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3D Harmonic Maxwell Solutions on Vector and Parallel Computers using Controllability and Finite Element Methods

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(1)3D Harmonic Maxwell Solutions on Vector and Parallel Computers using Controllability and Finite Element Methods Marie-Odile Bristeau, Roland Glowinski, Jacques Périaux, Tuomo Rossi. To cite this version: Marie-Odile Bristeau, Roland Glowinski, Jacques Périaux, Tuomo Rossi. 3D Harmonic Maxwell Solutions on Vector and Parallel Computers using Controllability and Finite Element Methods. [Research Report] RR-3607, INRIA. 1999. �inria-00073072�. HAL Id: inria-00073072 https://hal.inria.fr/inria-00073072 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. 3D Harmonic Maxwell Solutions on Vector and Parallel Computers using Controllability and Finite Element Methods. Marie-Odile Bristeau , Roland Glowinski , Jacques P´eriaux , Tuomo Rossi. No 3607 Janvier 1999 ` THEME 4. ISSN 0249-6399. apport de recherche.

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(100) 

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(121) g±=„4tcw ”Ò ‹ €c‚†w± É ‡c~†„4wzwa‚†wHvwa‡Z„‚†~¿°/3ƒC‘+ vwHƒ£‡cŠ„4watc‡c~†¼Z€cwaŠ · tc~†t · wHÌwrwHƒC‘‚†~†wH ‹ waŸCwa‚† C‰Kw ‹ ~†‡Ïƒg€c„4 ev¦ƒg„4~† ‹ ƒg„ƒa‚ƒgŠ4Š3~ É Hƒ£„4~† C‡X¸stc~†Š vwa„3tc ‹ Øcƒg‚†Š4 ¯Hƒ£‚¿‚†w ‹:‹ Œe‡/ƒCvx~¿a‚†€cŠ4„3wH‘ŠHØc~†Š~†‡c~†„4~ƒg‚†~†Èaw ‹ °eŒÆƒ É ‘Š4„‰/ƒ6‘„4~†„4~† C‡ · tc~†t:„4tcwa‡Æ~†Š ~†„4wH4ƒ£„4~†ŸCwa‚†ŒÏ~v‰/‘ gŸCw ‹ ~¿‡: e ‹ wHÃ„4 ¢Cwa„a C‡c‡cwaa„4w ‹ ‘wa¢C€c‚ƒCvwaŠ4tča‚†€cŠ4„4wH‘Šƒg‡ ‹ · wa‚†‚ °/ƒg‚ƒg‡Z´ aw ‹ ‡e€/v°KwH g±XŸCwH‘„3~¿awaŠV¸ëstcw 6°c„ƒg~†‡cw ‹¯‹ waa ev‰K CŠ4~†„4~† C‡Ä~†Šr„4tcwa‡Ä€cŠ4w ‹ ƒgŠƒg‡¯~†‡c‰c€c„k±³ Z=„4tcw <vwHƒg‡cŠrƒg‚†¢C Z‘~†„4t/vƸësÚtc~¿Šƒg‰c‰/‘ eƒ£tt/ƒgŠk°/wawa‡¯a evx‰/ƒC‘w ‹ · ~†„4t¯ C„3tcwHrvwaŠ4t‰/ƒCÌ„4~†„4~† C‡c~†‡c¢ vwa„3tc ‹ Š~†‡ - Vš 0¸ 2P‡¯ C€/=ƒg‰c‰/‘ ZƒgtXØVwHƒgt‰/‘ eawaŠ3Š4 e$t/ƒg‡ ‹ ‚†waŠ C‡cwŠ4€c° ‹ ev¦ƒg~†‡XØCƒg‡ ‹ „4tcw‘wa¼e€c~‘w ‹ ŸCwaa„4 e‘Š ƒg‡ ‹ v¯ƒ£„‘~†awaŠ ƒ6‘w ‹ ~†Š4„Ì~¿°c€c„3w ‹ „3 