DAI HOC QUOC GIA HA N O I TINH TOAN HIEU N A N G CAO VA LfNG D U N G VAO BAI TOAN MO P H O N G DONG L U C P H A N Ttf Bao cao tong hdp de tai nghien ciiu khoa hoc cap DHQG Trudng Dai hoc cong nghe quan ly) Ma so: QC.05.01 Chu nhiem de tai: Nguyen Hai Chau OAI HOC QUOC GIA HA NQi TRUNG TAM THONG ''iN ^HIJ VlE^ ' cU Ha Noi - 2006 M u c luc D a n h m u c h i n h ve D a n h muc b a n g D a n h sach can b o t h a m gia thUc hien de tai Tdm t a t nhiJng ket qua chfnh cua de tai nghien ciJu khoa hpc 2.1 2.2 2.3 6 6 7 7 Ten d^ tai Chu tri dg tai Nhu'ng ket qua chinh 2.3.1 Ket qua vk khoa hpc 2.3.2 K^t qua phuc vu thuc t€ 2.3.3 Ket qua dao tao 2.3.4 Kgt qua nang cao tilm luc khoa hoc 2.3.5 T m h hhih su* dung kinh phi N O I D U N G C U A D E TAI 3.1 Dat va,n d l 3.2 T5ng quan ve tfnh lire tu'dng tac nhanh mo phong dong luc phan tii 3.2.1 Cac thuat toan nhanh ITnh vuc mo phong dpng luc phan td 3.2.2 Thuat toan FMM va cac biin t h i 3.2.2.1 Thuat toan FMM 3.2.2.2 Thuat toan cua Anderson 3.2.2.3 Thuat toan ciia Makino 3.2.3 May tinh chuyen dung song song G R A P E va iing dung 3.2.4 Cai dat thuat toan nhanh tren phan ciing chuyen dung 3.2.4.1 Cai dat thuat toan tree tren p h i n ciing G R A P E 3.2.4.2 Cai dat thuat toan FMM tren p h i n ciing MD-ENGINE 3.3 Npi dung va kit qua nghien ciiu 3.3.1 Cac kho khan cin giai quylt 3.3.2 Giai phap va kit qua ciia chung toi 3.4 Thao luan 9 10 11 12 12 13 14 16 19 19 19 20 20 21 26 MUC LUC 3.5 28 Kit luan va kiln nghi Tai lieu t h a m khao 29 P h u luc 34 D a n h muc hinh ve 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 Y tudng chmh cua thuat toan tinh luc FMM PhUdng phap cua Anderson PhUdng phap P^M^ ciia Makino Kiln triic cd ban ciia mpt he may tfnh G R A P E May tmh MDGRAPE-2 (PCI) co t i c dp cue dai tUdng dUdng 48GFlops vdi chip MDGRAPE-2 (m5i chip co t i c dp cue dai tUdng duong 16GFlops) May tfnh MDGRAPE-2 (Compact PCI) co t i c dp cUc dai tUdng dudng 192GFlops vdi 16 chip MDGRAPE-2 (m6i chip co t i c dp cue dai tUdng dUdng 16GFlops) Cum may tinh G R A P E nhin tii mat trUdc [54] Cum may tinh G R A P E nhui txt mat sau [54] Cum may tfnh G R A P E nhin tii ben trai [54] So sanh thdi gian tfnh luc ciia thuat toan FMM va thuat toan tinh luc true tilp tren he I Dudng cong cd cac hmh trdn t h i hien hieu nang cua FMM tren may tinh MDGRAPE-2 Dudng cong vdi cac hinh ngu giac la hieu nang ciia FMM tren may chii Cac hmh trdn va ngu giac to den la hieu nang tUdng iing vdi dp chinh xac cao (p = 5), khong to den ling vdi dp chfnh xac t h i p {p = 1) Dudng cong khong cd ky hieu vdi net liln va net diit tUdng iing la hieu nang ciia thuat toan tfnh luc true tilp tren MDGRAPE-2 va may chu Tudng t u nhu hmh 3.10 nhung vdi he II So sanh thdi gian tfnh luc ciia thuat toan FMM va thuat toan tree tren he I Dudng cong cd cac hinh trdn t h i hien hieu nang cua FMM tren may tfnh MDGRAPE-2 Dudng cong vdi cac hmh tam giac la hieu nang cua thuat toan tree tren MDGRAPE-2 Cac hinh trdn va tam giac td den la hieu nang tUdng iing vdi dp chinh xac cao (p — 5), khong td den