Parallelization of Finite Element Codes with Automatic Placement of Communications
10
0
0
Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Parallelization of finite element codes with automatic placement of communications Laurent Hascoët. N° 3646 Mars 1999 THÈME 4. ISSN 0249-6399. apport de recherche.
(3)
(4)
(5) !#"$ % & ' ($ *) ! +, ! -(.. / .% 0/13246587:9;<1>=@?8ACBD9 E FHG IKJLNM OQPRITSHUWVYXZPR[D\J X][D^_X`PWIKPRaZVYX`PW[b\ c JdafegafX`GIKJaih[DIK^HURJ jQJa kmlf[YnoJ XpOQPR\8SHa q]Vb^H^3[DloX c Jdl`JhrF_Jl`hrF_Js\>tvuDwbLxwyM zyVblfa{6|D|D|M }D~N^VbDJ a 6Hbxi Ji^_l`JafJ\xX VdXZ[g[DU c J c PWhVYXZJ c XZ[VbS_X`[DI#VYXZPRhpO_kzy^Vbl`VbURUWJ UWPR6VYX`PW[b\<[b RP X`JlZVXZPDJIKJafFQVYa`J c h[bI#^_S_XrVYX`PW[b\HaVY\ c PRX`a Vb^H^HURPRh6VYX`PW[D\X`[ J jQPRafXZPR\HKh[ c J amE FHJ XZ[g[DUxVbS_X`[DI#VYXZPRh6VYUWUe^HUWVbhJ a h [DIKITSH\HPRh6VXZPR[D\TaoXrVYX`JIKJ\xXZaPW\xX`[]X`FHJ^_l`[DDl`VbI.@XZ[]IVY\Q VbDJpX`FHJ\HJh JafaZVbloe.SH^ c VYXZJ a]3J XJJ \[@bJl`UWVb^H^_PW\H#^VbloXZa [bX`FHJ^VbloXZPXZPR[D\HJ c IKJafF XPRaK^Vbl`VbIKJ XZJ l`PR6Vb_UWJ PRX`FV c JafhlfPW^_X`PW[b\[biXZFHJ$Xeg^ J[bp[¡bJlfU¢Vb^_^HPW\_£3J XJJ\ a`SHQIKJa`F_Ja J.^Hl`J a`J\xX<Vb\¤Vb^H^HURPRh6VYX`PW[D\¥[b]XZF_PWa XZ[g[DUXZ[¦X![ c PRIKJ\HafPW[D\HVbU]Vb\ c XZFHlfJJ c PRI#J \Ha`PR[D\VYU§iV6QPRJl¨oOgX`[D©bJ a]ªH[¡«a`[DUDJ l`akJ lf¬[DlfI#Vb\HhJl`J a`SHUXZaiVblfJDPRbJ\ ®x¯:°f±N² ³b ^Vbl`VbURUWJ UWPR6VYX`PW[b\O_kzy_^Hlf[DDlZVYI´VY\VbUeQafPWa H^Hlf[DDlZVYIµX`lZVb\_af¬[DlfIV¡ XZPR[D\HIKJafFy^VYlfXZPXZPR[D\H¶H\HPRX`JdJURJIKJ\xXZa :§iV6QPRJl¨oOgX`[D©bJ a. Unité de recherche INRIA Sophia Antipolis 2004, route des Lucioles, B.P. 93, 06902 Sophia Antipolis Cedex (France) Téléphone : 04 92 38 77 77 - International : +33 4 92 38 77 77 — Fax : 04 92 38 77 65 - International : +33 4 92 38 77 65.