τ4tcw ‹ ~ËÊ%wHÌwa‡e„‰/‘ ZawaŠ4Š4 Z‘Šza 6‡Z±³ e3v~†‡c¢¯„4tcw ‹ waa ev‰K CŠ4~Ë´ „4~† C‡ g±„4tcw ‹ ev¯ƒg~†‡X¸ÏsÚtcw¯‡c ‹ waŠƒg„„4tcw¯Š3€c° ‹ ev¯ƒ£~¿‡~¿‡Z„4wHù±Âƒgaw°/ 6€c‡ ‹ ƒC‘~†waŠ)ƒCÌw)Š3t/ƒC‘w ‹ ¸ st/ƒ£„~†ŠHØ/ƒg‚†‚X„4tcw‰/Ì eawaŠ4Š3 e‘Š · tc CŠ4wŠ3€c° ‹ ev¯ƒ£~¿‡cŠ1vwawa„zƒg„ƒ¢C~†ŸCwa‡:~†‡e„4wH¶± ƒgaw1‡c ‹ wt/ƒVŸCwƒ ‰/‘~†Ÿgƒg„4wa 6‰eŒÄ g±„4tcwŸCwaa„3 eka ev‰/ 6‡cwa‡e„4Š1‘wa‚ƒg„4w ‹ „4 ¯„3tc~¿Š1‡c ‹ wC¸stc~†ŠzŠ4„4ƒg„4wa¢CŒ~†‡cH‘wHƒgŠ3waŠ „4tcwa evx‰c€c„ƒg„4~† C‡/ƒg‚$ “Ÿ6wH‘tcwHƒ ‹ ƒÄ°c~†„HØ °c€c„1~¿„Š3~Ávx‰c‚¿~ É waŠ„4tcw~Ávx‰c‚¿wHvxwa‡e„ƒ£„4~† C‡X¸ &Š4~†‡c¢Æ„4tc~†Š Š4„4ƒg„4wa¢CŒCØ · wƒC‘wƒg°c‚†w„3 ¯Š4 C‚†ŸCw‚ƒC‘¢6wH‰/‘ C°c‚†wHvŠHØh ek„4 ¯Š4 C‚†ŸCwƒx¢C~†ŸCwa‡p‰/‘ 6°c‚¿wHv ± ƒgŠ3„4wHk°eŒ ~†‡cH‘wHƒgŠ3~¿‡c¢Ä„4tcw1‡e€/v°KwH g±ëŠ4€c° ‹ ev¯ƒg~†‡c' Š H ƒg‡ ‹ ‰/‘ ZawaŠ4Š4 e‘7Š Ka¸ 1€/‰/ƒC4ƒg‚†‚†wa‚~v‰c‚†wHvwa‡e„ƒg„4~† C‡!~†ŠÏƒg‚†¢Cwa°/4ƒ£~¿Hƒ£‚¿‚†Œ!wa¼Z€c~†Ÿ“ƒg‚†wa‡Z„¯„4 ,„4tcwĊ4wa¼Z€cwa‡e„3~Áƒ£‚zƒg‚†¢C g´ ‘~†„4t/vÒØ/€c‡c‚†~ ,gw„4tcw€cŠ3€/ƒg‚ ‹ Zv¯ƒg~†‡ ‹ waa evx‰/ CŠ4~†„4~† C‡vwa„4tc ‹ ŠHØ · tcwHÌwCØ/„‘ŒZ‰c~¿Hƒ£‚¿‚†ŒCØ ƒ¯‰/ƒ64ƒg‚†‚†wa‚ ‰/‘waa 6‡ ‹ ~¿„3~¿ 6‡cwH~†Ša C‡cŠ4„‘€ca„3w ‹ ±P e1„4tcw¦~¿„3wH4ƒg„4~†ŸCwŠ4 C‚†€c„4~† C‡ g±„4tcw¯‚†~†‡cwHƒCŠ4ŒZŠ4„4wHv ƒ6‘~†Š4~†‡c¢ ±Â‘ ev ‹ ~†Š4HÌwa„4~†ÈHƒg„4~† C‡X¸µ1€cw„4 Ą4tcwwaŽe‰c‚†~†a~†„„4~vw´Â~†‡Z„4wa¢e4ƒg„3~¿ 6‡ÆŠ4tcwHvxw)ƒg‡ ‹ v¯ƒgŠ4Š‚†€/v‰c~†‡c¢ ±P e&„4tcw¢Cwa‡cwH4ƒg‚†~†Èaw ‹ · ƒHŸ6wwa¼e€/ƒg„3~¿ 6‡c' Š HPšc¸ VV› KadØ HPšZ¸ g5  Kkƒg‡ ‹ H šc¸5  IVK¶´ HPšc¸† aVy KaØeƒ£‡ ‹ „4tcw~¿„3wH4ƒg„4~†ŸCw Š4 6‚¿€c„3~¿ 6‡Æ g±X„4tcw‚†~¿‡cwHƒ6r‰/Ì C°c‚†wHvJ Š HPšc¸÷Vœ K Ø HPšc¸ / KaØCƒg‚v CŠ4„ƒg‚†‚ „4tcwza Zv¯v€c‡c~¿Hƒ£„4~† C‡¯ Zaa€/‘Š~¿‡ „4tcwÄv€c‚†„4~†‰c‚†~†Hƒg„4~† C‡, £±Úƒ ‹ ~†Š4„‘~†°c€c„4w ‹ ŸCwaa„4 e&°eŒƒ ‹ ~†Š4„‘~†°c€c„4w ‹ v¦ƒg„‘~†Ž  a e4‘waŠ3‰/ C‡ ‹ ~†‡c¢ „4 ¦„4tcw~†‡Z„4wa¢e4ƒg‚ H/h¸ IVKa¸rs$ ‹ waŠ4HÌ~¿°Kw„4tc~†Š1~†‡Çv eÌw ‹ wa„ƒg~†‚PØ · wa C‡cŠ4~ ‹ wH&„4tcwHƒgŠ4w · tcwa‡ · w t/ƒVŸCw 6‡c‚¿ŒÄ„ · Š4€c° ‹ ev¦ƒg~†‡cŠH¸stcwz¢6‚¿ 6°/ƒg‚%v¯ƒ£„‘~†Ž%Ø ‹ wa‡c 6„4w ‹ °ZŒ  Øeƒg‡ ‹ „4tcw1ŸCwaa„4 eÌŠ ƒg‡ ‹ \ *ƒgŠ4~†‡c¢ C‡. . C. í. h C*.

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