ВУЗ: Не указан

Категория: Не указан

Дисциплина: Не указана

Добавлен: 28.04.2025

Просмотров: 2001

Скачиваний: 3

ВНИМАНИЕ! Если данный файл нарушает Ваши авторские права, то обязательно сообщите нам.

. . , .; . . . , . .-. ., . (#$ « % »)

!

""8 # " "#" 8 #/ A % / # 8# #, C/&- > # #8 #

3

(3u) 0,

t

x

13u2 P2 0,

(3u)

(1)

t

x

4

14u

Pu2 0.

t

x

D#" 8 ""8 # " $8 A &* # (x,t) (0, L) (0,T ) # -

$& " ? #8>8# &* >8# # A # >8# % # 8# #" 8> # .

" 8>8# & @ " $& " * 3(x,t), " " * u(x,t) # &* -C A# 4(x,t). & % 8> # "#" 8> (1) ? " ? & * # " " # P P(3,4).

< " &* # # # (1) $#"> @ # 8# #- " #, # A % , ?>& ?> % 8 # #"$&*% * # & $#" # #- # ! % / " > ? % A > & # ! %. # #% "$" ? " & * C — #"$&*% * # " " # "$# &* A # ($ - " /E#/ $#8 — # '- -' &*" ).

# # " " # " A E " " @ C "$#8 &* >8 >8, $C 8 $& >/ # " $" & #"$&*% # ? $& !#%# " # " /" 8 " # " # % #"#8 " /.

' / ? #% "* %8 " # " 8> #"& A E- # $" & / % # [1] $# #"$&*% ## # " > #/ " " # .

0 +

1. +! & . ., ' # ! . ., $ .D. 8 # " # - $"> #"& A E # A#$? " # "#" 8 #/. .: M#%8 , 2001.

20


. . , ".; . . . , . . ., " . (5 % 2. )

A # " * %8 " / C "$#8 &* A #""& # "& > "#" 8 & &* / % ? 8 # # # 8 - # . F " @ & " " ## # * " %8 > 8?# ## " ?> #/ # & #/ $"" ! # # # # "#" 8, # " % # ?= / 8 $# " # % E#8 [1].

< & 8?# # >/ / " / "$" ? 8 # "& > # " # "#" 8.

1.'> & # #$> " > C& 8 "#" 8>, $& # # $8 # % #8 " % /.

2.< " # A ! # A !# " / ! 8> ! # &* / 8- "#" 8>.

3.< " # 8 # > # # #/ "#" 8>.

4.< " # "#" 8> #/ " 8 # > # # #/ [2].

5.< & # E #/ "#" 8> #/ % > &* > "& # .

6.% ? #$#%# > / " > 8 & / & "- > C& 8 "#" 8>.

7.? # / " > 8 & / " E #/ "#" 8> - #/ # &* > "& #/.

8.? # #$#%# > / " > 8 & / " $8 =*@ # ! 8 ## &* ! # # @= 8 ?O .

9.?O # # 8 & / # @ 8 &* "#" 8>.

10.M 8# # / " A "$#% & # #!# ## %- 8 > E#? " # # / " > C& 8 # A ? # .

>/ "$" ? ?>& % $# 8 ## " $& " # A. A#& , & " >8 $#8 8 "& / #- " / "#" 8> [3].

0 +

1.( . ., +#! . ., 1 +! . . # 8 # " #. — .: # — & 8, 2007. — 284 ".

2..'. 8 # " 8 # # " # "#" 8: ? # & % . — # " : #% / < , 2004. — 640 ".

3.( . ., . . # " / " 8 &* "#" 8$& " ? # // A # , ! 8 # , ##-2011 — -2011. D?.. .-. !. .2. ., 2011.

21

1. . 3 , . . 4 , 0; . . '. ! , . . ., . (5 % 2. )

-

" $8 " # # " # # > $ — # #% /- E# C$ " " & # ?#% "-$& . < & A " &A # 8 E # - / % #, " >/ $#8 ## 8 $"" ! # # # !# 8> # % >/ %> #8# # A 8 # GPSS.

