Mathematical Simulation for 3-Dimensional Temperature Visualization on Open Source-based Grid Computing Platform

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1 009 Intenatinal Cnfeence n Machine Leaning and Cting IPCSIT vl. 0 0 IACSIT Pess, Singae Matheatical Silatin f -Diensinal Teeate Visalizatin n Oen Sce-based id Cting Platf Na Alias, Niza Sata, Zaith Safiza Abd. haffa, Rziha Dawis, Nhafiza Hazah, Md. Rajibl Isla Institte f Ibn Sina, Univesiti Teknlgi Malaysia, 80 Skdai, Jh, Malaysia Deatent f Matheatics, Faclty f Science, Univesiti Teknlgi Malaysia, 80 Skdai, Jh, Malaysia Abstact. New Iteative Altenating Exlicit NAE is a wefl aallel neical algith f ltidiensinal teeate edictin. The discetizatin is based n finite diffeence ethd f atial diffeential eqatin PDE with aablic tye. This ae sed the NAE ethd as a staight fwad tansfatin f seqential t aallel algith sing dain decsitin and slitting stategies. The cesses invlving the schedling f cnicatin, algetic and aing the sb dain int a nbe f cesss. The citical -Diensinal teeate visalizatin invlves lage scale f ctatinal clexity. This ctatinal challenge insiing s t tilize the we f advanced high efance cting esces. By the eans f highe efance cting, the ctatin cannt be elying n jst ne single set f clste. Theefe, this eseach takes the advantage f tilizing ltile set f clstes f gegahically diffeent lcatin which is knwn as gid cting. In ealizing this cncet, we cnside the advantages f data assing between tw web sevices which each ae cnnected with ne ltile set f clstes. F this kind f elatinshi, we chse sevice-iented achitecte SOA style. Each web sevices ae easily aintainable since thee is lse cling between inteacting ndes. The develent f this achitecte is based n seveal gaing langage as it invlves algith ileentatin n C, aallelizatin sing Paallel Vital Machine PVM and Java f web sevices develent. As the cnclsins, this leading gid-based alicatin latf has a bight tential in anaging highly scalable and eliable teeate edictin visalizatin. The efficiency f this alicatin will be eased based n the eslts f neical analysis and aallel efance. Keywds: aablic eqatin, New Altenating Exlicit NAE, aallel algith, en sce, web sevices, gid cting. Intdctin As a wefl aallel neical algith f ltidiensinal teeate edictin, New Iteative Altenating Exlicit NAE will be discetized based n finite diffeence ethd f atial diffeential eqatin PDE with aablic tye. U U U U hx, t, t x y z With initial cnditin, U x, 0 Fx, z, x, t 0, and bnday cnditin, U 0, t U, t U x,0, t U x,, t U x, 0, t U x,, t 0 Decsitin f atix A which is sitive and syetically defined by A.

2 A, f I I, I, I, I, I, I. Iteatin f this ethd will st ntil the slave had et the lcal sting citein that is, k j i,, and aste et the glbal cnvege citein,.. id Cting Platf As an advanceent f cnventinal secte, the eal and secific ble that ndelies the gid cncet is cdinated esce shaing and ble slving in dynaic, lti-instittinal vital ganizatins []. This eseach sed gid-based sftwae that ai t handle bles which have high ate f ctatinal clexity by viding lage sace f ey allcatin, ini cnstin f lticess syste cst as well as aintainable clste f wkstatins that is distance lcated. The -Diensinal ctatinal challenge dives the insiatin t tilizing the high ability ate f cting esces. By the eans f highe efance cting, the ctatin cannt be elying n jst ne single set f clste. Theefe, this eseach takes the advantage f tilizing ltile set f clstes f gegahically diffeent lcatin which is knwn as gid cting. In ealizing this cncet, we cnside the advantages f data assing between tw web sevices which each ae cnnected with ne ltile set f clstes. Each web sevices ae easily aintainable since thee is lse cling between inteacting ndes. F this kind f elatinshi, we chse Sevice Oiented Achitecte SOA faewk. As, gid cting is aied at shaing dynaically hetegenes esces, SOA lays le as a style that ehasize bsiness ability t be n in an inteeable way []. The se f SOA ense cntins syste iveent and able t g vais fnctinality as inteeable sevices. This faewk allws ebedded web sevices t exchange data between ne anthe