(6) d % "$ !#". % % . % T (. ) ! (T d ($ "$ % ! -(. / %
(7) §i[DS_ai^Hl afJ\xXZ[D\_a SH\ [DSQXZPRU c JafX`PW\ UWV^HVblZVbURU URPWa`VYXZPR[D\¦OQkzsVbS_XZ[ IVXZPgS_J c J ^Hl`[bDlZVbIKIKJa c J l a`[DURS_XZPR[D\ PX l`VYXZP¬a VYa adafSHl c J aIVYPWURU¢VYDJa T§][DSHa ^Hl a`J\xX`[D\HaUWV h [D\Hh J^_X`PW[D\ c JyU [bS_XZPRU J Xa`[D\ S_XZPRUWPRaZVXZPR[D\ !J X[DS_X`PWU PR\Ha`G l`J c Vb\Ha UWJ ^Hlf[DDlZVYI#IKJ UWJ a.h[DIKITS_\HPWhVYXZPR[D\Ha\ h JafaZVbPRl`J a ^ [bSHl$XZJ\_PWl yno[DSHl.UWJ aYVbURJS_l`a VbSQj ¬l`[D\xXZPRGlfJa c Ja$a`[bSHaoIVYPWURU¢VYDJa UpJaoX$^Vbl`Vb I X`lZVbHURJ Dl bh J SH\HJ c Ja`h l`PR^Q XZPR[D\ c SXeg^ J c Jl`J h[DS_glfJIKJ\xX]hrFH[DPRa`PJ \xXZl`JURJa af[DSHa¨I#VbPRUWUWVbDJ am§i[bSHa ^Hl a`J \8X`[D\Ha U Vb^H^HURPRh6VYX`PW[D\ c JKh J Xd[DS_X`PWU c Jada`[DUDJ SHl`a§pV6gPRJlo¨OgXZ[b©bJ! a c JSgj J XX`l`[DPRa c PRI#J \Q a`PR[D\HaJ X]\H[DSHa c [D\_\H[D\Ha c J aiIKJafSHl`J a c J^3Jlo¬[Dl`I#Vb\Hh Ja " ² ¡ ° $ # y ^VYlZVbUR%U UWPRaZVXZPR[D\O_kzyCVb\VbUega`J c JN^Hl`[bDlZVbIKIKJb XZlZVY\Haf¬[DlfI#VYXZPR[D\ c Jd^Hl`[DblZVbIKIKJb^VYlfXZPXZPR[D\ c JdI#VbPRUWUWVbDJY& U IKJ\xXZa]¶\HPRa>§iV@gPRJl¨oOgX`[D©bJ a.
(8)
(9)
(10)
(11) !"
(12) #$% &'
(13) ()* +(,&- .)0/1(, &2&2#$ .(3
(14) 4. u. K % 6 798 @ ² ³ b;: ² 8 < ] = >1? ®[email protected] MDGF.HJI 8 ³ON PRQCS HUT V XWY: ® °9Z ²\[>® # ² #W ® Y e ® Z_^!"a`cb H¡& # # ® # ®EdC® $ C;: ² 8 ² ³ ® # < >1? A uQW{ zJafF k VYlfXZPXZPR[D\HPR\H dd f uQ } O_kzy kvl`[bDlZVbh I gdJ \HJl`VYXZPR[D\ dd i l ² k ² 8 : D_; : ² 8 j C ² £_ : b # H ® ® 8 \ ] mC ² 8 & #on ² : ? ² ® # ²² # 6Xj ~gW{ ppURPWD\_I#J \xXp[b c VYXZVKVb\ c UW[g[D^Ha dd {6L ~g } OQ[DURS_XZPR[D\.¶URX`JlfPW\H dd {¡~ ~g u zSHUXZP ¨kvl`[ghJ c SHlZVYUPRa`afSHJadd {@w e bqb #r: D_; : ² 8 ² ? ® V E Ws: ® 9° Z \² [>® K ² #W ® 6t wQW{ uia`J[bXZFHJX`[Q[DU dd {;f wQ } kJlo¬[Dl`I#Vb\_hJa dd {i t <® #¬_ ® ³ ±T² [ =\v w x ² 8 $ # y : ² 8 =*< z { K#".( |>[bl I#Vb\xe¦Vb^H^_UWPRh6VYX`PW[b\ ^Hlf[DDl`VbIKaC^Vbl`VbURUWJ UWPR6VYX`PW[b\ PRadVb\ Vb^H^3J6VYUWPR\HHCHSQX c JURPWhVYXZJY /V6e¦XZ[PRI#^_l`[@DJ^ J lf¬[DlfIVY\HhJY<E FHPRaPRaJa`^3Jh P¢VYUWUe XZl`S_J#PR\£afhPRJ\xXZP¶hh[DIK^HS_X`PW\_H \KX`FHPRa c [DI#VbPR\8[D\HJ h6VXZJb[DlfeT[b3^Hl`[DblZVbIKa c J a`JloDJ a!a`^3Jh P¢VYUVYX`X`J\xXZPR[D\ E FHJafJpVblfJ XZFHJPRX`JlZVXZPDJ/h [DIK^HS_XrVXZPR[D\Ha [b\NSH\HaoXZl`S_h XZS_l`J c IKJ a`FHJ avE FHJ eNVblfJbJlfe P c Jaf^Hl`JV c Vb\ c h[D\_a`SHIKJV]afPWD\_PR¶hVb\xX ^HVblfX[bgXZF_Jh [DIK^HS_XZVYXZPR[D\VbUxlfJaf[DSHl`h Ja E FHJafJ^_l`[DDl`VbIKa Vbl`J\VXZSHl`VbUCh6Vb\ c P c VYXZJ a ¬[bl ^VblZVYUWURJURPWVYXZPR[D\ E F_Jl`JJ jQPRafXI#Vb\xe¥^VblZVYUWURJURPWVYXZPR[D\¥XZJ hrFH\HP gS_JaE FHPWa#PRa c SHJbXZ[ V UWVblfDJ.J j8 XZJ\xXXZ[<X`FHJ \8SHIKJl`[bSHadIVYhrFHPW\_JKVbl`hrFHPXZJ h X`SHl`J a} piapXZFHJKVYlfXJ D[DUDJ aVI#VYXZhrFHPR\H JIKJlfDJaK3J XJJ\¥XZF_J$hUWVba`afJaK[b]^Hl`[bDlZVbIKaKVb\ c XZFHJ$^VYlZVbURUWJ UWPR6VXZPR[D\ XZJhrF_\H%P 8SHJ a 5. ~q~h
(15) 99.