# &* A #% #/, $" & @=# ? # $, — # ? &*E A #"& "& / > ! , $" " @=# # C!! # " *. # > C # # , ?O $#"> &- " 8# ## 8 "" A ?"& # # .

# # 8 C!! # " # >"$ " $8 " # " " , %- > $# ? # # $# #"$8 " " ## ?- # , >" & 8 A $.

8# ?>& % ? $A 88 , $% & @= %# * # " &* # # $A ? # , & A # ?- # " * "& / >/ $ , 8 # # " #8 " # $ ? # , " #8 " # 8 . # > " C # "& / > ! >, "" # > " # 8 8 , % $# " " #- 8 " * $# ? A $ ? # .

< A 88 ?>& $#8 & " " $8 " # " A $ $# # , % #8 @= A " $8 & "#$. ' >8# >8# & $A 88> & @ " : n — " # ? # , $ - " & 8 A & $; " ? # i-A # , i = 1…n; " #8 " * # # > ? # i-A # ; ! # , % @= " #8 " * 8 / " 8 ? # i-A # ; ! # , % @= " 8 8 ? # % A # ; ! # , $& @= " #8 " * A " $ % A # ? # ; ! # , 8 @= &* " * $ 8.

'> > > : " $8 " # " $# 8 - # ; " 88 8 $ % $# ; " #8 " * " $ % $# " 8 8 ; ?= 8 $" ? # .

% &* > ? > $A 88> $" & @ " # " A -GPSS, " 8 $A 88 A #% , &* " * "$8 " #, $"& $# " , " " / $8 # # " " " @= 8 % & .

$A 88 , $"& " " @= / $##, 8 ?> * #"- $&*% & E # $" & / % # &@?> A #% # , %- #8 @=# " $8 ? # &@? A #$.

22


Dk,l

. . # , .; . *.7. = , . .-. ., . (#$ « % »)

! ,

' " = / ? 8> $& 8 #% # ! # &* > "#" 8 P(A) $ 8 " C!!# # 8# #% !# "# A 8 " A # # % 8 > & "" . ""8 > "& @=# # > C # & " /:

1. E # N0 , %?# 8 " N0 & ""> C #-

& " / "& @=#8 ? % 8:

N0 {0,1, ,l 1}5 {l km, ,l km k 1} . $& " " & ""

m N0

" # C A %?# # & P( N0 ) # ? %#" C A & "" .

2. E # Dk,l A Z,Q , %?# 8 " Z & ""> C #-

& " / "& @=#8 ? % 8:

A {(k 1)m x km} . $&

m Z

" " & "" " # C A %?# # & P( Z ) # ? %#" C A & "" .

$& " " & "" " # C A %?# # & P( Q ) .

3. E # Jm 8 "

A Z,Q,R,C , A m A , %?#

8 " A & "" : {m} # {a A, a 6 m}. $& > " " > & "" " # C A %?# # & L(A) $# A Z,Q, R,C . E-

# Im 8 " Z %?# Z & "" : {7m} # {a A,a 6 7m} .$& " " & "" " # C A %?# # & L(A). E #

Km 8 " Z %?# Z # & "" : {a A,a 6 7m} , {m} # {–m}.

$& " " & "" " # C A %?# # & L(A). / > E # &@ # 8 C #8# 8 & "" 8#.

4. E # " 8 & 8 " A = Z,Q,R: x~y, " |x| = |y|. / > > "& # $# & " # C 8 & "" &

P(A) $# A = Z,Q,R.

5. E # Sm 8 " A = N0, Z, Q, R %?# A & "- " : {x m} # {x m}. $& " " & "" " # C A %?# # & P(N0) # L(A) $# A = Z, Q, R. & "& L(Z) E ? % .

