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Parallel Linear Multigrid Algorithms Applied to the Acceleration of Compressible Flows

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(1)Parallel Linear Multigrid Algorithms Applied to the Acceleration of Compressible Flows G. Carré, Stephane Lanteri, L. Fournier. To cite this version: G. Carré, Stephane Lanteri, L. Fournier. Parallel Linear Multigrid Algorithms Applied to the Acceleration of Compressible Flows. RR-3462, INRIA. 1998. �inria-00073228�. HAL Id: inria-00073228 https://hal.inria.fr/inria-00073228 Submitted on 24 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Parallel linear multigrid algorithms applied to the acceleration of compressible flows G. Carré, S. Lanteri and L. Fournier. N° 3462 Juillet 1998 THÈME 4. ISSN 0249-6399. apport de recherche.

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(121) dfSUWtgibpxmosW!pxm] q o¥  h dmSUW#ºŒhUWosdJixm] q¹¸ ­&W!omgia°´iW!kŒbpxzdf]cbpa_a_rÂb a_]chUWbpx{ozr=osdfWV xsWom`la_dm]chU˜™xsgiVdfSUW[ac]_hUW:bexm]_³:bedm]cgih†gp˜‚dfSUWW¨?`Œbedm]cgphUo(i]°´iWh—]_hosWtdm]cgphÒ ^¥uÅÞWd `Uo q WhUgpdfW 0 bpxsW:b 2  - ž‹ Ÿ

(122) ( 5  5

(123) ­ SUWxmW  ‚]_o dfSUWdf]_VnW[]_hUtxsWVnWh„d ¸ 5 ¸ ¸ bph q xsWomkKWt df]°´iWa_r†xmWklxmWosWh„dudmSUWtgih„´iWtdf]°´iW ¸ dfSlW q ] E`lom]°´iW ž a§bpVn]_hŒbpx£bph q df`Uxs U`Ua_Wh„d Ÿ beh q dmSUW{osgi`UxmtW/dmWxmVÄWvlklac]_t]°d&«Œ`=vlWo¥  h¼dfSlW/gpdmSUWx SŒbph q¹¸ 5 ¸ ¸ bph q bexmWudfSlWtgixmxsWosk}gih q ]chl‡ibptgi U]cbph!VJb·dfxm]_tWo ž t:beact`Ua§b·dfW q ˜™xmgiV dfSUW à™áâÞà™ã . . . . Q. . Q . Q . . Q (' Q . Q. '. Q. ' Q. . . . ('.

(124) È sÈpÉ É§Æ É¹ÉEÆmÈ ^É Ç 

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(127) ( 

(128) ( ( , ­ SUWxmW

(129) ( tgpxmxmWomkKgih q odfg†dmSUW#bpkUklxmg:v^]cVXbedmW q omgia_`ldm]cgihE¥—›Œ`ldfSUWxmVngixsW ¸ ­£W q WºUhUWdfSUW xmWom] q `Œbpa ­ SU]_t~S±p]_´pWo7dfSUWxs]ciS„dzФSŒbph q os] q W#gp˜/dmSUW#a_]chUWbpx7osr=ozdfWV dmg© }W#osgia_´pW q gih

(130) dfSUW tgibpxmosWpxm] q 0 ž ˆŠÑ Ÿ

(131) ( ,   R'SUWWxmxsgix dfWxsV ¸ gp ld~bp]_hUW q  „r#dfSlWosgiac`^df]_gih†gp˜dfSUWxsWom] q `ŒbeaW¨=`Ubedf]_gih ž tg„bexmomWixs] q osr=oÝÐ dfWV Ÿ ]cokUxmgpacgihl„bedfW q dfg†tgixsxmWt d¢dfSlWomgia_`ldm]cgih½gih¾dfSUWXºŒhUWpxm] q ¥R'SUW#beacigpxm]°'dfSUV tgphUom]_osdmo ]_h3osgia_´=]_hU  beh q t:bphÒ }W7­ xs]_dsdfWh3bpo ž V`Ua°df]_ixm] q beacigpxm]°dfSUVÀ˜™gix(gihUW Ð tr=ta_Wn­ ]_dmS ‡ibptgi U]ÞomVng=gpdfSlWx Ÿ 0 0

(132)

