Parallélisation de calculs d' orbites
Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Parall´elisation de calculs d’ orbites Jocelyne Erhel , Bernard Philippe , St´ephanie Rault. N ˚ 3150 Avril 1997 ` THEME 4. ISSN 0249-6399. apport de recherche.
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(36) . .
(37) . Pression solaire. Attraction du soleil. Attraction de la Lune. Irregularites de la forme de la Terre. Frottements. ( altitudes de 150 a 1000 km). Aplatissement de la Terre. Attraction terrestre. >. 1. 10E-12 10E-10 10E-8 10E-6 10E-4 10E-2 10E-11 10E-9 10E-7 10E-5 10E-3 10E-1. ~. . ,+-. . _. k. 4 5 4 4 ,
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(50) U ~ #C (j(T t UVTc n Txqf tmt [g<T t ] _ _ j(f.^ R ~< s f.^ t qT_ba` <f.h£qa8_bq^`_]Ti_gTlpT6qf.h n U;TU `t T c a.T6qQqf.UVUVT lmT^`_]TVj>T t ce^ te adce[gf<h R qT_g_]T n t ^`TVa8^3cmT t RUVTTh t TcqT_baL,^`T_g_]Tl ,^`TVlpf<[gTh,c_]TlÂf t qT6l <^T_ f<h <T^kcCa8[ t T;[]h<ceT t .Th`[ t lea8^k ° a8^LcmTUVjl & f ^G_]aÂf qTqf.UVj`_ TceT lmT a;qa8_bq^_T T. f<h t Tqf.UVUVThqT_ T ca8j(Txuv^le,^ a}R qf.h\<T t .Th>qT. \q Tlpc a R n [ t T¬uv^le,^ aVR qT<^T_ f.h$a8[gc+* j. IR. . R. . R. . ?. ?. @$R. . . @ % % % % @$RN. . G. R @R. . @ % % % % @R. . ?. ?. ?. . . ?. R. . ?. ?. fS. G. R @$RN. S. @ % % % @$RN. R @$R. R @RO. h@. . @ % % % @$RN. @ % % % @R . PS. ] R ] ] f ?. f ^ R f«T6lvci_bacmf._T t a.hqT.f<^`_g^Tj>a t _ ^kce[g_][]leadceT^ t TcuQTlpcQ_]Tqf<UVjkcmT^ t n Tl[c`T t adce[gf<hl ° t a;qf.h\.T <ThqTa8cpceT[]h<ceT. kf<h t Tcef.^ t h`T a;R _ T ca8j(TV~Th j t f< t Tlelma.h,c n ^`h ja.l `q Tlpc a R n [ t Ta8^GceTUVjl & a!¥>.^ t ;T #0> (¬[]_]_g^lpc t TqTcxa8_].f t [gc P UVT n a8h>lQ_gTqa<lQf.^ _ f t n t T W Tlpc.CTc n f.h>q Lda8^`cx|` ,S. &. n. n+1. n+2. y. X. X. X. X. y’. X. X. X. X. n-4. n-2. n-3. n-1. n+3. t. y’’. Z. valeurs connues étape 4 étape 5. Z X. étape 6 étape 7. . k. P4 ; ! . #"$". O. ñÂ×Bì*ñÅò.
(51) .
