1

Visualizing the Physical Phenomena for Computational Science

with MATFORMATFOR®® 44

Liger Chen AnCAD Inc.

2

Outline

Introduction to MATFOR®

MATFOR® Functions

Cases Using MATFOR®

Visualization of Physical Problem

by MATFOR®

3

Introduction to MATFOR®

4

What’s MATFOR® ?

� MATFOR® is a new generation graphics library fully exploiting the

modules and the array features of Fortran 90/95 and C++ languages.

� MATFOR® is a collection of high-level graphical procedures

developed with the mission of reducing time spent on the program

development.

� MATFOR® is a set of numerical and visualization

libraries especially designed for programmers in

scientific computing field.

5

MATFOR® Structure

MATFOR®, a set of numerical and visualization libraries, is

developed to enhance programming in C++ and Fortran

environments. Especially designed for scientists and engineers,

MATFOR® fulfills the needs of speed and advanced visualization

capabilities simultaneously.

MATFOR

Graphics LibraryGraphics Library Numerical LibraryNumerical Library

VTK OpenGL Intel MKL

6

Numerical Library

Based on Intel® MKL, the numerical library contains over 200 easy-to-use numerical functions subject to assist users with computational problem-solving.

– Data Manipulation Functions: mfSort, mfMin, mfMax, …

– Elementary Math Functions: mfSin, mfCos, mfASin, mfExp, mfAbs, …

– Elementary Matrix-Manipulating Functions: mfEye, mfDiag, mfRand, mfZeros, …

– Matrix Analysis: mfEig, mfInv, mfSvd, mfQz, mfLu, mfDet, mfNorm, …

– Sparse Array:

msSpAdd, msSpSet, mfSpNNZ,mfSpLDiv,…

– File IO: mfSave, mfSaveAscii, mfLoad, mfLoadAscii, …

7

Graphics LibraryVisualization Modules I

surf mesh

plot

plot3

contour contour3

quiverquiver3

trimesh trisurf

pcolor molecules

surf mesh

solidcontour

8

Graphics LibraryVisualization Modules II

ribbon

contour3 solidconour3 molecule image

tetmesh tetcontour tetisosurface cube, sphere, …

slicesisosurface tube

tricontour

tetsurf

streamline

9

What Does MATFOR® Do?

By adding few lines of By adding few lines of

MATFORMATFOR®® codes to codes to

your Fortran/C/C++ your Fortran/C/C++

program, you can easily program, you can easily

visualize your visualize your

computing results, computing results,

performperform runrun--timetime

animations, or even animations, or even

produce an interactive produce an interactive

movie presentation as movie presentation as

you execute your you execute your

program.program.

…

call msSurf(x)call msDrawNow

10

MATFOR® Functions

11

MATFOR® Dynamic Array ImfArray Overview

mfArray is an advanced dynamic array defined by MATFOR® using

modern features of C++ and Fortran 90/95. The mfArray data type

consists of descriptors and values.

Values

2(3,3)

9(3,2)

4(3,1)

7(2,3)

5(2,2)

3(2,1)

6(1,3)

1(1,2)

8(1,1)

Descriptors

•Data Type

•Shape

•Status Flags

mfArray

12

MATFOR® Dynamic Array IImfArray Feature

A key to integrate MATFOR® toolkit into high-level

programming environments

� Automatic data typing and dimensioning

� Dynamic memory allocation

� Simple calling routines with Matlab-like syntax

type(mfArray)::x,y

x = mfMagic(5)

y = mfInv(x)

mfArray x,y;

x = mfMagic(5);

y = mfInv(x);

FortranC/C++

Construct and initialize the mfArray

13

Simple Using Mathmatical functions

� Calling msSVD in MATFOR® to perform singular value decomposition gives the same result as calling DGESVX in LAPACK. However, MATFOR® function only takes 3 pre-initialized parameters while LAPACK function takes 22 pre-initialized parameters.

Call DGESVX( FACT, TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV, EQUED, R, C,

B, LDB, X, LDX, RCOND, FERR, BERR, WORK, IWORK, INFO ) LAPACK

Call msSVD( mfOut(A, B), C )

MATFOR

� Besides its simple and powerful visual functions, MATFOR® enables scientists and engineers to code in Matlab fashion using the simple calling concept in Fortran and C++ environments.