(133) V[`Ua°df]_ixs] q omgia_`ldm]cgih²bpkUklxmg„bpt~Sl]chU

(134) ( gih#dfSUW(ºŒhUWixs] q ­ ]°dfS   Ñ ¸  R   ! 0A]_hU]_dm]§bea¹omgia_`ldm]cgihgp˜dfSlW(xmWacb·vlbedm]cgih!VnWdmSUg q ˜™gix'osgia°´^]_hUndfSUW(ozr=osdfWVgih  ¸ ˜™gix   ž ­ SUWxsW  ]_o dmSUWh?`UV[ KWxjgp˜acW ´iWa_o Ÿ¸ *  (   bph q    ( xmWomkKWt df]°´iWa°r q WhUgedfWndfSUWXkUxmgpacgihl„bedf]_gihÒbph q xmWosdfxs]ct df]_gih½gpk}Wxfbedmgixmo ž q WºŒhlW q acbedmWx Ÿ¸ # bph q # bpxsWudfSUWh?`UV }Wxmo{ge˜kUxsW Уbph q kKgiosdzФosVXg=gpdmSU]chl ¸  ]co'dmSUWxmWacb·vlbedm]cgih˜Qbpt dfgix'gp˜dfSlW]°dfWxfbedm]_´pWVXW dfSUg q¹¸   !   ! ]_ojdmSUW(VXbedfxs]°v#gi ld~be]chUW q  „r#dmSUW q ]costxsWdf]_³:b·df]_gih†gih  ¸    ! ]_o'dfSUWxm]_iS„d SŒbph q os] q Wgp˜osr=osdmWVgih  ¸ bpxmWb 2  - ¥  }’ Ö Ð !#"%$&(')"!(*+ 0, !  ž omgia_`ldf]_gih!gi ldfbp]chlW q bed'dfSUWkUxsW´=]_gi`Uo ' Фt r^tacW Ÿ }’ Ö-¬Ð/.10325476589*:*1<;>=?"A@CB"%$(B>D%$("!(*+E*GFHB5*%0I0J2B5! *+>6 0¡˜™gi&x * K  . . . +. . . . . . . . . ". . . . . . . . .  +. \+. A. @. . . . . . . . . . .  +.   ! L  ]°]°˜˜ *N* M R'SUW(˜™gia_a_gG­ ]_hUXhUg q W­ ]_omW C O l  acg=t ¶ i‡ bptgi U]Þ]°dfWxmbedf]_gih!]cojbpklkUac]_W q â"âÀþUl÷çøå . Y +. ^+. +. ž ˆiˆ Ÿ. . . . 0.

(135) Ê A> È"}Ê ¹B ȌǤÆ"AÈ! ¡B Ê. ˆŠƒ. K # !  ! ,      !   !     ! ,     !     !    ( !     (    ! ,        ! .   ! ­ SUWxmW   ( ! ]_o/dmSUW¢xsWosdmxm]_tdmW q xmWom] q `Œbpa˜™xmgiVa_W´iWa *!dmgacW ´iWa * beh q xsWomWh„dfo/b q ]_omtxmW df]_³:bedm]cgih²gp˜dfSUWtgph?dm]ch?`Ugp`Uo/gpk}Wxfbedmgix'gih#dfSUWa_W´pWaA*}¥ }’ Ö