(16) L. 4(,. >[bl J j_VbIK^HURJbh[bI#^_S_XrVYX`PW[b\Had[D\¦SH\HaoXZl`S_h XZS_l`J c IKJa`F_JaVbl`JN\_[¡ DJ\_JlZVYUWUe¦^Vbl`VbU UWJ UWPRJ c X`FHl`[bSHDF VybJ[DIKJ X`l`PRh^VbloXZPXZPR[D\HPR\H [b X`FHJ<IKJ a`F¥PRX`a`J UR¨ E F_J$^VblZVYUWURJURPW J c ^Hl`[DblZVbI SHafJa X`FHJ O_kzy \
(17) & "#$ *L
(18)
(19) I#[ c J U \NXZFHPRa IK[ c JU J6VbhrF ^Hlf[Qh Ja`af[Dl [bV c PWaoXZl`PRHS_X`J c IKJIK[Dlfeyh[DIK^HSQXZJllfSH\HapX`FHJ aZVYI#JT^Hl`[DblZVbI [D\ [D\HJ¦^VbloXZPRhSHUWVbl$^3[DlfX`PW[b\,[bX`FHJ¦[DlfPWDPR\VbUpI#J a`F ![bI#ISH\HPRh6VYX`PW[b\HaVbl`J¦lfJ 8SHPRl`J c FHJ\ VYVbURSHJITSHaoXXZlZV6bJU¬lf[DI VafSHQIKJ a`F¦XZ[$VY\H[bXZF_JlC uiafSVbURUReb:XZFHPRa FVY^H^ J \Ha [D\HUe<¬[Dl!YVbURSHJ a]UR[gh6VYX`J c [D\$XZFHJ3[Dl c Jl [bafSHQIKJ a`FHJ a!X PRa h[bI#IK[D\.^Hl`Vbh X`PWh JXZ[ c SH^HURPWhVYXZJ<Vh JlfXZVbPR\ VbIK[DSH\xX[b/XZF_Ja`J ¨3[Dl c J l YVbURSHJ aT[D\ XZFHJ\HJPRDF8 [bl`PR\H a`S_Q I#J a`FHJ amE FHPRa!VYUWUR[@ aSHavX`[ c J ¬Jlmh[bI#ISH\HPRh6VYX`PW[b\Ha!SH\xX`PWU3VbURU_XZF_J c S_^HUWPRh6VXZJ c YVbUWS_Ja Vbl`J[DSQXi[Y c VXZJdVb\ c \HJ J c X`[K JdSH^ c VYX`J c VbxVbPR\ E F_JTV c Vb^_XZPR[D\.[b V ^Hl`[DblZVbI+X`[ XZFHPRaiO_kzy ^VYlZVbURUWJ UWPR6VXZPR[D\aoXZl`VYXZJ be$l`J 8SHPWlfJa X![ I#VbPR\ [D^ J lZVYX`PW[b\Ha A,4,!
