The Performance of Geothermal Field Modeling in Distributed Component Environment

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1 Porows A., Peta A., Kowal A., Dane T.: The Performance of Geothermal Feld Modelng n Dstrbuted Component Envronment. In: Innovatons n Computng Scences and Software Engneerng, Sprnger,, pp Ths s the accepted verson. The offcal verson s avalable on: The Performance of Geothermal Feld Modelng n Dstrbuted Component Envronment A. Pórows A. Pęta, A. Kowal, T. Dane Department of Geonfomatcs and Appled Computer Scence, AGH Unversty of Scence and Technology, Cracow, Poland. {poro, Abstract An mplementaton and performance analyss of heat transfer modelng usng most popular component envronments s a scope of ths artcle. The computatonal problem s descrbed, and the proposed soluton of decomposton for parallelzaton s shown. The mplementaton s prepared for MS.NET, Sun Java and Mono. Tests are done for varous operatng systems and hardware platform combnatons. The performance of calculatons s expermentally ndcated and analyzed. The most nterestng ssue s the communcaton tunng n dstrbuted component software proposed method can speed up computatonal tme, but the fnal tme depends also on the networ connectons performance n component envronments. These results are presented and dscussed. Index Terms heat transfer modelng, component platforms H I. INTRODUCTION eat transfer phenomenon plays an mportant role n such physcal problems n Earth scence as volcanoes, ntrusons, earthquaes, mountan buldng or metamorphsm. Analytcally exact soluton of heat transfer equaton exsts only for geologcal models wth smple geometry. In many geologcally realstc stuatons t s necessary to use numercal approaches to obtan vald models of these mportant processes. Heat-conducton equaton and ts fnte dfference soluton s a problem whch s easy to parallelze. Ths fact s a great advantage because modelng n huge complex meda carry on for a long perod of tme and n presence of thermal ansotropy can be a very tme consumng process [], []. The man dsadvantages of created program codes s ntroducton of newer and newer software and hardware solutons that caused n very short lfe cycle of created codes. One of the methods used to overcome the problem of short lfe cycle s use of the component technologes. P II. COMPONENT TECHNOLOGIES ortablty, securty and ndependence of hardware are the man advantages of component-based software. A possblty of component code reuse enables coders cooperaton. The most popular component platforms are Sun Java [3] and MS.NET [4]. These platforms are developed by commercal provders. There s a free and open alternatve for one of them (MS.NET) a platform Mono [5]. The.NET applcatons can be run under control of Mono. The component platforms use a managed code technque to enable hardware ndependency and portablty. Ths technque s a bytecode n Sun Java and CLI n MS.NET. The translaton to natve code by Just-In-Tme method s a bottle-nec n terms of performance. There are numerous algorthms for optmzaton to speed up calculatons. The subsystem of communcaton s one of the most mportant parts of component envronment n terms of performance n case of parallelzaton. Sun Java offers a RMI mechansm [6] that enables remote procedure callng, the same functon s doman of.net Remotng for MS.NET and Mono. III. TEST ENVIRONMENT AND APPLICATIONS A. Hardware specfcaton The expermental tests of heat transfer modelng computatons were performed n two dfferent envronments. The frst envronment was a noteboo: - processor (Intel Pentum M,86 GHz), - GB RAM. The second envronment was a cluster of 3 PC computers: - processor wth cores (Hyper-Threadng Technology Intel Pentum 4,8 GHz), - GB RAM, - Ggabt Ethernet networ adapter. All nodes of cluster were oned by Ggabt Ethernet swtch. B. Used Operatng Systems and Component Envronments The performance of component sesmc computng was measured n followng operatng systems: Lnux (Fedora Core 3, ernel: [smp]), MS Wndows (SP4), MS Wndows XP (SP) and MS Wndows Vsta. There are two applcatons for heat transfer modelng wrtten n Java and C# language. To run Java code we use Sun