iing vdi dp chfnh xac t h i p {p = I) Tudng tu nhu hinh 3.12 nhung vdi he II So sanh hieu nang cua hai ban cai dat FMM sii dung cac cong thiic (3.11) - ban 1.0 va (3.12) - ban 2.0 Dudng cong cd hhih vudng la hieu n t o g ciia ban 1.0 Dudng cong cd hinh trdn la hieu nang cua ban 2.0 Cac dudng cong cd hinh td den iing \'di chinh xac cao (p = 5), khong to den iing vdi chfnh xac t h i p (p = 1) 12 14 15 16 16 17 18 19 20 22 23 24 26 27 D a n h muc bang 1.1 3.1 3.2 3.3 Danh sach can bp, cong tac vien, hpc vien cao hpc va sinh vien tham gia thuc hien d l tai Cac pha tfnh toan va cac cdng thiic tUdng iing dUdc sii dung hai ban cai dat FMM Cac p h i n in dam dUdc thuc hien tren may tfnh GRAPE P h a n tfch thdi gian thUc hien cac pha tfnh toan cua ban 2.0 tren he II vdi so lUdng hat A^ = 1024 x 1024 = 1048576 Chii y ring cac pha "Tao cay" va "Tao danh sach lan can va danh sach tUdng tac" thuat toan FMM khong dUdc chiing tdi md ta bao cao vi cae pha chi cd tfnh chit chuan bi cho tfnh toan va chilm r i t ft thdi gian tfnh to^n nhu ta thiy bang So sanh vdi ban cai dat DPMTA 3.1.3 cua Wrankin [49] 21 25 25 Danh sach can bo t h a m gia thu'c hien de tai Bang 1.1: Danh sach can bp, cdng tac vien, hpc vien cao hpc va sinh vien tham gia thuc hien dl tai STT H o va t e n Hpc ham hpc vj Cd q u a n cong tac TS Nguyin Hai Chau (chu nhiem d l tai) T Ebisuzaki TS A Kawai TS Vu Bdi H i n g ThS T r i n Manh Tudng CN Dd Thi Minh Viet CN Nguyin Thi Thuy Linh CN Pham Quang Nhat Minh SVK47 Le Thi Lan PhUdng SVK47 10 Chu Quang Thiiy SVK47 Khoa Cdng nghe thdng tin, trudng Dai hpc cdng nghe, DHQGHN Trung tam tfnh toan cao cip, Vien nghien ciiu vat ly va hda hpc Nhat Ban Hpc vien Cdng nghe Saitama, Nhat Ban Khoa Cdng nghe thdng tin, trudng Dai hpc cdng nghe, DHQGHN Khoa Toan Cd Tin hoc, trudng DHKHTN, DHQGHN Khoa Cdng nghe thdng tin, trudng Dai hpc cdng nghe, DHQGHN Khoa Cdng nghe thdng tin, trudng Dai hpc cdng nghe, DHQGHN Khoa Cdng nghe thdng tin, trudng Dai hpc cdng nghe, DHQGHN Khoa Cdng nghe thdng tin, trudng Dai hpc cdng nghe, DHQGHN Khoa Cdng nghe thdng tin, trudng Dai hpc cdng nghe, DHQGHN Tom t a t nhiJng ket qua chinh cua de tai nghien ciJu khoa hoc 2.1 Ten de tai Tfnh toan hieu nang cao va iing dung vao bai toan md phong ddng luc phan tii (High performance computing and its application to molecular dynamics simulation) M a s d : QC.05.01 2.2 Chii tri de tai Ngudi chu tri: TS Nguyin Hai Chau Cd quan: Trudng Dai hpc Cdng nghe, Dai hpc Qudc gia Ha Ndi Dia chi: 144 Xuan Thiiy, C i u Giiy, Ha Ndi Dien thoai: 04-7547813 2.3 2.3.1 NhiJng ket qua chfnh Kgt qua ve khoa hoc • Da hoan 02 bai bao khoa hpc giM dang tap chf Tin hpc va dilu khiln hpc va Tap chf Khoa hpc (Dai hpc Quoc gia Ha Ndi) • Da hoan 01 bao cao tai hdi thao qudc t l vl tfnh toan hieu nang cao dUdc td chiic tai trudng Dai hpc Khoa hoc tu nhien • 03 bao cao chuyen d l (technical report) vl: Lap trinh song song vdi OpenMP nghien ciiu hieu nang ciia he thdng file song song ao PVFS va tdng quan ve tfnh toan song song T6MTAT 2.3.2 NHIING KET QUA CHINH CUA