23


/. . 8 " , .; . . . , . .-. ., " . (#$ « % »)

-

,

""8 # " % # #-# A $& ?8 "#- " 8 , " " = / #% N $&& &* > # 8 & " # $& " # (C ), % & > A % >8# $"& / 8#. " 8 / # / &-

" ?" &@ 8$

u u(x, t) .

&* "$& #

u0(x) , 8$>

u (t)

# u

r

(t)

@= / " > "& #

"$ "#" 8> % >.

"$" # $& $#"> " # 8 $&$" #, $# #8 @=#8 % > $8 > 8 && # A % .

$& " # ?8 # " $& / C A# / " " " / $& " #- / $" " 8 #%& # # " " " / $"& / / A % — $" " 8$& ?8 8. "#" 8> $#" # $& ?8 #%&- # 8 " @= / " /. #% A % > $"& ?8- # " $& 8 &* " " " #8# $& " # 8# 8 && .

& E # C / % # $" > "$# &* > $#? > $&- #" > # "#8$# " # 8 >. % ? > #"& > %- ## C # 8 , $> > #" &* > C "$#8 >. ""8 #- " % #"#8 " * # $A E " # $8 % #, " ? " #&=# > $& " # # $"& .

& & A# / % # # #-# A $& ?8 "#" 8 C , % & > 8 >8# $"& / 8#, " " @- =# 8 > $" > # #""& > [1—3].

0 +

1.$ . ., +! . . < & #" > # "#8$# " # $$"#8- ## % # $" $& "#" 8 " > C $# ## #%& # // ' " # , 2008. R 6.

2.$ . . " # % # #-# A $& ?- 8 $# # " / "#" 8 " > C // < ?& 8> 8 8 # " A - % . 2010. '>$. 47. C. 3—42.

3.$ . . < & #" > # "#8$# " # $#? # & " #- / % # # #-# A $& ?8 $# # " / "#"- 8 " > C // < ?& 8> 8 8 # " A % . 2011. '>$. 47. C. 3—44.

24

*. . , ".; . '. . 7 , . . ., " . (#$ « % »)

-

< #" #% ## # "" & # (< ') "- $" > "& / > $"" ?>& ""8 ? [1], $&-E # % & "* "*8 "& >8 % ##, # [2] ?>& $& & A# " # $" E # % # & $#% &* > A& # 8 $?> # . < " > & "* 8 $" 8 8 # $&@ # (1):

mq (n, f ) Hqsms ( p, n),

q 0,

(1)

s 0

A mq ( j,k) — 8 8 $ q $ #% " " # j k ,

H

(n, f ;8,T )

(1)s

Tn tq f (s) (8

t)R

(T t)dt,

(2)

s!

qs

n

,

n

f

n

0

8 — 8 $?> # " " ##, Tn — # & $> = A $ - .

< # $# " / % ## $> 8 A # # *" - >8 #"& 8 8 8 , . . ! # " # #"$&*% * $#? @ < ', " * / % #"# " #"$&*% 8> 8 8 . < # A # ## 8 &>8 #"& 8 8 8 % # @ E#? # $#?- # # $" # " $$"#8 ##.

' " = 8 & % # " $#" >/ [2] $: > # " # & # & #" #% ##, $#"> @ " $#? > $>, # " # " . '>$#" > $" > ! 8 &> & "$& #/ " $& " 8# # / / 8?# ## C "$ (3):

N

EN (t | )

i 1

N

aiE(t,i ) ai ie it .

(3)

i 1

< % % #"#8 " * " > #" # $> (# & #" #% ##, 8 8 # " A # # # #"$"## # $&@- # ) " #"$&*% 8> 8 8 $" . < # > "- > $#8 >.

0 +

1.% & D. ., - . . < #" #% ## "& / > $ - "" " A # >8 $"& /" # 8 // ' " # . 2006. R 6. D. 12—17.