3 ding aallel cessing exectin. The ideas f SOA develed based n evis ecetins f dla gaing and distibted cting []. Fige : Achitecte f -diensinal gid-based teeate visalizatin slve Fige shws the achitecte f -diensinal gid-based teeate visalizatin slve. The develent f this achitecte is based n nbes f gaing langage as it invlves algith ileentatin n C, aallelizatin sing Paallel Vital Machine PVM and Java f web sevices develent. In this eseach, Web Sevices Definitin Langage WSDL is being selected as web sevices XML standadized technlgy and develed sing NetBean IDE tls. lassfish.0 will be se as alicatin seve f this achitecte. The gid cting latf is an en sce-based and will be devel nde Linx envinent. This latf develent will acceleate the seeds f exectin and scaled-t acss a vitalized gid. The clstes f cesss invlved in this latf ae develed n inceasingly lage ctatinal hadwae with inexensive secificatins.. Neical Analysis Neical analysis f the NAE cves the aea f neical eslt, cnicatin cst, ctatinal clexity and -diensinal teeate visalizatin. A neical eslt based n seqential algith in slving the eqatin is given in Table. Red-Black ass Seidel RBS is sed t ake caisn between classical iteatin ethd and new iteative ethd. Table : Neical eslt f seqential NAE and RBS ethd Methd NAE RBS NAE RBS exectin tie µs n. f iteatin ean sqae e.98 E -.8 E E E -8 abslte e 9.88E E - 8. E -.E - t ean sqae e.9 E -.89 E -.0 E -.0 E - axi e.80 E -. E -.0 E -.0 E - x.0000 E E -.8 E -.8 E - y.0000 E E -.8 E -.8 E - z.0000 E E -.8 E -.8 E - t. E -. E E E - cnvegence citein.0 E -9.0 E -9.0 E -9.0 E -9 Table shws the cnicatin cst f aallel NAE f diffeent atix size.

4 F Table, it can be bseved that NAE cnveged faste than RBS and this sitatin led t less tie cnsed in btaining final vale. Table : Cnicatin cst f the aallel NAE and aallel RBS ethd Methd Cnicatin cst Cnicatin cst NAE 80 t 90 t t 0 t 0 t t RBS 90 /t data +0t stat +t idle data stat idle 800 /t data +900t stat +t idle data stat idle Table shws the cnicatin cst f NAE and RBS f diffeent atix size. Cnclsin can be ade that aallel NAE ethd able t slve lage ble with lw ate f cnicatin cst. F lage atix size, NAE efs well whee it edces the cnicatin cst ding ga exectin. In easing ctatinal clexity f NAE, the veall needs f basic ctatin eatins ae cnted. The analysis is as saized in Table whee NAE dces less ctatinal clexity caed t RBS. Table : Ctatinal clexity f the aallel NAE and aallel RBS ethd Methd Additin Mltilicatin Additin Mltilicatin NAE [8- [80- [0- [ ]/ RBS [ ]/ ]/ [ ]/ ]/ [ ]/ ]/ [ ]/ Fige : Silatin eslts and snasht f web based alicatin. Pefance Measeent f Visalizatin Pcess id cting technlgy gives significance sitive iact t the efance f visalizatin efance. The visalizatin cess sccessflly acceleate t bece exteely fast while aintaining its eliability and accacy f the tces. The efance f aallel algith and alicatin can be eased in tes f seed, efficienc effectiveness and teal efance which sed the fllwing