D^ TAI NGHIEN ClfU KHOA H0C7 K i t qua phuc v u thu'c t l Da hoan bp chudng trinh cai dat thii nghiem thuat toan FMM tren may tfnh MDGRAPEI-2 Cac kit qua nghien ciiu cua dl tai cho thiy, thuat toan chung tdi thilt kl va cai dat cd hieu nang cao va dp chfnh xac thoa man cac yeu ciu cua nhilu ling dung linh vUc md phong dpng luc phan tii Thuat toan cai dat CO kha nang tfch hdp vdi mpt so iing dung vl MD da dUdc triln khai nhu NAMD May tfnh MDGRAPE-2 cd tai Ha Npi va kha nang sii dung may tfnh vao md phong la kha thi 2.3.3 K i t q u a d a o tao • Da hudng din tot nghiep 03 sinh vien bao ve thang 6/2006 vl dl tai tfnh toan hieu nang cao (xem cac bia luan van kem theo) • Dang hudng din 01 hpc vien cao hpc vl dl tai tfnh toan hieu nang cao, du kiln bao ve 12/2006 2.3.4 K i t q u a n a n g c a o t i e m \\ic k h o a h o c Nghien ciiu vl cac thuat toan, tlm hilu vl tfnh toan song song, tfnh toan hieu nang cao, tfnh toan cum va tfnh toan thdng lUdng cao Da hudng din sinh vien, td chiic seminar va giang day vl ITnh vUc tfnh toan hieu nang cao, tfnh toan song song va tfnh toan cum cho cac sinh vien tii nam 2004 Nam hpc 2006-2007 se giang day vl tfnh toan song song cho hpc vien cao hpc cua khoa Cdng nghe thdng tin, trudng Dai hpc Cdng nghe 2.3.5 T i n h h i n h sdf d u n g k i n h phi Da Sli dung hit kinh phf dUdc cip ciia dl tai CHU NHIEM DE TAI XAC N H A N CUA DON VI XAC N H A N CUA Cd QUAN CHU QUAN T6M TAT NHIJNG KET QUA CHINH CUA DE TAI NGHIEN CHU KHOA HOCS Abstract We have implemented fast multipole method (FMM) on a special-purpose computer G R A P E (GRAvity piPE) The FMM is one of the fastest approximate algorithms to calculate forces among particles Its calculation cost scales as 0(-/V), while naive algorithm scales as 0{N'^) Here, TV is the number of particles in the system GRAPE is a hardware dedicated to the calculation of Coulombic or gravitational force among particles Its calculation speed is 100-1000 times faster than that of conventional computers of the same price, though it cannot handle anything but force calculation We can expect significant speed up by the combination of the fast algorithm and the fast hardware However, a straight forward implementation of the algorithm actually runs on G R A P E at rather modest speed This is because of the limited function of the hardware Since G R A P E can handle particle force only, just a small fraction of the calculation procedure can be put on it The rest part must be performed on a conventional computer connected to GRAPE In order to take full advantage of the dedicated hardware, we modified the FMM using Pseudoparticle Multipole Method and Anderson's method In the modified algorithm, multipole and local expansions are expressed by distribution of a small number of imaginary particles (pseudoparticles), and thus they can be evaluated by GRAPE Results of numerical experiments show that G R A P E accelerates the FMM by a factor of 3-60 depending on the accuracy Its performance exceeds that of Barnes-Hut treecode on GRAPE at high accuracy (root-mean-square relative force error ~ 10~^), in the case of closeto-uniform distribution of particles K e y w o r d s : Molecular dynamics, numerical simulation, fast multipole method, tree algorithm, Anderson's method, pseudoparticle multipole method, special-purpose computer NOI D U N G CUA DE TAI 3.1 Dat v4n d l Md phong dpng lue phan tii la mpt nhiing phUdng phap phd biin dUdc sii dung vat ly/hoa hpc d l nghien ciiu cac he nhilu hat Md phdng ddng luc phan tii dUa tren dinh luat Newton ve chuyen ddng: F = ma^ dd F la luc tac dung tren hat; m, a tUdng iing la khdi lUdng va gia tdc cua hat Tuf cac thdng tin ve luc tac dung tren mdi hat, xac dinh gia tdc cua mdi hat he Giai phudng trinh chuyin dpng d l sinh mdt dudng cong md ta vi trf, van toc, gia toc cua cac hat tai cac mdc thdi gian khac Tii dudng cong nay, trang thai tilp theo hay trang thai trUdc ciia he se dUdc du bao Xet tren khfa eanh tfnh toan, viec thuc hien bai toan md phong ddng luc phan tii cd t h i dUdc md ta qua cac budc sau: Chpn vi trf ban d i u cua cac hat vdi dien tfch cho trude he Chpn mdt tap hdp van tdc khdi tao ciia cac hat Cac van toc thudng dUdc chpn theo phan phdi Boltzmann ddi vdi mdt vai nhiet dp, sau dd dupe chuin hda cho tdng ddng lUdng ciia toan he bing Tfnh ddng ludng cua mdi hat tu" van toc va khoi lUdng cua chiing Tfnh lUc tUdng tac tlnh dien (Coulombic force) tren mdi hat Tfnh vi trf mdi cho cac hat sau mdt khoang thdi gian ngin sau dd Khoang thdi gian dUdc gpi la bude thdi gian (time step) Viec tfnh toan dUdc thuc hien bing each giai phudng trinh chuyin ddng dua tren dinh luat Newton Tfnh toan van tdc va gia tdc mdi cho cac hat he Lap lai cac budc tu" budc din budc Lap lai qua trinh du lau d l cho he dat tdi trang thai can bing Khi he dat tdi trang thai can bing, ghi lai vi trf cua cac hat sau mot sd vdng lap n h i t dinh Cac thdng tin thudng dUdc ghi lai sau tii din 25 vdng lap Danh sach cac tpa dp tao quy dao chuyen dong ciia he hat Metadata File Hinh C4u hinh cua he th6ng Chiing toi bang thong doc/ghi cua mot tiln trinh tren mdi may ddi vai mot file tren may Cac tiln trinh doc/ghi file vai kich co thay d6i tir 128KB din 128MB ^ 400 f^^'^^Sr 4P^X Ay - V i f 100 'mm^ii^ 28K 512K 2M 8M Request size 32M 128M Bilu d6 Bang thong ghi truy cap cac file PVFS, NFS, VFS Phan tich kit qua: (Bilu d6 1) D Bilu db chi bang thong doc/ghi t6i da cua cac he thong file PVFS, NFS, VFS Bang thong lan nhSt cua VFS va NFS dir lieu khong di chuyin tren mang la 620MBps cua PVFS la 210MBps.Thi nghiem la ca sd dl chiing ldi xac nhan ket qua cac thi nghiem sau la hgp ly 17 D Kk qua thi nghiem cung cho th§y hieu nang bang thdng doc/ghi cac file cua PVFS kem han cua NFS va VFS Do sir dung PVFS tren mot may la khong thich hgp b Thi nghiem Chung toi ciu hinh he thdng nhu sau: a NFS: he thdng co NFS server, I NFS client b PVFS: he thdng co Manager, I/O node, client TCP/IP Network KE!:S.sei:ver T ;?f=rTS Tr -n 300 250 - - Stripe 32- stride 64 * - S t r i p e 64 - stride 128 ^ - S t r i p e 128-stride256 8K 16K 32K 64K 128K 