(20) . VY\ c J 3
(21) &
(22) E FHJafJ PRUWU 3J c PRa`hS_a`a`J c PR\ c J XrVbPRU PR\ afJh X`PW[b\u_ l`PXZPR\H¦XZFHJO_kzy ^Hl`[bDlZVbI 8e£FVb\ c PRaKV c JURPWhVYXZJXZVba`©> XNl`J 8SHPRl`J a©8\H[@ URJ c bJ[Y]X`FHJ.Vb^H^_UWPRh6VYX`PW[b\¥X`[ ¶\ c XZFHJi^HU¢VYhJa FHJlfJpYVbUWS_JaX`lZV6DJ U:3J XJJ \afSHQI#J a`FHJ aX VbURa`[Tl`J 8SHPRl`J a/©8\H[@ UWJ c DJ [bXZF_J [@DJlfU¢VY^H^HPR\H J X!J J\.a`S_QIKJafFHJa HXZ[Nh [Dl`lfJh XZUe<SH^ c VYX`J c SH^_UWPRh6VYX`J c YVbURSHJa E FHJlfJ ¬[DlfJbQJ ^Hlf[D^3[Da`JpVXZ[g[DUXZFVX/DJ \HJl`VYXZJ a!XZFHJ O_kzy«^Hlf[DDlZVYI IKJ hrFVb\HPRh6VbURUeD XpPRaiPRIK^ [blfXrVY\8X X`[<\H[bX`JXZFVYX]XZF_PWa]PWaiVaf^ J hPWVbURPW J c ^VYlZVbURUWJ UWPR6VXZPR[D\X`[Q[DU mXZFHPRaiX`[Q[DU IVY©bJaa`J \Ha`J[b\HURe ¬[Dldh [DIK^HS_XrVXZPR[D\HaT[b\£SH\HaoXZlfSHh X`SHl`J c IKJa`F_JaE FHPRaTPRaT[DS_l c J UWPR J lZVYX`JhrF_[DPWh Jb XZ[ XZl`V c JDJ\HJ lZVbURPXe¤¬[bl#J #hPRJ\Hh e[D\V ^HlfJhPRa`J c [DI#VbPR\ SHl noSHafX`PR¶hVYXZPR[D\Ha]VblfJXZFVYX h[DIK^HSQXrVYX`PW[D\_a[D\ SH\HaoXZl`S_h XZS_l`J c IKJ a`FHJ a Vbl`JVbJloe ¬lfJ 8SHJ\xXT©gPR\ c [Y/^Hlf[Y DlZVYI#a gJ\_Jl`PRh^VYlZVbURUWJ UWPRJ l`aN3JFHV@bJ$^ [g[DlfURe c S_J<XZ[XZFHJPR\xXZJ \Ha`PDJ$SHafJ[b PW\ c PWlfJh XZPR[D\yVYl`lZV6ega XZFHJd©8\H[@ URJ c DJ[b FH[@«IKJafFHJapVbl`JdafX`l`SHh XZSHlfJ c 3Vb\ c FH[@^Hl`[DblZVbIKa J FV6DJ [D\¥IKJa`F_Ja/VbUWUR[@ a#Vb\VYS_XZ[DI#VYX`PWh$hrF_[DPWh J[Yp[D^QXZPRIVYU h[DIKITS_\HPWhVYXZPR[D\Ha#PR\Q a`J lfXZPR[D\dE FHPRa [DSHU c 3JN[DSQX[bl`JVbhrF¦[bVDJ\_Jl`PRh ^Vbl`VbURUWJ UWPRJ lC3Jh6VYSHa`J PX h6Vb\_\H[bX PR\_¬Jl XZF_PWa ©8\H[@ UWJ c DJ¬l`[DI XZFHJd^Hlf[DDlZVYI \XZFHPRap^HVb^ J lJT^HlfJa`J \xXV#X`[Q[bU¬[Dl]VbS_XZ[bIVXZPRhDJ \HJl`VYXZPR[D\[bmVO_kzy ^Hlf[Y DlZVbI-¬[DlSH\HaoXZl`S_h XZS_l`J c IKJafFHJa E FHPWaX`[Q[bU c J XZJ l`IKPW\_JaXZF_J [D^_X`PWI#VbUiUW[gh6VYX`PW[b\Ha [b h [DIKITSH\_PWhVYXZPR[D\ hVbUWURaX`[DPDJ3JafXi^3Jlf¬[bl`I#Vb\Hh J[bXZF_J^VYlZVbURUWJ UWPRJ c ^Hlf[DDl`VbI. E FHPWavX`[Q[DUQPWamVYa`J c [D\ X`FHJ I#J XZFH[ c Vb\ c VbURD[DlfPRX`FHIKav^Hl`J a`J\xX`J c PR\ L xXZFHVYX J]afFVbURU a`SHIKI#Vbl`PRJPR\afJh X`PW[b\LH JVYUWaf[iafFH[@ FHJ l`JbYFH[@£X`FHPWaCX`[Q[DUY/VbaSHafJ c XZ[ ^Vbl`VbUWURJURPRJ |. q~! ".
(23)
(24)
(25)
(26) !"
