+ 2Nlog(N)mFFT] + NSMCG [72Nlog(N)mFFTJ in .NET

Create QR-Code in .NET + 2Nlog(N)mFFT] + NSMCG [72Nlog(N)mFFTJ
+ 2Nlog(N)mFFT] + NSMCG [72Nlog(N)mFFTJ
VS .NET qr code jis x 0510 maker in .net
generate, create qr code 2d barcode none in .net projects
(6.3.39) where NCGM and NSMCG are the number of iterations in CGM matrix solver and the number of right-hand side updates, respectively, n is the number of sample points per >.2, and mFFT is the total number of FFT's and inverse FFT's. Note that in the above equation, the total number of iterations required for convergence depends on rd. As an example, consider a simulation with the following number of iterations NCGM = 110 and NSMCG = 4, with sampling of n = 64, r d = 2.5>', N = 16384, and mFFT = 120. The term containing the r d dominates with 1.55 x 1011 computational steps. Therefore, SMCG is effective for a moderate rms height so that the number of Taylor series expansion terms can be manageable and the neighborhood distance r d can be much smaller than the surface length. In this section, an error norm of 0.01 is used for all numerical simulations.
Quick Response Code recognizer with .net
Using Barcode scanner for VS .NET Control to read, scan read, scan image in VS .NET applications.
Integral Form of Matrix Equations
.net Framework Crystal bar code printer in .net
using barcode creator for vs .net crystal control to generate, create barcode image in vs .net crystal applications.
For completeness, we list the detailed integral form of the six matrix equations in the following
VS .NET barcode recognizer in .net
Using Barcode recognizer for .NET Control to read, scan read, scan image in .NET applications.
6 3-D WAVE SCATTERING FROM 2-D ROUGH SURFACES
Control qrcode size for .net c#
qr code iso/iec18004 size in .net c#
+ ikl771br;;)(PR) [;~]m F~n)(f') [Of~~Y) Of~~;Y') +
Qr Bidimensional Barcode barcode library on .net
using web.net topaint qr code 2d barcode on asp.net web,windows application
= _ Ix
Control qr codes image in vb
generate, create qr none for visual basic.net projects
(n+l) (_) r
Barcode barcode library for .net
use vs .net barcode printer toprint bar code for .net
~R"STd
Bar Code encoder on .net
using .net framework toreceive bar code in asp.net web,windows application
{ dx'dy' I~n+l)(f')G2(R) x') - (z - z')] ax'
Visual .net 2d barcode creation for .net
using barcode creation for .net control to generate, create 2d matrix barcode image in .net applications.
. [of (x, y) (y _ y') oy
Code 128 Code Set B barcode library for .net
using vs .net crystal toinclude uss code 128 on asp.net web,windows application
+ of(x' , y') (x _
.NET Crystal usps postnet barcode printer for .net
use .net crystal delivery point barcode (dpbc) integrating toreceive usps postal numeric encoding technique barcode for .net
+ I~n+l)(r')G2(R)
Control ean 128 image in word documents
using office word touse ean/ucc 128 with asp.net web,windows application
[- Of~;Y) (x _ x') [Of (x, y) (z - z') oy
Control code 128 code set a image for visual c#.net
generate, create code 128 code set b none for visual c#.net projects
+ Of~~;Y') (x + (y _
DataMatrix printing on visual basic.net
use visual studio .net (winforms) crystal gs1 datamatrix barcode integrating todevelop datamatrix on vb
x')]
Control qrcode data on .net c#
to display quick response code and qr code data, size, image with c# barcode sdk
+ I~n+l)(f') E1 G2(R) +
Control upca data with c#
to access gtin - 12 and upc-a supplement 2 data, size, image with visual c#.net barcode sdk
y')]}
Visual Studio .NET ean13 generating on visual c#.net
generate, create ean 13 none for .net c# projects
PR"STd
Control ucc ean 128 image with .net
using barcode encoding for .net windows forms control to generate, create gs1 128 image in .net windows forms applications.