512K 2M Group size Bieu dd Bang thdng ghi thay ddi cac tham sd striping va partitioning • Phan tich ket qua (bi€u dd 4): • Trong trudng hgp kich cd stripe la 32KB, kich cd stride la 64KB: > Khi group size la 8KB, hoac 16KB, hoac 32KB thi bang thdng ghi cao Dieu hoan toan hgp ly vi dd du lieu rdi rac ma client truy cap chi thuoc mdt I/O node > Khi group size la 64KB, 128KB, 512KB, 2MB, bang thdng ghi thkp vi du lieu thugc hai I/O node • Tuang tu ddi vdi cac trudng hgp kich cd stripe la 64KB, stride la 128KB, va kich cd stripe la 128KB, stride la 256KB => K a qua thi nghiem cho thky tham sd striping (stripe) phii hgp vdi tham sd partitioning (stride, group size) thi hieu nang cua he thdng la cao, ngugc lai hieu nang bi giam di nhieu Thi nghiem Giai doan 1: Chiing tdi ti^n hanh cai dat PVFS \a NFS tren ma\ 21 Cau hinh he thdng nhu sau: ^ NFS: he thdng cd NFS server, NFS client ^ PVFS: he thdng cd Manager, I/O node, client NFS?sef|e| NFS client ^NFS:cli'enl Filel ^Manager " jJsSlietitA::,'^ Metadata File2 File] I/O Node Client, •^- File2 b)Cau hinh PVFS Hinh 30 a ) C k hinh NFS - Ddi vdi PVFS: Chung tdi tien hanh bang thdng cua lien trinh dgc/ghi ddng thdi File2, mdi tien trinh chay tren mdt client File2 dugc stripe tren I/O node vdi ca stripe la 16KB Kich cd dgc/ghi file (request) thay ddi tir 16MB d8n 750MB - Ddi vai NFS: Chung tdi bang thdng ciia lien trinh dgc/ghi ddng thdi Filel, mdi i\kn trinh chay lren mot client Kich cd dgc'ghi thay ddi tir2MB ddn 750MB 22 -A-NFS *-PVFS 750M 500M 250M Request size Bieu dd Bang thdng dgc hai lign trinh ciing truy cap mdt file 50 45 ifciS^ii^w^^-^ 40 '^' ''•^'•i'^;!.,i~~^" m^^yyx'-''-^^0^,^ 35 •'•:::• ^ i ^ > - r ^ l i ^ ^ > ^ ^ f e ^ ^ ' ^ • " m 30 • •'••••: f': • •• •• • rniMM'^'^ ' ih «-NFS -1 ^—NFS - ^ - P V F S -1 -X- PVFS - 2M 4M 8M 16M 32M 64M 100M 250M 500M 750M Request size B i k dd Bang thdng ghi mdl tiSn trinh truy cap mdt file va hai tiln trinh ciing truy cap mot file 23 Trong biSu dd 6, dudng NFS - bi^u diln bang thdng ghi cua NFS mot ti€n trinh truy cap mot file, duomg NFS -2 bidu diln bang thdng ghi ciia NFS hai ti6n trinh ciing truy cap mdt file Tuang ty ddi vdi dudng PVFS -1 va PVFS -2 Giai doan 2: Chiing tdi cai dat PVFS va NFS tren may Cku hinh he thdng nhu sau: ^ NFS: he thong cd NFS server, NFS client ^ PVFS: he thdng cd Manager, I/O node, client rt: ' ; server: • Clieiit-:'' • Filel Hinh NFS Client C NFSCIien! Filel b)C4u hinh PVFS a ) C k hinh NFS - Ddi vdi PVFS: Chung tdi tiln hanh bang thdng ciia tien trinh doc ddng thdi File2, mdi tidn trinh chay lren mot client File2 dugc stripe lren I/O node vdi cd stripe la 16KB Kich ca doc file (request) thay ddi lu 20MB i^n32MB 24 - Ddi vol NFS: Chiing tdi bang thdng cua tiln trinh dgc/ghi ddng thai Filel, mdi tiln trinh chay tren mdt client Kich cd dgc thay ddi tir 20MB din 32MB 50 45 40 'WiK!^ yy '^.i: •'' i^ ^ A'r.iA; "^— I 35 CQ • •—; .f^.,-,^-^- axJi^-i ,'4^%r - • T-.^ -r*-.' •iWr ^ "^.'.•^y.-.'i- S 30 i 25 —: rtU^-i^vV/•-.•••> w^^'-"^!