MATFOR a = mfInv(x) e = mfEig(x)

MATLAB a = inv(x) e = eig(x)

14

• Solving the symmetric tridiagonal matrix problem :

subroutine tridib(n,eps1,d,e,e2,lb,ub,m11,m,w,ind,ierr,rv4,rv5)

lamda= w LAPACK

eps1,lb,ub ,m11 , lb ,eps1,lb,ub ,m11 , lb ,eps1,lb,ub ,m11 , lb ,eps1,lb,ub ,m11 , lb ,indindindind , , , , ierrierrierrierr ,rv4 ,and rv5 = ????,rv4 ,and rv5 = ????,rv4 ,and rv5 = ????,rv4 ,and rv5 = ????

lamda = mfEig(x)MATFOR

(this eigsystem problem maybe be the reduction of a 2nd order differential equation

0))(()()(2

2

=−++ yxcdx

dyxb

dx

ydxa mλ

1,,1

2

1

2

1

,1,

,1

2,3

3,22,21,2

2,11,1

00

0

00

0

00

++

−

−

=

=

pppp

nnnnnn

nn

CC

y

y

y

y

y

y

CC

C

C

CCC

CC

M

M

M

M

L

OOM

OO

M

L

λ

15

Real-Time Animation

MATFOR® features real-

time program-monitoring mechanism to reduce time and effort spent on

post-processing and

debugging.

• MATFOR presenting simulation while calculating the data.

The simulation can be

presented as an animation

while the calculation is

proceeded and shown in

the console window.

16

MATFOR® Sample Code3D Presentation

program main

use fmluse fgl! Declare mfArray variablestype(mfArray) :: x, y, z

! Construct grid matrices for 3D plotcall msMeshgrid(mfOut(x, y), mfLinspace(-3,3,30), mfLinspace(-3,3,30))! Calculate Z valuez = mfSin(x) * mfCos(y) ! Plot surfcall msSurf(x,y,z)! Display the graphcall msViewPauseend program demo codes • MATFOR presents standalone

executables.

• MATFOR Standalone Executables

EXE

17

MATFOR® Sample CodeMovie Presentation

program main

use fmluse fgl

type(mfArray) :: x, y, z, h ! Declare mfArray variablesinteger(4) :: I ! Declare an integer variable

! Construct grid matrices for 3D plotcall msMeshgrid(mfOut(x, y), mfLinspace(-3,3,30), mfLinspace(-3,3,30))call msRecordStart('demo.avi') ! Begin AVI recording

do i=1,50 ! Do loopwrite (*,*) 'step=', iz = mfSin(x+i/8.0d0) * mfCos(y) ! Calculate Z valueif (i==1) then ! Initialize handle

h = mfSurf(x, y, z)call msDrawNow

elsecall msGSet(h, 'zdata', z) ! Update Z valuecall msDrawNow

end ifend do

call msRecordEnd ! End recordingcall msViewPause ! Pause to display the graph

end program

demo codes

• Viewing the recorded AVI file with media player.

• Movie FilesAVI

18

Runtime Data Manipulation

MATFOR® allows manipulation of the data displayed during execution; data can be examined with higher precision and customization at

runtime.

• Data Viewer• Graphics Viewer

19

Data Viewer

Snapshot Panelcaptures the snapshot of

the distribution and size of

the two dimensional data.Analysis Panel

shows the distribution of

the data including its

average, standard

deviation and min/max

values.Filter Panel

defines a range using

conditions of inequalities.

MATFOR® Data Viewer is a powerful tool that displays simulating data in a

spreadsheet format.

• Snapshot Panel

• Analysis Panel

• Filter Panel

20

Supported Data File Formats

MATFOR 4 supports common software data formats and 3-D object formats to enhance the reusability and interchangeability of data.

– Matlab

– Tecplot

– 3DS, OBJ, and STL

21

Graphics Viewer

MATFOR® Graphics Viewer provides a full range of graphical editing

procedures which can be manipulated directly using the menu and the toolbar.

• Axis Setting Editor • Colormap Setting Editor

• Material Setting Editor

22

Enhanced Graphics Viewer(Full-Screen Function)

The full-screen function allows users to view and/or present data at full screen. This function also serves to eliminate the context for on-screen data capturing and printing.

• Use the button indicated to show the graphs in full screen mode

Full Screen Mode

23

MATFOR® mfPlayerAn exclusive Visual Tool

mfPlayer is an exclusive visual tool by which the previously saved numerical data is read and displayed as an interactive movie presentation. As MATFOR® saves the simulated data into a MATFOR®-defined MFA file, mfPlayer is one approach to present the recorded animation. The complete video clip can then be viewed from different angles.

� resize

� rotate

� zoom

� pause

� forward

� reward

� view data

� change colormaps

• mfPlayer

• Data Viewer

24

mfPlayer Standalone

� Currently, the proprietary format dominates in most

visualization tools generates files that can only be executed on one specific application.