(27) #$% &'
(28) ()* +(,&- .)0/1(, &2&2#$ .(3
(29) 4. ~. J jQPWaoXZPR\H}b Vb\ c uD §pV6gPWJ looO8XZ[D©YJa af[DURbJlfa E FHJl`J afX[b XZFHJ^Vb^3Jl]PWai[Dl`xVY\HPW J c Vba¬[DURUR[¡ a OQJh XZPR[D\¤}HlfPWJ ªHe£PR\xXZlf[ c S_hJaNX`FHJ<[bl`PRDPW\HVbUafJ 8SHJ \8X`P¢VYU §pV6gPWJ lo¨OgXZ[D©YJa a`[DUDJ l`a OgJh X`PW[b\¥uy^Hl`J a`J \8X`a ^Hl`J hPRa`J URe XZFHJ.OQkz IK[ c JU[b ^VYlZVbURUWJ UJjQJhSQXZPR[D\ OQJh XZPR[D\$L c J a`hlfPW3Ja/X`FHJ ^HlfPW\_hPR^HUWJp[b[DSHl!VbS_XZ[bIVXZPRhO_kzy ^Hlf[DDlZVYIsDJ\HJ lZVYX`PW[b\ OQJh XZPR[D\ ~J jQ^HUWVbPR\Ha XZFHJaf^ J hP¶h.^Hl`[bHUWJ IKa l`JUWVYX`J c XZ[ X`FHJ l`J6VYU <^Hl`[bDlZVbIKa mVb\ c FH[@ X`FHJ e Jl`J$af[DUDJ c £OgJh X`PW[b\¥w ^Hl`J a`J\xX`aNXZFHJ$VY^H^HURPWhVYXZPR[D\ [b [DS_lXZ[g[DUmXZ[yX`FHJ §pV6gPWJ looO8XZ[D©YJa af[DURbJl CVb\ c XZFHJDJ\HJ lZVYX`J c OQkz ^Hl`[DblZVbI.iOQJh XZPR[DA\ f#h [DIK^VblfJa XZFHJd^HlfJa`J \xXpIKJ X`FH[ c PXZFl`J U¢VYX`J c XZJ hrFH\HP gS_Ja '.
(30)
(31) ." * < T %+%C T % S_l!Vb^_^HUWPRh6VXZPR[D\<JjHVYI#^_UWJ a Vbl`J]X![ c PRIKJ\HafPW[D\HVbU:VY\ c X`FHl`J J c PWIKJ\_a`PR[D\VbU3ª[@ a`[DU DJlfaCXZFHVYX!J afFVbURUvl`J ¬Jl XZ[.VY"a !$# &%
(32) ( ' &C&%
(33) :Vb\ *c ) (+-, :E FHJ e¦a`[bURbJKX`FHJ h[DIK^HlfJa`afPW_UWJ#§pV6gPRJlo¨OgXZ[b©bJadJ gSHVYXZPR[D\HaSHafPW\_.VI#P jQJ c ¶\HPXZJ J UWJ IKJ\x/X .¶H\HPRX`J D[DU SHIKJ$I#J XZFH[ c c JafPWb\HJ c [D\¥SH\HafX`l`SHh XZSHlfJ c XZlfP¢Vb\_DSHUWVbl IKJa`F_Ja¤O8XZJ6V c exafXZVYXZJ.af[Y UWS_X`PW[b\HaKVbl`J$[b_XrVbPR\HJ c SHa`PR\H V ^Ha`J S c [Y XZlZVY\Ha`PRJ\xXVb^H^Hlf[xVbhrF FHPRhrF PRa VbafJ c [D\¥V UWPR\HJ6VYl`PRJ c ¬[Dl`ISHU¢VXZPR[D\ |[D0l !1# &%
(34) XZF_PWaK¬[Dl`ISHUWVYXZPR[D\PRa # *( FHJlfJ6Vba#¬[Dl ' &C&%
(35) Vb\ 2c ) (+-, X`FHJ¬[Dl`ISHUWVYXZPR[D\ PRa &C*( E FHJlfJ ¬[DlfJ.PW3\ ' &C&%
(36) Vb\ c ) (+-, vJ6VYhrF XZPRIKJyaoXZJ^ l`J gS_PWlfJaX`FHJa`[DURS_XZPR[D\ [bdV U¢VblfDJ.a`^VYl`a`JUWPR\HJVblaoegao XZJI. pp^H^Hlf[6j_PRI#VYXZJa`[DURS_X`PW[D\_a[biXZFHJ a`JafegafX`JIKaVblfJ[b_XrVbPR\HJ c xe¤SHa`PR\H5 4DVbh[D_P l`JUWVj_VYX`PW[D\_a |lf[DI V ^_l`[DDl`VbIKIKPW\H ^3[DPR\8XK[Y]gPRJ dPRXTXZSHlf\HaK[DS_XNX`FVYXNX`FHJ$IK[DafX ¬lfJ 8SHJ\xX [D^ J lZVYX`PW[b\Ha [D\$XZFHJIKJ a`F VYl`J[bXZF_JdXeg^3Jd©g\_[¡ \Vba R
(37) !. /6 _(3