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(54) qf tmt Tlmj>f<h n a8^h`f.U `t T n TQja<l*Tc qf tmt Tlmj>f<h n a.^cmTUVjl n []h`[gcm[ba8_][]leadce[gf<hd©a.hlqT¬UVf n TR _]Tf<h!h`TQqf<hlp[ n T R t T ,^`T¬_gT6# lBÂf t qTlBj(t T t cm^ R te P adc t [bqT6l n T t [gda.h<c n t ^!j(P f8ceTh,cm[]T_\ceT tet T6lvc t T< Ç_ t TlpcmT a R n T cmT R t UV[]h`T t _gTQh`f<U `t T n a.j`j>T_]l axR _]axÂf.hqcm[]f.h qa8_bq^`_ba8h,ci_]aÂf qT t aVtq a<,^`n T ja.t lQTcj>f<^ t q a.R ,t ^`Tcvo\j(<T #CtlmR [gUVnj`_][¥iT T Tcxt qf.UVj`_ TceHT ( ´ hCa8[blma.h,c;da []T _]Tl [g¡xT Th,celja a.U Tc TlTc}a8j Tl Tªhf.U T^lpT6l!Tr T q^kcm[]f.hl *hf.^lVa.f<hlj^¤Tlpcm[]UVT t _gT6l qf. hlpcea.*h<ce T|,l .ndW;^ lpUVT6q f n TR _g:T * *( k~.Ñ. *~< , h$j(R T^kcU T t [¥>T t _ba}da8_][ n [c`T n ^UVU f n TR _gTTh_]T!qf< U;j>a t a8h,cxat .T6q P _gT6licmTUVjl t T T_bl n Tr T q^kcm[]f.h>l hlmT!j_]a<qT n a.hl _]Tqa<lQf ^ ~ E¦~I C a<T q |. hGf ce[gTh<c_]T a8j Tx¥>V$| * *`cmTUVjl. S . S?. . *`cmTUVjl # n T j>Th. . ?. ;. ;. US . %. . h;. Comparaison des temps réels de COWELL et de son modèle 14. temps cowell (sec). per=30 12. temps évalué expérimentalement. 10. temps évalué par le modèle. per=24 per=18. 8 per=12 per=2 6. 4. 2. 0 0. 500. 1000. 1500 T_T0/h. | H B ; B . k. I
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(129) . ¢ © xw ¢ U y YY ¢ w # e] , ( s Y ¢ ´ © Os ´ U Y s *´ ® [ Ê `¶§e~ J I U ³® ¢ a8_bq^`_ n T ] , _]a n f<h`hQT T [gh`[gcm[ba8_]TK ¢ a8_bq^_ n T # #g] , (¬j>a t _baU«T c P f n T n T ¢ fdµ¬T_]_ K ( ® O , s + C # M t , ( f ³ ® t Y qf<h\.T .ThqTTh ª[gc`T adcm[]f.h>l K 4 7 P4 ;B >= ® [ U ~< `! ¶i§~ J I ¢ a8_bq^_ n T #" % #Âf<^ n Tlpf<hGa.j`j t frk[gU}adce[gf<h (OK c;. ;. ;. TG)@. B. B. . . ?. ;. B. Bh. ] , . . * U # #g] M , * U ] R , ( ® * U ~K ?. . ?. , C ( ] , . !. ? d. K. % g# ] , C . ?. ?. . R ] , C (,K ?. ° ° G Tlpc_]a n [ t T6q%ce[g<T n T;ja t a._g_T _][blma8cm[]f.h n ^`h`T f.^q_gT< G T6lvc_ ThlpTU _]T n Tlda t []a _]Tl n T6 q_ba t T T6l _]fkqa8¢ _]TUVTh<cij(t f.^ t q P a.,^`Tj t f\qTlelpT^ t _gT6R lt a8^`c t t TlLt T cea8h,cQja t cea.n T Tl ja t n T Ca.^kt c n TcpcmT ja a._g_T _g[blma8cm[]f.h£t ,^`[n qf.hlm[]lpcmT a T t ja cm[ n _gT6l¬qa8_bq^`_bt l P Tcmf<^kc_ []h<ceT da8_]_gT TcmTU;j>lilp^ t _]Tl n [g¡xT t Th,P cel j R t fkqTlp§ t lmT^ lT6lvcqT_]_gT,^`[(a8j`ja a.[c TCa qf<hh>adcm^ T_g_]T a8h>l_ a8_].f [gc U;Tl`T6 <^Th,cm[]T_S~<.¶f<^lh`f<^l#lmf.UVUVTladcmcea<q T l aqTcmcmT j t TUVP [ TR n t TVn U¤T c P f n T n T}ja t a._g_T _][blma8cm[]f.h t n a8R hl_]T ^kc n t a<f.