d 'd '{ Ok F(n+l)(-,)of(x,y) of(x',y') x y 2 1771g2 x r a a ' [of (x, y) of (x', y') oy oy'
Control code128 data for office word
to display ansi/aim code 128 and barcode standards 128 data, size, image with word documents barcode sdk
+ 2ok 1771g2 F(n+l)(-') y r +
JpR>Td
dX'dY'{I~n+l)(f')a62)(PR)
+ of (x', y') (x _
ax' x') - (z - z')]
. [Of (x, y) (y _ y') oy
+ I~n+l)(f')a62)(PR)
E2 0
(- Of~~Y) (x - x') [Of (x, y) (z - z') oy
+ Of~~;Y') (x + (y _
y')]}
x'))
+ I~n+l)(f') El a(2)(PR)
d'd ,{ok b(2)( )F(n+l)(_,)of(x,y)of(x',y') x y 2 1771 0 PR X r a y ax' [of(X,y) of(x',y') oy oy'
+ 2ok1771 b(2)(pR )F(n+l)(-') 0 y r
(6.3.40)
m=l JpR>Td
dX'dY'{I~n)(f')ar;;)(PR) [Zd]m
. [Of(X',y')(y_y')_ Of(X,y)(y_y')]
+ I(n) (f')ar;;) (PR) [ZdJm
. [-(Z - Z')
+ of (x', y') (y _
+ of(x, y) (x ax
x')]
3.1 Integral Equation and SMCG Method
+ I~n)(f')~a~)(PR) [Zd] m E2 PR
a f(x, y) (z _ z') ax PR
+ (x _ x')] }
ax ax'
JpR>Td
dX'dY'{iklTJlb~)(PR)[!! ]mFJn)(f')[-l- af(x,y)af(X',y')]
. +iF~n)(r')klTJlb~)(PR) [Zd]m [_ af(x,y) af(X"y')]} PR ax ay'
/n+l)(_)
~R<Td
dX'dY'{Iin+l) (f')G 2(R)
. [af(x"y') ( _ ,)_af(x,y)( _ ')] ax' y y ax y y + I~n+l)(f')G2(R) [-(Z - z')
+ af~~; y') (y - y') + af~~ y) (x - x')] + (x - x')]}
+ I~n+l)(f') :~ G2(R) [- af~~ y) (z - z') +
JAA<~
dX'dY'{iklTJlg2FJn+l)(f')
[-1- af(x,y) af(x"y')] ax ax'
[af~'~Y') (y _ y') _ af~x,y) (y _ y')]
+ iF~n+l)(f')klTJlg2 [_ af~~ y) +
JpR>Td
af~~; y')]}
dX'dY'{Iin+l)(f')a62)(PR)
+ I~n+l)(f')a62)(PR) [-(Z - z')
+ af~~; y') (y - y') + af~~ y) (x - x')] + (x - x')]}
2 + I~n+l)(f') :~ a6 )(PR) [- af~~ y) (z - z') +
JpR>Td
dX'dY'{iklTJlb62)(PR)FJn+l)(f')
[-1- af(x,y) af(x"y')] ax ax'
(6.3.41)
+ iF~n+l) (f')k 1TJlb62)(PR) [_ a f~~ y) af~~; y')] }
_L r
JpR>Td
dX'dY'{af!;)(PR) [Zd]m Ix (f') [_ af(x, y) of(x'; y') (y _ y') PR ax ax
+ af(x,y) [af(X',y')( x - x ') - (Z - Z')] - (Y - Y')] ay ax'
63-D WAVE SCATTERING FROM 2-D ROUGH SURFACES
+a~)(PR) [;:]m Iy(r,)[af~~Y) [(Z-Z')- af~~;Y')(y_y')]
af~~Y) af~~;Y') (x _ x') + (x -
X')]
+ a~) (PR) [Zd] mIn (r') [af(x, y) (x _ x') PR ax
+ a f(x, y) (y ay
y') -
(z - z')]}
_ r t
m=l JpR>Td
dX'dY'{ik1T/1b~)(PR)
[Zd]m Fx(r') [af(x,y) _ a!(x';y')] PR ax ax _
+ik1T/1b~)(PR) [;:]m Fy(r') [af~~Y)
= In(r) +f d 'd
af~~;Y')]} +I~nc(r)
'{G (R)Ix(-') [_ af(x, y) af(x', y') (y - y') ax ax'
+ af(x, y) [af(x" y') (x _ x') - (z - z')] _ (y _ y')] ay ax' + G 1(R)I (r') [af(X, y) [(z _ z') _ af(x', y') (y _ y')] ax ay' y +
af~~Y) af~~;Y') (x _ x') + (x -
x')] ay y') - (z - Z')]}
+ G 1(R)In (r') [af(x,y) (x - x') ax +
+ af(x,y) (y ax'
Jd x'dy,{ ok T/1g1
F (-') [af(X,y) _ af(x"y')]
+ 2ok 1T/1g1 FY (-') [af(X, y) _ af(x', y')] } r ay ay'
AA>~
(l)(p dx 'd y '{ a o R )1x (-') [_ af(x,y) af(x',y') (y - Y') r ,:) ,:),
uX uX
+ af(x, y) [af(x" y') (x _ x') - (z - z')] _ (y _ y')] ay ax'
(1)( )1 + ao PRy (_') [af(X,y) r ax
[( _ ,)_af(x',y')( _ ')] Z Z ay' y y
af~ y) af~~; y') (x
_ x')
+ (x -
x')] ay y') _ (z - z')] }
+ a(l) (PR)In(r') [a f(x, y) (x _ x') o ax
+ a f(x, y) (y -
3.1 Integral Equation and SMCG Method
dX'dY'{iklTJlb~l)(PR)Fx(r')
D (-')
PR>Td
[a!(x,y) _ ax
a!(x'~Y')]
(6.3.42)
'k + z 1 TIl b(l)( PR) r 0
[a!(x,y) a!(x',y')]} ay ay'
63-D WAVE SCATTERING FROM 2-D ROUGH SURFACES
JpR>Td
dX'dY'{a 61 )(PR)FJn+l) (r')
. [Of (x, y) (y _ y') + of (x', y') (x _ x') - (z - z')] oy ax' + a(l) (PR)F(n+l) (r') [- of (x , y) (x _ x') + of (x', y') (x - x')] o y oy oy'
+ a61)(PR)F~n+l) (r')
[a f~~ y) (z -
+ (y - y')] }
(6.3.43)