� MATFOR® possesses the ability to convert visualization files into standalone executables.

� Through the conversion, data sharing and publishing become much easier.

Compiling and linking the programs with MATFOR library.

Running compiled executables without installing MATFOR.

25

MATFOR® GUI Builder

MATFOR® GUI Builder allows users to customize an interface of their own; the interface can be saved into a MFUI file (based on XML format).

• MATFOR GUI Builder

MFUI

26

MATFOR® GUI System (An Use Case)

btnSurf1

!////////////////////////////////////////////////////////////!// MxUI Callback BEGINsubroutine btnSurf_Click(sender)use fmluse fgluse mxui

CHARACTER(*) :: senderinteger :: kindtype(mfArray) :: x, y, zexternal btnClose_Click

call msFigure()kind = mfUIGetPropertyInteger( sender, 'tag' )call msCreateSurfData( mfOut(x,y,z), mf(kind), mf(30), mf(30) )call msSurf(x,y,z)call msDrawNow

end subroutine btnSurf_Click

!// MxUI Callback END!////////////////////////////////////////////////////////////

Actor

Application

Click

• How does the communication work between the user and the application?

UI Engine

27

Cases Using MATFOR®

AnCAD Incorporated

28

Applied Fields

Solid Mechanics

Fluid Dynamics

Astrodynamics

Electromagnetic Analysis

Heat Transfer and Geology Analysis

Optical propagation

Molecular Dynamics

29

Thin-plate Vibration Analysis

(Data courtesy of Yuan-Sen Yang, National Center for Research on Earthquake Engineering)

Force Impulse

Fixed Boundary

Plate

Displacement

Speed

Acceleration

Stress

30

(Data courtesy of Professor Edward C. Ting/Chih-Cheng Lin, National Central University)

Simulation of the nonlinear, nonconsecutive destructive phenomenon of the dam structure based on the finite element method.

Destructive External Force

Elastic Material

3D Co-rotational Explicit Finite Element Analysis

31

Structural Earthquake Response

Beam Structure

Observation PointDisplacement

Moment

(Data courtesy of Professor Yuan-Sen Yang, National Center for Research on Earthquake Engineering)

32

(Data courtesy of Professor Edward C. Ting/Yeh-Chan Lin/Chih-Cheng Lin, National Central University)

Acting Force

Crack SupportSupport

Concrete Fracture 2D Analysis

33

Fluid Field Direction

Contaminant Obstacle

Reynolds number=100

Obstacle

Contaminant

(Data courtesy of Ming-Hsin Su, AnCAD, Inc.)

Fluid Field Turbulence I

34(Data courtesy of Dr. Lin and Dr. Huang, Institute of Science and Technology)

High-pressure wave

Sharp Obstacle

High Pressure Reflection

35

Channel Narrowing

Floodway

(Data courtesy of Ming-Hsin Su, AnCAD, Inc.)

Fluid Field Turbulence II

36

3D Inkjet System Simulation I

Blue Print

(Data courtesy of Weng-Sing Huang/Hsuan-Chung Wu, National Cheng Kung University) O

pen E

nd

Clo

se E

nd

Cavity

Flu

id

Sup

ply

Orific

e

Nozzle

L

PZ

T

Squeeze Tube Mode Inkjet Printhead

80 40 80

160

800

Unit: μm

37

(Data courtesy of Weng-Sing Huang/Hsuan-Chung Wu, National Cheng Kung University)

Computer Simulation

3D Inkjet System Simulation II

Time: 0 20 26 32 38 44 50 56

62 68 74 80 [μs ]

break

38

3D Solar System Model

(Data courtesy of Li-Ger Chen, AnCAD, Inc.)

39 (Data courtesy of Chun-Hao Teng, AnCAD, Inc.)

EM-impulse

Perfectly Matched Layer

Amplitude

EM-wave Scattering on Perfectly Matched Layer

40

(Data courtesy of Ruey-Beei Wu/Kuang-Hua Hsueh, National Taiwan University)

Single microstrip line crossing slot

CurrentSlot

Current Layer

Ground Layer Amplitude

Multi-layer Ground Noise in a Current Field I

41

Differential microstrip line crossing

slot (coupling factor = 0.305)

ground plane

power planeSlotline

CurrentSlot

Current Layer

Ground Layer Amplitude

(Data courtesy of Ruey-Beei Wu/Kuang-Hua Hsueh, National Taiwan University)

Multi-layer Ground Noise in a Current Field II

42

Micro-magnetic Simulations

(Data courtesy of Professor Lee, Ching-Ming, Chungchou Institute of Technology. )

43(Data courtesy of Department of Physics & Astronomy, University of St Andrews, UK)

The blueprint of future integrated optical circuits.

