1. S.S. Yang and J.K. Lee FEMLAB and its applications POSTEC H Plasma Application Modeling Lab. Oct. 25, 2005

2. Plasma Application Modeling @ POSTECH 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

3. Plasma Application Modeling @ POSTECH FEMLAB (COMSOL Multiphysics) 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” COMSOL Multiphysics Ver. 3.2 19951999200020012002200320042005 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). (Package name is changed)

4. 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             

5. Plasma Application Modeling @ POSTECH FEMLAB – modeling flow Application areas 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 FEMLAB modeling flow

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

7. Plasma Application Modeling @ POSTECH Draw toolbar Mesh generation SolverZoomView mode FEMLAB geometry and CAD environment 2-D In [Draw] menu, you also has the same toolbar buttons!

8. Plasma Application Modeling @ POSTECH FEMLAB geometry and CAD environment 3-D

9. Plasma Application Modeling @ POSTECH FEMLAB geometry and CAD environment 2-D draw toolbar 3-D draw toolbar

10. Plasma Application Modeling @ POSTECH Create Composite Object 2-D geometry drawing (1) Or Draw rectangle Draw triangle Open the Model Navigator and select 2D in the Space dimension list, then click OK

11. Plasma Application Modeling @ POSTECH In [Option] menu 2-D geometry drawing (2)   

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

13. Plasma Application Modeling @ POSTECH 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. 3-D geometry drawing (1)

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

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

16. Plasma Application Modeling @ POSTECH 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. 3-D geometry drawing (4)

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

18. Plasma Application Modeling @ POSTECH Then, using mesh buttons ( ), we can generate initial meshes and control the mesh density.    Generating mesh (2) Domain 1 Domain 2

19. Plasma Application Modeling @ POSTECH 1299 elements5196 elements 20784 elements Initialize MeshRefine Mesh Refine Mesh (again) 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. Generating mesh (3)

20. Plasma Application Modeling @ POSTECH Maximum element size scaling factor : 1 Element growth rate : 1.3 Maximum element size scaling factor : 2 Element growth rate : 1.3 Maximum element size scaling factor : 2 Element growth rate : 2 Element number :15 Element number :8 Generating mesh (4)

21. Plasma Application Modeling @ POSTECH The Mesh curvature factor determines the 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 : 0.3 Mesh curvature cut off : 0.001 Mesh curvature factor : 1 Mesh curvature cut off : 0.001 Mesh curvature factor : 0.3 Mesh curvature cut off : 0.1 Generating mesh (5)

22. Plasma Application Modeling @ POSTECH Generating mesh (6)

23. Plasma Application Modeling @ POSTECH Example 1 – model & structure Choose 2D, Electromagnetics, Electrostatics mode in Model Navigator At first, draw a rectangle and a small circle in the rectangle.

24. 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).

25. Plasma Application Modeling @ POSTECH 100V 0V Example 1 – boundary setting

26. Plasma Application Modeling @ POSTECH Example 1 – mesh and solver Generating mesh Postprocess - potentialPostprocess – electric field Postprocess - potential Running solver

27. Plasma Application Modeling @ POSTECH Example 2 – 2D PDP model & structure 200V0V 100V  = 1  = 12

28. Plasma Application Modeling @ POSTECH Generating mesh Postprocess - potentialPostprocess – electric field Postprocess - potential Running solver Example 2 – 2D PDP mesh and postprocess

29. Plasma Application Modeling @ POSTECH Example 2 – 3D PDP

30. Plasma Application Modeling @ POSTECH 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   

31. Plasma Application Modeling @ POSTECH Example 3 – Spherical Capacitor (2) Set boundary conditions Set subdomain 1 to Glass (quartz) material in Subdomain Setting. Generating meshPostprocess – electric potential Running solver   

32. Plasma Application Modeling @ POSTECH Example 3 – Spherical Capacitor C = 3.171097e-11 Calculation of capacitance C = 3.170985e-11 Postprocess – 3D plot