S.S. Yang and J.K. Lee

S.S. Yang and J.K. Lee

FEMLAB and its applications

POSTECH

Plasma Application Modeling Lab.

Oct. 25, 2005

Plasma ApplicationModeling @ POSTECH

Contents

Introduction of FEMLABHow 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


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

1995 1999 2000 2001 2002 2003 2004 2005

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)


FEMLAB - Key featuresFast, 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


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


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.

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.

You can combine several modules using Multiphysics function. Click OK, then you can meet the interface to design the structures.


Draw toolbar

Mesh generation

Solver Zoom View mode

FEMLAB geometry and CAD environment

2-D

In [Draw] menu, you also has the same toolbar buttons!



3-D



2-D draw toolbar

3-D draw toolbar


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

Open the Model Navigator and select 2D in the Space dimension list, then click OK


In [Option] menu





Open the Model Navigator and select 3D in the Space dimension list, then click OK.

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.

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 (3)In [Draw] menu


Go to the Draw menu and choose Extrude. Select CO2 and enter 0.2 in the Distance field. Click OK.

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.

Click the Zoom Extents button to optimize your view of the new geometry object.



Generating mesh (1)


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

Generating mesh (2)

Domain 1

Domain 2


1299 elements 5196 elements

20784 elements

Initialize Mesh Refine 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)


Maximum element size scaling factor : 1Element growth rate : 1.3

Maximum element size scaling factor : 2Element growth rate : 1.3

Maximum element size scaling factor : 2Element growth rate : 2

Element number :15

Element number :8

Generating mesh (4)


The Mesh curvature factor determines the size of boundary elements compared to the curvature of the geometric boundary

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

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

Mesh curvature factor : 0.3Mesh curvature cut off : 0.001

Mesh curvature factor : 1Mesh curvature cut off : 0.001

Mesh curvature factor : 0.3Mesh curvature cut off : 0.1

Generating mesh (5)


Generating mesh (6)


Example 1 – model & structure

Choose 2D, Electromagnetics, Electrostatics mode in Model Navigator

Choose 2D, Electromagnetics, Electrostatics mode in Model Navigator

At first, draw a rectangle and a small circle in the rectangle.

At first, draw a rectangle and a small circle in the rectangle.


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).

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).


100V

0V

Example 1 – boundary setting


Example 1 – mesh and solver

Generating mesh

Postprocess - potential Postprocess – electric field

Postprocess - potential

Runningsolver


Example 2 – 2D PDP model & structure

200V 0V

100V

= 1

= 12

= 12


Generating mesh

Postprocess - potential Postprocess – electric field

Postprocess - potential

Runningsolver

Example 2 – 2D PDP mesh and postprocess


Example 2 – 3D PDP


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


Example 3 – Spherical Capacitor (2)

Set boundary conditions

Set subdomain 1 to Glass (quartz) material in Subdomain Setting.

Generating mesh Postprocess – electric potential

Runningsolver


Example 3 – Spherical Capacitor

dVW, W

QC e

e

ED2

2

C = 3.171097e-11

Calculation of capacitance

0

11

40

RR

QdRV

i

R

R

i

reE

0

114

RRV

QC

i

C = 3.170985e-11

Postprocess – 3D plot

Documents

S.S. Yang and J.K. Lee