(38) r% E F_Ja`Jd[D^3Jl¨ VYXZPR[D\Hamh[b\Ha`PRafX[bCVUR[Q[b^[D\VbURU_XZF_JiIKJafF<J UWJ I#J \xXZa![YCVDPDJ\<©gPR\ c 8a`V@ebgX`l`PWVb\HDURJa |>[bliJVbhrF XZlfP¢Vb\_DUWJY X`FHJNIKJafF¦afXZlfSHh X`SHl`J bPRbJaV c PWlfJh XVbhh Ja`a X`[PXZaiX`FHl`J JN\H[ c Ja E FHJd[D^ J lZVYX`PW[b\Ha [D\$XZFHPRa]X`l`PWVb\HDURJdVblfJ c Jh[bI#^3[DafJ c PR\.XZFHlfJJd^HFVbafJa {D8 7 _ ? ® 8 a`[bI#JYVbURSHJaiVYXfXrVbhrFHJ c X`[ XZFHJXZF_l`JJ\H[ c Ja]VblfJl`JV c }Q x ² b C ® X`FHJafJ YVbURSHJ aVYl`J SHa`J c x PRX`F[YXZFHJ l`axX`[h [DIK^HS_X`J X`FHl`J J ^VblfX`P¢VYU l`J a`SHUXZa E F_[Da`JVbl`J X`FHJdh[D\xX`l`PRHS_XZPR[D\[bXZFHJX`l`PWVb\HDURJ XZ[ XZF_JdX`[bXrVYUl`J a`SHUXZa [b PRX`a \H[ c Ja u_ Z DQ6 ® 8 J6VbhrF^VbloXZPWVbUl`J a`SHUXiPWa]Vbh hSHISHU¢VXZJ c PW\xX`[#X`FHJXZ[bXZVbUCl`J a`SHUX][bX`FHJ h[Dlfl`J a`^3[D\ c PR\H#\H[ c Jb ~q~h
(39) 99.
(40) w. 4(,. /XX`FHJ J\ c [b3XZFHJ UR[Q[D^#[D\ XZlfP¢VY\HDURJagJ6VYhrF<\H[ c J PWURUFH[DU c XZFHJ h[bl`l`J h X¶\VbUlfJafSHURX P JbvXZF_JVYhhS_ITSHUWVYXZPR[D\[bXZFHJd^VbloXZPWVbUCl`J a`SHUXZa][b VbURUPRX`a \HJPRDF8 [bl`PR\H#X`l`PWVb\HDURJa EVbHURJ{DPDJ aNV.l`[DS_DF P c JV[bXZFHJ#a`PRJ[b!X`FHJafJh [ c J a ![bI#IKJ \8X`a VblfJ#\_[bX h[DSH\xX`J c PW\.XZFHJd\8SHI J li[bURPW\HJ a OQ[DUDJ l !1# &%
(41) ' &C&%
(42) ) (+-, a`SH_l`[DS_X`PW\_Ja {@u { i uYL UWPR\HJ a {@~ y{ i EL i p. E VYHUWJK{ OgPW Ja][b VY^H^HURPWhVYXZPR[D\J j_VbIK^HURJa. '. . ) d /( T #". ppa J]a`V6PR\Ka`Jh XZPR[D\{DbXZF_J]O_kzy^HVblZVbURURJUHJj_J hS_X`PW[b\IK[ c JUHlfJ 8SHPRl`J aX[dIV¡no[Dl [D^ J lZVYX`PW[b\Ha ,4,!U)
(43) r . Vb\ c J
(44) &
(45) r ppa]a`F_[¡ \[D\ ¶DSHlfJ¦{DX`FHJafJ.[D^ J lZVYX`PW[b\Ha#Vbl`J$PR\ c J ^ J \ c J\xX ][¡J bJl / [YXZF¥l`J gS_PWlfJPR\_¬[DlfIV¡ XZPR[D\Vb [bS_X XZFHJd^VYXfXZJ l`\[b c SH^HURPWhVYXZJ c JURJIKJ \8X`a
(46)
(47) E*
(48) r%
(49) ppURa`[_>J a`FVbURU:afJJXZFHVYX/XZF_J ^VbloXZPRhSHUWVbl O_kzy ^Hlf[DDlZVYI´aoXeQURJSHafJ c FHJlfJblfJ 8SHPRl`Ja X`FVYX!X`FHJ ^VblfX`PRX`PW[b\HJl lfJ^HlfJa`J \xXZapafSHQI#J a`FHJ apPR\yV ^HlfJh PWafJTI#Vb\H\HJ l . . . Original mesh Partitioning. Sub-meshes + Communication lists Parallel execution. Overlapping Pattern Our Tool. Results. SPMD program. Original program. PWDS_l`J { |. JO
(50)
(51)
(52) r * (,,4,4. q~! ".