^'-,''^:,^^^:: 'ri }:• \^' •• \\ ':^.m\"x.' c,r- ^iti^ •••'.;.N:»'i-.i^ •• I 20 -• '•'•• - - - , • ' • - tv"**' I 15 10 ^•^•';^'.'''-''*^'^""''-"*'-''v:-'^-^r^*r; * •,'•;••">"• 20M ^?^./.^!^- 24M 28M 32M Request size Bilu dd Bang thdng dgc ba tiln trinh ciing truy cap mdt file • Phan tich kit qua: • Bilu dd va bilu dd cho thiy bang thdng doc/ghi cua PVFS cao han cua NFS hai liln trinh doc/ghi file vdi kich ca ldn • bilu dd 6, bang thdng ghi cua NFS hai client ciing truy cap mdt file chi tang len il so vdi trudng hgp mdt client truy cap mot file (khoang 1,4 \kn) Trong bang thdng ghi ciia PVFS tang len 2,4 lin bilu dd 7, bang thdng doc cua PVFS ldn han ciia NFS kich cd dgc file la ldn (tir 20MB din 32MB) O Dilu chirng td sd client ddng thdi truy cap mdl file tang len thi bang thdng doc/ghi ciia PVFS cao han NFS NFS b that cd chai nhilu client cung truy cap mot file, PVFS stnpe du Heu lren nhilu dia nen tranh dugc hien lugng na>' ^NFS •-PVFS K^T LUAN • PVFS la mot he thdng file cd bang thdng doc/ghi cao ddi vdi cac file c9 ldn Dk dat dugc hieu nang doc/ghi cao ddi vdi file PVFS cin lira chon cac tham sd striping va cac tham sd phan vung file mot each thich hgp Cac ung dung thich hgp vdi he thdng file PVFS la cac ung dung song song va cac ung dung sii dung file vao/ra cd ldn nhu cac ung dung tinh toan khoa hoc hoac cac iing dung xii ly da phuong tien Cac ling dung khdng thich hgp vdi he thdng file PVFS la cac iing dung xii ly vdi cac file nhd nhu cac trang html tlnh, cac iing dung van phdng 26 PHIEU DANG KY KET QUA NGHIEN CU'U KHOA HOC CONG NGHE Ten d l tai: Tinh toan hifu nang cao va ufng dung vao bai toan mo phong dong lire phan t\i (High performance computing and its applications to molecular dynamics simulations) M a s6: QC.05.01 Cd quan quan ly d§ tai: Dai hoc Qu6c gia Ha Npi Dia chi: 144 Xuan Thuy, Cau Giay, Ha Noi Dien thoai: 8340564, Cd quan chu t r i d l tai: Trudng Dai hpc Cong nghe, Dai hpc Quoc gia Ha Npi Dia chi: 144 Xuan Thuy, Cau Giay, Ha Npi Dien thoai: 7547813 T n g chi p h i thu'c chi: 40.000.000 d6ng Trong 40.000.000 d6ng - Tir ngan sach nha mrdc T h d i g i a n n g h i e n cufu: 12 thang Thdi gian bat dau: 13/9/2005 Thdi gian ket thuc: 13/9/2006 T e n cac c a n b o p h i h d p n g h i e n cxhi: Chu tri de tai: TS Nguyen Hai Chau Cd quan: Bp mon cac he thong thong tin, khoa Cong nghe thong tin, trirdng Dai hpc Cong nghe, Dai hpc Quoc gia Ha Npi Dien thoai: 7547813 Nhutig ngUdi tham Ria: H p c h a m Cd q u a n c o n g t a c S T T H o va t e n h o c vi Trung tam tinh toan cao cap, TS T Ebisuzaki Vien nghien cijfu vat ly va hoa hpc Nhat Ban Hpc vien Cong nghe Saitama TS A Kawai Nhat Ban Khoa Cong nghe thong tm ThS Vu Boi Hang trudng Dai hpc cdng nghe DHQGHN Khoa Toan Cd Tin hpc, trudng CN Tran Manh Tudng DHKHTN, DHQGHN Khoa Cong nghe thong tin, CN Do Tin Minh Viet trudng Dai hpc cong nghe DHQGHN CN Khoa Cong nghe thong tni Nguyen Thi Thuy Linh trudng Dai hpc tong nghe DHQGHN Pham Quang Nhat Minh SVK47 Le Thi Lan PhUdng SVK47 Chu Quang Thuy SVK47 So dSng k y de tai Khoa Cong trudng Dai DHQGHN Khoa Cong trudng Dai