Photonic Band Gap Waveguide Transmission I

44

(Data courtesy of Dr. Pei-Kun Wei, Academia Sinica, Taiwan)

AmplitudeLight Source

Line Defect

Photonic Band Gap

Photonic Band Gap Waveguide Transmission II

45(Data courtesy of Yu-Jen Lin, Precision Instrument Development Center)

Wave Source

Obstacle

Wave Source

Obstacle

Finite-difference Time-domain Analysis

46

(Data courtesy of Tung-Lung Fu, Precision Instrument Development Center)

Light Source

Micro-lens

Analysis of Optical Thin-film Coated Micro-lens

47 (Data courtesy of Chin-Hsiang Cheng, Tatung University)

30 nm

Water Molecules

Water Molecule Phase Transition

48

Ion Perturbation Analysis

(Data courtesy of Yu-Chang Sheng, National Taiwan University)

Ion A

Ion BDistance between ions A and B

49

Visualization of Physical Problem

by MATFOR®

50

Electromagnetic Radiation

• Dipole

• Quadrupole

axial separation

laterial separation

2

2

3

42

0 1)(sin

42

1

rc

pnS θ

ω

π=⋅

vv

[ ]2

22

5

6

2

2 1)cos(sin)(sin

322

1

rkd

c

QnS θθ

ω

π=⋅

vv

2

22

3

42

0 1)cos()sin(

2sin)(sin

2

1

r

kd

c

pnS

=⋅ ϕθθ

ω

π

vv

逸奇科技. www.AnCAD.com

Visualizing the Radiation Pattern

52

Diffraction Integral

• Fresnel-Kirchhoff :

• Frauhofer :

∫ +=σ

θλ

ψψ da

r

e

iP

ikr

))cos(1(2

1)( 0

∫+−=

σ

βηαξ ηξλ

ψβαψ dde

Z

e

i

ik

ikR

)(01),( )

))(( βηαξλ +≈∴>>>> RrDR

53

Slit Diffraction

• In one dimensional ,The Fraunhofer Diffraction Integral becomes :

• If the slit is of width 2a, then the integral is :

∫−=

σ

αξ ξαψ deCik)(

∫−

− ====a

a

ik akauu

uCadeC )sin(

2,)

)sin((2)( θ

λ

παξθψ αξ

逸奇科技. www.AnCAD.com

Visualization of the Slit Diffraction

55

Circular Aperture

)sin(),cos()( )( ϕρηϕρξηξψσ

βηαξ === ∫+−

ddeCPik

)'cos( ϕϕρθβηαξ −=+

2

0

22

2

02

0

0

0

2

0

cos

)(,2

))(

(2)(2)(

ψλ

ππθ

λ

π

πρρθπρθρθψπ

ϕρθ

Z

aCaau

u

uJCadkaJCddeC

aa

ik

==

==⋅=∴ ∫∫ ∫−

逸奇科技. www.AnCAD.com

Visualizing the Circular-Aperture

Diffraction

57

Optical Soliton : Kerr Effect

This refractive index variation is responsible for the nonlinear optical effects of self-focusing and self-phase modulation, and is the basis for Kerr-lens modelocking.

Type Kerr effect:

Innn 20 +=

.

58

Slow Vary Approximation

βα

λλ

≡≡

⋅+∂

∂=

∂

∂⇒

≈+−=−

∂

∂>>

∂

∂→>>∆

=+

∂

∂+−+

∂

∂⋅+

∂

∂

∂

∂+

∂

∂=∇=+∇

2,

2

1

)2

(2

1.

)2())((

,1

~

0)())(1()2(

,0

2

00

00

22

00

2

2

00

000

2

0

2

2

2

0

2

02

22

00002

2

2

2

2

222

0

22

nkn

knset

aankn

ix

a

kni

z

aeq

Innnnnnnnand

z

a

z

akzkfor

ankx

akn

z

akni

z

a

zxEknE

59

Split Step Fourier Method

( )

][

ˆˆ

)(

22 )(

1

0

ˆˆ

0

)ˆˆ(

2

2

2

n

aizki

n

zNzLzNL

aeFea

aeeaeaaNLz

a

aaix

ai

z

a

βα

βα

∆⋅−+

⋅⋅+

=⇒

≈=⇒+=∂

∂⇒

⋅+∂

∂=

∂

∂

逸奇科技. www.AnCAD.com

SSF simulation result for Kerr soliton.