(53)
(54)
(55)
(56) !"
(57) #$% &'
(58) ()* +(,&- .)0/1(, &2&2#$ .(3
(59) 4. .
(60) . f. E FHJ$PW\_PRX`P¢VbUIKJa`F¤ITS_afXK3J^VbloXZPXZPR[D\HJ c PR\xXZ[ Vba I#Vb\xe afSHQI#J a`FHJ a<VYaTXZFHJ l`J.VblfJ V@YVbPRUWVbHURJ#^_l`[ghJafa`[Dlfa pp\xe IKJa`F ^VbloXZPXZPR[D\HJlh6VY\ c [.XZFHVYX6^Hlf[¡gP c J c PRXlfJa`^3Jh XZa XZFHJdh[b\HafX`lZVbPR\xXZa]DPRbJ\ J UW[@d psYVblfPWJ Xe [bX`JhrFH\_%P 8SHJ a afSHhrF VbaX`FHJlfJh SHl`afPRbJ<HPRa`J h XZPR[D\ I#J XZFH[ c Vbl`JKSHafJ c XZ[dIKPW\HPRIKPW J]X`FHJ a`PRJ][b3XZFHJ PR\xXZJ lf Vbh Ji3J XJJ \<a`S_QIKJafFHJa QX`FHJlfJ ¬[DlfJ I#PR\HPRIKPW PW\H XZFHJi\HJJ c ¬[Dl!Jj_^3J\_a`PDJdh[DIKISH\HPRh6VYX`PW[D\_a !S_XQ FVYX`J bJl IKJafF$^VblfX`PRX`PW[b\<!JpJ\ c SH^ PRX`FQX`FHPRa/ PWURU:\H[YX V Jh X/XZFHJpl`JafSHUX [b[DSHl/O_kzy ^Hl`[DblZVbI DJ\_JlZVXZ[Dl \HUReb XZFHJNlfJafSHURX`PW\_O_kzys^Hl`[DblZVbI PRUWU^ J lf¬[DlfI 3J XfXZJ lp[D\ V<3J XfXZJ lpIKJafF ^HVblfX`PRX`PW[D\: E FHJ^VbloXZPXZPR[D\HJlPWa J \xXZPRl`JUePR\$hrFVblfDJ[b c JVbURPW\HN PXZF "!$#,
(61)
(62) ( FHJ \[b\HJ ^Hl`[ghJ a`a`[blPRaK[¡bJl¨SHafJ c [DlKSH\ c Jl¨SHafJ c /[blK F_J\ &-,4,! ,&% &- . hrFVb\HDJ a#X`FHJ \gS_IT3Jl [bIKJafF.JURJIKJ\xXZa PR\$a`SHgIKJafFHJa >X`FHJ ^VYlfXZPXZPR[D\$ISHafX 3J SH^ c VYX`J c mE FHPRa XrVbaf©$ J UW[D\_Da]X`[#X`FHJI#J a`F^VblfX`PRX`PW[b\HJl ' !S_X]XZF_JNO_kzy ^Hl`[bDlZVbI+PRX`a`JUm\HJ J c \_[bX JdIK[ c PR¶J c |[DURUR[¡ PR\H XZFHJ c J hPRa`PR[D\[YpXZF_JS_a`Jl X`FHJ.^VblfX`PRX`PW[b\HJlKITS_afXhl`JVYXZJV¦hJ lfXrVYPW\ \gS_IT3Jlp[Yv[@DJlfU¢VY^H^HPR\Ha`S_QIKJafF¦JURJIKJ\xX`a]E FHPWa] PWURUVbURUW[@ I#Vb\xeh[DIKITS_\HPWhV XZPR[D\HaCXZ[ 3JvxVYXZF_Jl`J c ¡eQPRJU c PR\H V c l`VbI#VYXZPRhml`J c SHh X`PW[b\[bQh[bI#ISH\HPRh6VYX`PW[b\T[@DJ l`FHJV c E FHPWa lfJ 8SHPRl`J a/XZFHJ ^HVblfX`PRX`PW[D\_Jl!X`[ ^Hl`Jh[bI#^_S_XZJVY\ c afX`[Dl`JpX`FHJ URPWaoXZa [b[@DJ l`UWVb^H^HPR\H I#J a`F J UWJ IKJ\xXZa J X!J J\ Vb\xe$X[DPDJ \ a`SHgIKJafFHJa iE FHJ a`JNURPRafXZapVbl`JUWVYXZJ liSHafJ c 8eXZFHJph[DIKITS_\HPWhVYXZPR[D\l`[DSQXZPR\HJa vX PWa/[DloXZF.h[DIK^VYl`PR\HNXZFHPRa Vb^_^Hl`[xVYhrF. PXZFX`FHJ hUWVba`afPWhVbU 4%.,(% /63 # ,(#$% ^VYlZV c PRDI.L pi\xXZPRhPR^VYXZPR\H[D\afJh XZPR[D\ fQJlfJI#Vblf© XZFVYX]XZF_J^HlfJafJ\xXIKJ X`FH[ c VbIK[DSH\xXZa]XZ[UWJV@gPR\H<X`FHJ 4%.,(% XrVbaf©XZ[#XZFHJI#J a`F ^VblfX`PRX`PW[b\HJl |[Dl#[DSHlVb^H^_UWPRh6VYX`PW[b\ VbURU]X`FHJlfJyPRaXZ[£hrFH[Q[ba`JyPRaX`FHJ VYI#[bSH\xX[bd[@DJ l`UWVb^H^HPR\H J X!J J\yafSHQI#J a`FHJ a3XZFVYX Jh6VbURU:XZF_J
