POSTECH
2-D geometry drawing (2)
                          




    In [Option] menu


                           




                               Plasma Application
                               Modeling @ POSTECH
2-D geometry drawing (3)




                           Plasma Application
                           Modeling @ POSTECH
3-D geometry drawing (1)
  Open the Model Navigator         Go to the Draw menu and open the Work Plane
  and select 3D in the Space       Settings dialog box. Proceed to the Quick tab,
  dimension list, then click OK.   select the x-y button, and then click OK.




                                                                   Plasma Application
                                                                   Modeling @ POSTECH
3-D geometry drawing (2)
                          




                           




                               Plasma Application
                               Modeling @ POSTECH
3-D geometry drawing (3)
       In [Draw] menu




                           Plasma Application
                           Modeling @ POSTECH
3-D geometry drawing (4)
Go to the Draw menu and choose Extrude.
                                           Click the Zoom Extents button to optimize
Select CO2 and enter 0.2 in the Distance
                                           your view of the new geometry object.
field. Click OK.




                                                                    Plasma Application
                                                                    Modeling @ POSTECH
Generating mesh (1)
                     




                      




                          Plasma Application
                          Modeling @ POSTECH
Generating mesh (2)
 




                                        Domain 1




 

                                        Domain 2



                       Then, using mesh buttons (          ),
                         we can generate initial meshes and control
                         the mesh density.


                                                     Plasma Application
                                                     Modeling @ POSTECH
Generating mesh (3)
        Initialize Mesh                  Refine Mesh
        1299 elements                    5196 elements




       Refine Mesh (again)
                             By default, the maximum element size
        20784 elements       used is 1/15 (in 2D) of the maximum
                             axis parallel distance in the geometry.

                             However, we can control element size
                             and mesh density.



                                                         Plasma Application
                                                         Modeling @ POSTECH
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
   Maximum element size scaling factor : 2   Element growth rate : 2
   Element growth rate : 1.3




                                                                         Plasma Application
                                                                         Modeling @ POSTECH
Generating mesh (5)
                                             Mesh curvature factor : 0.3
 The Mesh curvature factor determines the    Mesh curvature cut off : 0.001
 size of boundary elements compared to the
 curvature of the geometric boundary

 The Mesh curvature cut off prevents the
 generation of many elements around small
 curved parts of the geometry




       Mesh curvature factor : 1             Mesh curvature factor : 0.3
       Mesh curvature cut off : 0.001        Mesh curvature cut off : 0.1




                                                                     Plasma Application
                                                                     Modeling @ POSTECH
Generating mesh (6)




                      Plasma Application
                      Modeling @ POSTECH
Example 1 – model & structure




   Choose 2D, Electromagnetics,   At first, draw a rectangle and a
   Electrostatics mode in Model   small circle in the rectangle.
   Navigator


                                                       Plasma Application
                                                       Modeling @ POSTECH
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).


                                               Plasma Application
                                               Modeling @ POSTECH
Example 1 – boundary setting




                               100V




                               0V




                               Plasma Application
                               Modeling @ POSTECH
Example 1 – mesh and solver



                             Running
                              solver


   Generating mesh                     Postprocess - potential




   Postprocess - potential             Postprocess – electric field

                                                                 Plasma Application
                                                                 Modeling @ POSTECH
Example 2 – 2D PDP model & structure



                   200V           0V

                       = 12

                      =1

                       = 12

                               100V




                                       Plasma Application
                                       Modeling @ POSTECH
Example 2 – 2D PDP mesh and postprocess



                             Running
                              solver


   Generating mesh                     Postprocess - potential




   Postprocess - potential             Postprocess – electric field

                                                                 Plasma Application
                                                                 Modeling @ POSTECH
Example 2 – 3D PDP




                     Plasma Application
                     Modeling @ POSTECH
Example 3 – Spherical Capacitor (1)
                                                 




         Axial symmetry (2D)
         Electromagnetics
         Electrostatics                               Axes/Grid setting in [Options]


                                                 




                                                       Draw the structure using circles,
     Define variables and expressions or values        rectangle, and composite object
                                                       function
                                                                            Plasma Application
                                                                            Modeling @ POSTECH
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

                                                      Plasma Application
                                                      Modeling @ POSTECH
Example 3 – Spherical Capacitor
                                        Calculation of capacitance




  Postprocess – 3D plot


                             1  1 
          Ri
                        Q
     V   E  er dR          
                             R R 
                       4    i  0        Q2
                                                , We   D  E dV
         R0
                                        C
                                           2 We
               Q         1 1                         
      C         4     
                         R R 
               V          i 0               C = 3.171097e-11
               C = 3.170985e-11

                                                          Plasma Application
                                                          Modeling @ POSTECH

				
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