[ t ^`h`T£[ n T T n ^qf.UVj(f t cmTU;Th,t cTc R n T6lj(f8cmt Th,t cm[ba8_][c`T l t n Tª_]a U«T c f T T ¶TµQcef.hGTr¬T6 q^kc`T TThªja a._g_ T_gT<P 8xh`Tj>a a8_]_T _g[bleadcm[]f.h}j_g^l¬T32}qa.qTqf.hlm[]lpcmT a.[c a!h []h,c`T T ,^`T lm^ ^`h`T ÂTh Tc t T n T Y lmf.^>lv§¨[gh,ceT t a._g_]Tl Tc aR Ca.[ t T._][]lelmT t _]aÂTh Tc t T ThªÂf<hq%ce[gf<h n T_]aVqf<h\.T t .ThqT aVR q P a.,^`T [gc`T t a8cm[]f.h ¯® !, ³0 \ ° \H \ ². ° 0® ( ³C³ , ³0 ©TVR _]aLÂf t U!^_gT n T;cmTU;j><l #vH~ C (xTc n TV_ a._g<f t [c P UVT;k Sf<h3j(T^`cTh n T n ^`[ t T!^h¦UVf n TR _gT n T;cmTUVjl n Tr T q^kcm[]f.h3Th t ja a._g_ T_gZT * & ," N & ," N C ~ f f R R U # R ( #v~6 ( f N . Y > > . _]Tlida t [ba _]Tl¬f<h<ci`_baVt U n TUVT t lp[].h`[g¥>qadt cm[]f.h ,^ a8^Gja t a8 t a.j P Txj t T6 qÊT n Th,cQT+c * Y T6lvci_]Th`f.U T Tj fkqT6lmlmT^ l % 'TlpcQ_]TqT[g_]_][gh` n T r #Cq Tlpc a R n [ t T_ Th,cm[]T t lm^`jQT t []T^ t _]T j`_g^>lij t f\q P T<T t l
(130) ( Tlqf.t hlpcea.h<ceTl¬f.n h,R ci_baVU Tt UVTda._gT^ t n n P t t t t nTVh£U j t T fkq[g¥T6lmTilmT_]Tx^ tUVl >f f<h3T_gTf ThVcm[]Tc h,acq Sa8j>h,a ct _]TTrklTcmUVTUVj`j_]TVlj>c f<T^ f t ^`[b,h`^`T;Tl c t # a8uvf.Th`q%cehQf.T [ lt Tja Th #v ~P (0lm(#^ Tt c f TrkR j¬T f []U;U Th,Ccea8uv^`f.r!^ t Tlh}  f<hU q%ceE<[gf<Lh lmT^£qf.hh f.n U T6lTTc C_ba¥.^ t 5 T E` t hf cm[]Tt h,cª^hUVf n TR _]T t T_badcm[].Tn UVTh,cªj t T qt []lª<^[t h`f<^l£j(T t UVTc t n T3qf.hU lpcea8cmT t <^T n n a.hl£_]T3qa.l£f ^ R _ f.n h j t Th n C j fkqT6lmlmT^ l ,hf.^lia<f.hl¬^`h$lmj>TT §¨^`j$qf<U;j [bl¬Th,c T W}Tcj>f<^ Y ~ Tc f<hq^`h`TT 2£qa.q[gc`T T!. % Q #3
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(138) . MODELE DES TEMPS D’EXECUTION DE NEWTON EN PARALLELE: 8 jours, 8 intervalles de temps. 18 niter= 5 modèle théorique. 16 niter= 4 14. temps expérimentaux niter= 3. temps (en sec). 12 niter= 2 10 8. niter= 1. 6 4 2 0 0. 1. 2. 3 4 5 nombre de processeurs. E. 6. 7. 8. k. nTTq P t f<T [r n T6n lQ^GcmT6UVlmlmf T n t TRa8_g^kT r *` f t n t T n T6l¬cmT6lmlmT t a8^kr *` Tleq P n T U}ah\t^`U¤T t [],^`P T ja.l []h,c`T adcm[]f.h # ( *E.VlpT6q8 TlQja t a.U TR c t Tl¬,^`[t da t []T t f.h,cQlmf.h,c* Tn U *`_ Tr`qTh,c []q[c`T. f R f *`_]a n ^ t T T n T_ T j P T U«T t [ n TTh;uvf.^ t l h= t * n T t Tx U}adrk[]UVa._ n T$ l =f.h>a8^krS h`[gcmT *`_gT h`f<U `t T n [c`T t adce[gf<hl n T¶TµQcef.h ¶ t *`_gT h`f<U `t T n T n T6n qf<^`t ja8<Tl n T _ []h<ceT t da8_]P _gT t n T ceTUVn jl t Tc_]aVj [blpTt Th qf<UVjkcmTf<^Lh`f<h ^G f.cpcmTUVTh,cadcmUVf,lpj T [],^`T< T_]a;j Tlelm[gf<h n T t a n [badce[gf<hGlmf._ba8[ t TTc n TlQj(f8ceTh,cm[]T_bl _]^`h`[g§¨lmf._ba8[ T.
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