DHQGHN Khoa Cong trudng Dai DHQGHN So chihig nhan dang ky ket qua nghien cij^u nghe thong tin hoc nghe nghe thong tin, hpc cong nghe, nghe thong tin, hpc cong nghe, Bao mat A Phd bien rpng rai, B Phd bien han ch^ C Bao mat Ngay Ngay Tom tat ket qua nghien cvtu: - Chung toi da nghien ctjfu tdng quan ve tfnh toan hieu nang cao, tfnh toan song song; da nghien cu'u ve moi trUdng lap trinh OpenMP, he thdng file song song ao PVFS; da nghien ciiu v^ cac phUdng phap va cdng cu tfnh lUc nhanh mo phong dpng luc phan tiJf, dac biet la thuat toan khai tri^n da cue nhanh FMM (Fast Muthpole Method) va may tfnh song song chuyen dung MDGRAPE-2 - Chung tdi da cai dat cdng thuat toan FMM tren may tfnh chuyOn dung MDGRAPE-2 va tim cdng thi'rc mdi d^ tang toc dp tinh luc lUdng tac tiiuat toan FMM Khi ap dung cong thik mdi, hieu nang cua thuat toan FMM tren may tfnh MDGRAPE-2 da dUdc tang len tir lan (vdi dp chfnh xac tinh luc thap - 10"-) d^n lan (vdi dp chfnh xac cao ~ 10"^) - Kit qua nghien cufu cua de tai cho thay, thuat toan chung toi thiet ke va cai dat CO hieu nang cao va chfnh xac thoa man yeu can ciia nhilu ijfng dung md phong ddno- luc phan t\i Thuat toan FMM chung tdi cai dat tren may tfnh MDGRAPEden 60 lan (vdi dp chii da dudc tang toc tir lan (vdi dp chfnh xac thap 10 ^] so vdi thuat toan FMM cai dat tren cac may tfnh thdng thudng xac cao ~ 10 K i l n nghi v e qui m o va doi tu'dng a p dung ket qua nghien ci^u: Cac ket qua cua de tai gdm bao cao, bai bao, chUdng trinh ijfng dung cd the chia se cho nhung ngUdi quan tam den hUdng nghien cu:u cua de tai Chu tich Hpi Thu trUdng co Chu nhiem de taiyD^hu d6ng danh gia quan quan ly d^' tai "^'- ^~ chinh tln'rc T^^ J_^\'t/l4i Zy DAI HOC QUOC GIA HA NOI TRl/ONG DAI HOC CONG NGHE Pham Quang Nhat Minh AP DUNG PHirONG PHAP SVD TINH LlTC XAP xi TRONG BAI TOAN MO PHONG DONG LlTC PHAN TLT KHOA LUAN TOT NGHIEP DAI H p C HE CHINH QUY Nganh: Cong nghe thong tin Can bo huo-ng d i n : TS Nguyin Hai Chau HA NOI - 2006 B^ HOC QVOC GIA HA NOI TRirdNG DAI HQC CONG NGHE Le Thi Lan P h u c n g SONG SONG HOA THUAT TOAN BARNES-HUT V6l OPENMP KHOA LUAN TOT NGHIEP DAI HOC HE CHINH QUY Nganh: Cong nghe thong tin Can bo h u a n g dan: TS Nguyen Hai Chau HA NOI - 2006 DAI HQC QVOC GIA HA NOI TRl/cnVG DAI HQC C N G NGHE Chu Quang Thuy TINH TOAN THONG LlTONG CAO V l CONDOR KHOA LUAN TOT NGHIEP HE DAI HOC CHINH QUY Nganh: Cong nghe thong tin Can bo hu-ffng dan: TS Nguyen Hai Chau HA NOI - 2006 ... (Dai hpc Quoc gia Ha Ndi) • Da hoan 01 bao cao tai hdi thao qudc t l vl tfnh toan hieu nang cao dUdc td chiic tai trudng Dai hpc Khoa hoc tu nhien • 03 bao cao chuyen d l (technical report) vl: Lap... ve thang 6/2006 vl dl tai tfnh toan hieu nang cao (xem cac bia luan van kem theo) • Dang hudng din 01 hpc vien cao hpc vl dl tai tfnh toan hieu nang cao, du kiln bao ve 12/2006 2.3.4 K i t q u... song song, tfnh toan hieu nang cao, tfnh toan cum va tfnh toan thdng lUdng cao Da hudng din sinh vien, td chiic seminar va giang day vl ITnh vUc tfnh toan hieu nang cao, tfnh toan song song va tfnh