(136) ¬Ð/.*6 74 689*:*G<; >=C"A@N.103*+$ *:>=%">! *+ *GFHB5*%0I0J2B5! *+>6 0¡˜™gp&x *  , K    !    !  (      ( !    !    ! K #    ! -    !    ! ,   !   !    ! .        . . . . . . . . . . +.  +. . IÆ. @A 6 ". ^+. ž ˆG Ÿ. . 2 0. :. . . =.  +. . . .  . \+ . 0. . . ! xsWk^Ð. DA. . . .  . .   !.   . . . +. .  +. ^+. @. ž ˆŠ Ÿ.     !     !    !    ! ­ SUWxmW  (     ( xmWklxmWosWh„dfo(dmSUW¢kUxsgeyzWt dfW q tgixmxsWt df]_gih˜™xmgiVa_W´pWa * dfgJacW ´iWa* ž tg„bpxsomWixs] q tgpxmxmWtdm]cgih Ÿ ¥ }’ ÖÐ A"%$ D%.%@%" 2 0,  (   ! R W   \ lg f\ WYg   tgih q ]_dm]cgih3dfg†gp ld~bp]_h½V`Ua°df]_ixm] q W ÁJt]cWhUtr Ë M Í£]_odmSŒbeddfSlW¼om`lVXVXbedm]cgph¾gp˜%dmSUWJgpx q Wxmo[ge˜ dfSlW¢dfxfbehUos˜™Wxgpk}Wxfbedmgixmou]_oixmWbedfWx{dfSUbph—dfSUWngix q Wx(gp˜AdmSUWnkŒbpxsdm]§bea q ] EWxmWh?dm]§bea‚W¨?`Œbedm]cgih©dfg  KW²osgia_´pW q ¥ªR'SU]_o¼tgih q ]°df]_gih ¸%q W´iWacgpk}W q ]ch Ë p‰·Í{beh qÓË ‹eÍ ¸ xmW¨=`l]cxsWo]_h gix q Wxndfg3omgia°´iW!dfSUW Ü{b:´=]_WxzÐÝ\=dfg ¶ Wo(W¨?`Œbedf]_gihUo ¸ dfSUbed{W]_dmSUWx{kUxmgia_gihUibedf]_gih†gpx{xmWosdmxm]_tdf]_gih— KW[a_]chlW:bpxI¥ G/gŠ­£W´pWx ¸ b a_]chUWbpx¡]_h„dfWxsk}gpa§bedm]cgph7]co¡hlgpd¡Wbpom]_a_r[ U`U]_a_d¡]ch7behnbpiia_giVnWxmbedf]_gih¢tgih„dfW v=d¥¡¦¤h7gi`Uxt:bposW ¸ ­£W ¶ WWk dfSlW¢ofbpVnW7gix q Wx/˜™gix{ KgpdfS—xsWozdfxm]_tdm]cgph3beh q kUxmgpacgihl„bedf]_gih†­ Sl]ct~S©]_o(]ch©bpttgix q bphUtW[­ ]°dfS—dfSUW à™áâÞà™ã. . . ,. . . . . A. . . . .

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(140) acW ´iWa ¸ ­£WhlgpdfW(dfSlWu´pbeac`UW + 0/   ]_h#dfSUW +  K   ¥  Jozr=osdfWVgp˜a_W´pWAa * K   ( Ö ‘’:“ Q•p’ Ú ÂÚ ‚Ö “G”l’ Ú “ ˜™gix + / osgiac`^df]_gihUo 0     ( bpxsW:b     . ž ˆ:Y Ÿ     (    (  ! bpxsW:b  ( . . ­ SU Wxm W  q WhUgedfWoXdfSUW!omW d¼ge˜{dfSlW u]_h q W v^Wo¼gp˜  ³gihUWo¼gihÂdfSUW²acW ´iWIa *

(141) ­ ]_dmS ( 1  . ! ¥*R'SU]_oJgikKWxmbedfgpxXdmxfbphUoz˜™WxsoXdmSUW²osgia_`ldf]_gih ˜™xsgiV a_W´iWIa *

(142) dfg3acW ´iWa * ]chgix q Wx%dmg7 U`U]_a q gihUa°r¼dmSUW q ]_omtxmWdm]c³bedf]_gih²gp˜"dfSUW(tgih„df]_h=`lgi`Uojgik}Wxfbedmgix%gih#dmSU]co a_W´pWa}bph q ]co5hUgpd5`UosW q ]_hndfSUWjV[`Ua°df]_ixs] q tr=ta_Wp¥A¦ d5]co£bu­&W]cpS?dmW q bekUkUxmg:v^]_VJb·df]_gih¼gp˜}dfSUW a_W´pWAa *osgia_`ldf]_gih¹¥  | Gu\gih!a_W´iWCa * Ö ‘’:“ Q•p’ Ú Ú ‚Ö “G”l’ Ú “ ˜™gix%dmSUWxs]cpS?djSŒbeh q os] q W 0  

(143)    ( ¥5R'SUW[& ]_o gi ld~be]chUW q  „r#os`UVnVXbedf]_gih†ge˜¡|&Gu\¼˜™xmgpV acW ´iWa%*K¥‚¦ d/]_o q WºUhUW q bpo 0 . . +S . .  +. .  . . . . .  +. S. ^+. . 

(144) . . . . . . 

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