5 definitins, seed, S T, efficienc T S S C, effectiveness, F and teal efance C L whee T and T ae exectin tie f aallel algith. Fige shws the efance T easeent analysis gah ltted against nbe f cesss. Fige a shws the seed inceent n additin f e cesss t the syste. Pefance inceent can als be bseved when easing effectiveness and teal efance. This eflects that adding e cesss will tentially incease the efance f aallel cessing syste. On cnta inceent f cesss nbes deceases the efficiency ate. Accding t [] inceasing f cesss edces the ttal exectin tie, and sbseqently deceases the ate f efficiency. The edctin f efficiency ate is de t sitatin whee each cess esnsible f fewe tasks as cesss nbes incease with cnstant ble s size. Ths, efficiency will incease f inceasing ble size with cnstant nbe f cesss. a Seed b Efficiency c Effectiveness d Teal efance NAE ethd efs bette than RBS esecially in lage atix size. It can be cnclde that this new ethd able t slve lage ble while aintaining its efance. The evalatin f aallel efance shws that NAE ethd has bight tential caed t classical iteative ethd naely RBS and bings the efance t a bette stage esecially in slving lage size f ble.. Cnclsin Fige : Paallel efance evalatin f teeate visalizatin This eseach had exeientally ved that the gid-based NAE ethd has significance efance iveent ve the lcally based aallel exectin. This -diensinal teeate visalizatin slve available t dce highly accate eslts and can be se t slve any size f bles. As cently the clstes nly sing vais kinds f cesss anging f Penti III t dal-ce, we ae lking fwad f fte advanceent f the clste s we by iving the Rand Access Mey RAM caability and the ey stage f each cess. Cntins syste gades will enhance the efance f the hetegenes clstes t a bette stage. id cting advantages flaved the gid-based alicatin eliability as the clstes will cve the efance defects in case f clste

6 faile. This is eely diffeent with taditinal distibted syste whee each cessing eleent PE is cnsideed as always available and bden the devele t ense the PE t be in eady-t-se cnditin.. Acknwledgeent The aths acknwledge Institte f Ibn Sina, UTM and Ministy f Science, Technlgy and Innvatin, Malaysia MOSTI f the financial st nde eseach vte 99.. Refeences [] H. Nathan, W. Bkhad, T. Ewan, A Faewk f Inteactive Web-Based Visalizatin, Seventh Astalasian Use Inteface Cnfeence AUIC00, Cnfeences in Reseach and Pactice in Infatin Technlgy CRPIT, Vl. 0. Wayne Piekaski, Ed, 00. [] L. Denic, Via. Mzzi, Fabizi Silvesti, Ranking f id-enabled Wkflw Sevice Pvides, HPDC 08, Jne, 008, Bstn, Massachsetts, USA. ACM /08/0. [] A.Y. H. Zaya, Paallel and Distibtin Cting Handbk Macaw Hill, 99. [] Na Alias, Shaii Mydin, Md. Rajibl Isla, Nhafiza Hazah, Zaith Safiza Abd. haffa, Niza Sata, Rziha Dawis, id Ptal Technlgy f Web based Edcatin f Paallel Cting Cses, Alicatins and Reseaches. in Pc. f The 8th Intenatinal Cnfeence n Web-based Edcatin WBE 009, Phket, Thailand, Ma. -8, 009,. 9-. [] Bing W, Matthew Dve Man Hng Ng, Kaihs Tai, Stat Mdck, Hans Fangh, Steven Jhnstn, Pal Jeffeys, Sin Cx, Jnathan W. Essex and Mak S.P. Sans, A Web / id Ptal Ileentatin f BiSiid: A Bilecla Silatin Database, Jnal f Digital Infatin Manageent, Vl., 00, -8. [] eist, A., Begelin, A., Dngaa, J., Jiang, W., Manchek, R., Sndea, V., PVM: Paallel Vital Machine & Use's ide and Ttial f Netwked Paallel Cting, MIT Pess, Cabidge, Mass, 99. [] A. D. Plyanin, Handbk f Linea Patial Diffeential Eqatins f Enginees and Scientists, Chaan & Hall/CRC Pess, Bca Ratn, 00. 8