2.% & D. ., - . ., $! A. . #" #% # % #/ "& / > $"" " >8 #"& 8 " " #/ # A& #8# "$& # 8# 8 $?> # // D? # 2-A A " 8# , $" = A $ - 8 # F. . U " . 'x . 2012. D. 23—31.

25


. . > , .; . . . , . .-. ., . (#$ « % »)

CUDA

"$&*% # A !# " # $"" & 8 ""# > > #"& #/ $"& 8 " # " " ? & &* >8. < & 8$ - # / NVIDIA & A# CUDA [1] 8 # " # 8 #$ # 8#

# $8#, "$& $8 *, $A 88 >/ $#E " "E#- 8 %> D, "#&* $= $#" # $A 88.

% " @ "& #"$&*% * "@ > #" &* @ 8 =* A !#- " # $"" . 8 ?> * " % &* " $& #8 "$ - && # 8 8 , # " " ? %# 8 # >, " % / #%- &* & " A !# #. D = " " &* "$" ? $ $#- 8#% ## [1, 2] & # C!! # " # $#& # .

9< ? $#8 &* A & A $#& # #"& # //?& .

9"$&*% # % & 8 / $8 #.

9"$&*% # " / $8 #.

9"$&*% # $.

9"$&*% # 8 > $#/.

9F 8 " > ! #/ " >8# & A 8#, ?& @=#- 8# 8 *E / " *@.

9'> # # ?& $8 #.

A !# " #/ $"" ? " ? &*E#8# 8 ""# 8# - > , A& @ &* #A @ 8 > & " # "$ $8 #. <- C 8 $"$>/ # " $" & @ > # # ?& $8- # # #"$&*% # % & 8 / $8 #, > 8 A " # % " # * >$& # $A 88.

> "$" ?> $#8#% ## ?> $" # > $" /E 8 $#8 " & A $#% # . ' % &* 8 ?>& " 3 % .

0 +

1.( . ., [ !$ . . " > ? > " & A# / CUDA. .:< "", 2011.

2.A\., E C. & A# CUDA $#8 : ' # $ - A 88# # A !# " # $"" . .: < "", 2011.

26

. 1. ! ??+- - # / # -!+*
! /

.7. , ".; . . . , . .-. ., " . (#$ « % »)

-

= " $" " R3 "$& # # "# " # #%& # $E 8 "& . <$& A " , $E " " # #% "! # " # " # . { " # > " " #% / $A& = @= / "" # @= / "- > " C!!# # 8 C " # ## Œ , C!!# # 8 &*? • # $%- & 8 $& 8& # n . ' E " , / # " $E , -& " / $A& = @= / "" # @= / " / " & A#- >8# $8 8#: 0e , e # ne . %& # $" # " # - " # $& 8& " $ % 8 A 8 # " / $# # " " ## " % 8# M & [1].

< & &A # 8, " >/ 8--& . & % ## &A- # 8 $#" $A 88 >/ 8$& ", $%- & @=#/ $# * #"& > C "$#- 8 > " #"$&*% # 8 8 A$""- > 8 E# , 8 #"& & " .

< #% # % #"#8 " # C!- !# # $ $" # # # "$ - " ? $# $E # #$ $@= A #%& # ( &# A # #!! %- A ( #". 1)). ""8 # "* $" - ?# " $, $& /E A " A &*-# $& /E ?# " $# [2]. < #% # # #%8- # # " " # "$& # #%&- # $# $" / &=# "& .

< % &* 8 #"& > C "$#8-" & , #$ $# # $ - @= A #%& # " = " @

$# # #%& # . %8 # # " " # $E " " # 8 &=# > "& # $A& = &* > " /" "& $E .

! " #$ % (" &' - 2033.2012.1) / $% ( " 4 + 14.<37.21.0864).

0 +

1.( ., !"? C. " > $# #. .: , 1973.

2.@ !" .'. #" && A !# . .: '>"E E & , 1984.

27