(63)
(64) E*
(65) % v\.X[ c PRIKJ\HafPW[D\_a !J$hrFH[ba`J$XZ[¦afJ XV [D\HJXZlfP¢VY\HDURJ< P c J[@bJl`UWVb^H^_PW\H [b\HJbVba afFH[@ \ [D\ ¶HDSHl`J}g OQPWIKPRU¢VYl`Ue<PR\XZFHlfJJ c PRIKJ\HafPW[b\HaHJ a`J X]VT[D\HJ XZJ XZlZVYFHJ c lf[D\$ P c J [@DJlfU¢VY^H^HPR\HK[D\HJY E FHPWa]hrFH[DPRhJ PWURUafX`l`[D\HbUReV Jh X XZFHJ^HUWVbhJ I#J \xX [b h[DIKITS_\HPWhVYXZPR[D\Haixe.[DSHl XZ[g[DU E FHJlfJ ¬[DlfJb 3JhVbSHa`J [b[@DJlfU¢VY^«Vb\ c h [DIKITSH\HPRh6VXZPR[D\h [DafXpXZFHPRa$ PWURUV Jh X$X`FHJ ^ J lf¬[DlfIVY\HhJ a[Y X`FHJ l`JafSHUXZPR\HNOQkz ^Hlf[DDlZVYI\ u x[D\HJ h6VY\#¶\ c V c PRa`h SHa`afPW[D\ h[DIK^VblfPW\_#YVblfPW[DS_a [¡bJlfU¢Vb^_^HPW\_<^VYXfXZJ l`\Ha E F_J3JaoXihVb\ c P c VYX`Ja]a`J JI XZ[K3J {D \HJpUWV6eDJl![bC[@DJ l`UWVb^H^HPR\H XZlfP¢Vb\_DUWJ ag PRX`F\HJPRDF83[Dl`PR\H J c DJa VY\ c \H[ c Ja (o/ ¶DSHlfJ}
(66) }Q \HURe[D\HJUWV@ebJl][b[¡bJlfU¢Vb^_^HPW\_<\H[ c Ja (o/ ¶bSHl`JdL
(67) ~q~h
(68) 99.
(69)
Documents relatifs
To test whether the vesicular pool of Atat1 promotes the acetyl- ation of -tubulin in MTs, we isolated subcellular fractions from newborn mouse cortices and then assessed
Néanmoins, la dualité des acides (Lewis et Bronsted) est un système dispendieux, dont le recyclage est une opération complexe et par conséquent difficilement applicable à
Cette mutation familiale du gène MME est une substitution d’une base guanine par une base adenine sur le chromosome 3q25.2, ce qui induit un remplacement d’un acide aminé cystéine
En ouvrant cette page avec Netscape composer, vous verrez que le cadre prévu pour accueillir le panoramique a une taille déterminée, choisie par les concepteurs des hyperpaysages
Chaque séance durera deux heures, mais dans la seconde, seule la première heure sera consacrée à l'expérimentation décrite ici ; durant la seconde, les élèves travailleront sur
A time-varying respiratory elastance model is developed with a negative elastic component (E demand ), to describe the driving pressure generated during a patient initiated
The aim of this study was to assess, in three experimental fields representative of the various topoclimatological zones of Luxembourg, the impact of timing of fungicide
Attention to a relation ontology [...] refocuses security discourses to better reflect and appreciate three forms of interconnection that are not sufficiently attended to