61

Sin-Gordon Equation

• Considing a 1-D chan of identiacl pendu;la connenctedby a torsion bar.

• The euqation of motion for pendulum j follows from Newton’s law for rotational motion in terms of torques:

2

2

11

)()sin()()(

dt

tdImg

I

j

jjjj

ij

jji

θθθθκθθκ

ατ

=−−−−−

=

+−

≠

∑

62

2D Sin-Gordon Equation

• If the wavelength in a pulse are much longer than the repeat disance a, the chain could be approximated as a continuous medium.

• Then generalizing the spatial derivatives:

( )

)sin(lim

)()(

2

2

2

2

0

2

2

2

11

1

θθκθ

θθθθθ

θθθ

I

mg

xI

a

t

ax

ax

a

jjjj

jj

=∂

∂−

∂

∂⇒

⋅∂

∂≈−−−−

⋅∂

∂+≈

→

+−

+

)sin(2

22 θβ

θαθ ⋅=

∂

∂⋅−∇

x

63

Sin-Gordon Equation: 1D solution

1-D analytic solution :

So the 2D initial gauss be :

where c be some constant.

( )

( )

+

−

−−

−

−

=−

±

−=

±=

=∂

∂−

∂

∂

−

−

π

θ

θξ

θ

ξ

θθθθ

2

12

1

2

12

1

2

2

2

2

2

2

2

2

1

exptan4

1

exptan4

)(

1~

)sin(1

),(,)sin(

v

vtx

v

vtx

vtx

vfor

v

v

d

d

v

xt

txxt

( )

+−== −

2

1221 exptan4)0,,( yxctyxθ

64

2D Dynamical Sin-Gordon Equation

Initial condition, left: above equation; right: Gaussian form.

65

Quantum bound

• In multiple-particle nature, the interaction leads the nonlocal potential :. It changes the interaction term in Schrodinger equation :

• Then the equation becomes :

∫ ′′′→ rdrrrVrrV )(),()()( ψψ

ψψ EH =

)()(),(2

)(2

0

22

kEdppkkpVkp

nnnn ψψπ

ψµ

++ ∫∞

66

• One way to deal with the equation is by going to k-

space(Bessel transformation):

the k-space potential is obtain by a double Bessel transform

Numerically, The Schrodinger equation be :

)()(),(2

)(2

0

22

kEdppkkpVkp

nnnn ψψπ

ψµ

++ ∫∞

∫∫ ∫∞∞ ∞

′=

′′′

0

23

0 0

3 )()()()2()(),()()2( drrrpjrVkrjrdrprjdrrrrVrkj llll ππ

)()(),(2

)(2 1

22

kEkkkkVkkk

nn

N

i

jnjjjn ψψπ

ψµ

=⋅∆+ ∑=

67

• In matrix form :

• To solve the eigensystem problem, we could receive several eigenvalues, but only one satisfys

(boundary condition). Once we find the , by inverse Bessel transformation we could get the wave function in r-space without any difficault : .

[ ] [ ] [ ]nnn EH ψψ =⋅jjjiij

i

ij kkkkVk

H ∆+= 2

2

),(2

2 πδ

µ

[ ]

=

)(

)(

)(

2

1

Nn

n

n

n

k

k

k

ψ

ψ

ψ

ψM

IEH n−

∫∞

=0

2)()()( dkkkrjkr lnψψ

)(kψ

68

The simplest case :

.

)(2

)( brrV −= δµ

λ

)()(2

)()()(),(2

0

2prjkrj

bdrrprjrVkrjpkV llll

µ

λ== ∫

∞

.

),(2

)( brrV −= δµ

λ

69

Summary :MATFOR Components

• mfArray

– integrates the entire MATFOR toolkit into high-level programming environments such as C++ and Fortran, simplifying the syntax and facilitating object-oriented programming.

– Basic data structure.

• Numerical Library

– contains useful linear algebraic functions subject to assist users with computational problem solving.

– Use mfArray to do numerical computation

• Visualization Library

– collects well-designed graphical procedures and controls to support a variety of 2D and 3D visual functions.

70

MATFOR Components (Cont)

• Data Viewer

– organized in spreadsheet format, is one convenient platform for data management, filter, and analysis.

• Graphics Viewer

– besides its highly customized user interface, overthrows the convention of post-processing as it instantly visualizes scientific and engineering data.

• mfPlayer

– captures picture frames, animates simulation results, and allowsadditional graphical manipulations.

71 AnCAD Incorporated

- MATFOR®-A Simple Yet Powerful Solution to Meet Your Needs!