2 8 Java SE vrtual machne, verson.6.. The C# code was tested under control of MS.NET Framewor. and Mono..6. IV. HEAT TRANSFER MODELING A. Bascs of heat transfer modelng Component solutons were tested usng heat-conductve equaton. In two-dmensonal sotropc medum ths equaton can be wrtten as: where T(x, z) s temperature, λ(x, z) s thermal conductvty, c(x,z) s specfc heat capacty, ρ(x, z) s densty, t s tme and Q w denotes the heat generated n the volume element of the medum durng unt tme (heat producton rate). Adoptng the fnte dfference to approxmate the above equaton and usng the Smple Explct Method [7] one can obtan: t, t + + t = t + α t =, K, n ; =, K, n x λ T T Qw = t c + x z + ρ ρ c where α s thermal dffusvty, t s the tme samplng nterval, x and y are dstances between grd ponts n the x and z drectons respectvely, n x and n y are grd ponts amount n the x and z drectons respectvely. To acheve numercal stablty the followng relatonshp must be fulflled [7]. α t ( x) ( z) z + t, t t ( x) ( z) + t () () (3) B. An expermental model There s a smple model prepared for smulaton. The parameters of ths model are presented n Table I and ths model s presented on fg.. The model contans of a part of roc at the left and water at the rght. The solutons of heat transfer smulaton for and years are presented n the fg. and fg. 3. TABLE I. PARAMETERS OF SIMPLE MODEL Parameters of the expermental model model dmensons [m x m] x spatal grd steps [m] depth to heat layer [m] temperature of heat layer [ o C] thermal conductvty of land [W/m*K], thermal conductvty of water [W/m*K],8 end tme [years] tme step [days] ntal temp. of land (m) / water o C / o C ROCK Fg. The smple model for smulaton. WATER We used two types of boundary condtons: convectve boundary condtons (4) at the top and bottom of the model and Neumann boundary condtons (5) elsewhere. 8 λ n r + h T λ n r ( r, t) = f ( r, t) = f ( r, t) where: r - coordnate at the boundary, - one of the boundares, n - the outward-facng normal vector on the body surface, h - the heat transfer coeffcent, f - the specfed functon, λ - thermal conductvty. (4) (5) Fg. The soluton of heat transfer smulaton for years. 6

3 8 Fg 3. The soluton of heat transfer smulaton for years. C. Seral case D. Parallel case Geologcal model descrbed n the prevous chapter and the same set of parameters were used for the parallel modelng of the heat transfer equaton. Parallelzm was ntroduced by doman decomposton of the computatonal doman (Fg. 5) and master paradgm (Fg. 6). A A3 A4 A8 A A A3 A5 [m] A6 A A9 A A7 a) b) c) At the start we have measured the tmes of heat transfer modelng computatons for the seral case. The experment too a place n two hardware envronments. The reached tmes are collected n Table II and presented n fg. 4. TABLE II. AVERAGE TIMES OF COMPUTATIONS FOR SINGLE MACHINE Avg. tmes n E [s] Avg. tmes n E [s] MS Vsta MS XP FC 3 MS FC 3.NET 99, 95,73-4,43 - Mono,86 7,4 7,93 3,93 8,84 Java,64 3,88 3,3, 36,49. avg. tmes [s].net Mono Jav a [m] Fg 5. The doman decomposton schema. Global computatonal doman (a) s dvded nto smaller subdomans. Results of computaton performed by nodes (b) are collected by master node (c) Global computatonal doman was dvded nto as much subdomans as ndependent processors got nvolved n concurrent heat transfer equaton solvng. Assgnment of computatonal subdomans to ndependent processors made computatonal process much faster and lmted the rs of local RAM exceedng. One of the machnes hosted master process, other hosted only processes. Master was responsble for creaton of numercal model representaton, dvson of the global computatonal doman, assgnng and sendng data to nodes and fnally collectng heat flow modelng results. Slave processes performed computaton and were exchangng subdoman border nodes after every step of calculaton. master MS Vsta MS XP FC 3 MS FC 3 Envronment Envronment model soluton Fg. 4. Graphcal comparson of tmes of computatons for varous operatng systems, programmng platforms and hardware. The fastest computatons have been reached n envronment, under control of MS Wndows XP, usng.net Framewor. In second envronment the fastest code was run under control of Lnux usng Sun Java platform. Fg 6. The envronment for dstrbuted heat transfer modelng.

4 8 The ntra communcatons was the most tme consumng part of parallel algorthm. For a test model descrbed above s exchanged 8MB of data for about two thousand tmes. Parallel algorthm wth such dense communcaton pattern strongly lmts number of nodes especally for small computatonal models. The entre tests were performed n computatonal hardware envronment descrbed n the prevous secton. Computaton tmes receved for varous component-based software solutons are presented n Table IIIA and Table IIIB. There are mnmal and average tmes of computng for consecutve numbers of nodes presented n fgure 7. The speed up of parallelzaton s shown n the fg. 8. T TABLE IIIA MINIMAL TIMES OF PROCESSING FOR HEAT TRANSFER MODELING a) Mnmal tme of processng [s] No of proc.net Mono Java Mono Java Wn Wn Wn FC 3 FC 3 79,47 4,3,33 69, 66,54 6,7 6,86,58 5, 3,6 3 9,9 6,4 7,95 3,5 9,79 4 8,9 4,5 6,,3 9,7 5 4,6 34,8 4,7 3,63 8,9 6 7,77 35, 95,94 9,6 7,67 7 7,7 37, 89,79 98,7 74,3 8 4,3 34,59 85,49 98,86 8,3 TABLE IIIB AVERAGE TIMES OF PROCESSING FOR HEAT TRANSFER MODELING b) Average tme of processng [s] No of.net Mono Java Mono Java proc. Wn Wn Wn FC 3 FC 3 8,87 4,48 4,4 69,84 67,7 8,35 63,7 4, 5,95 6,34 3 5,38 6,6 8,9 33,8,9 4 3,55 4,58 7,35 3,53 95,47 5 6,9 37,3 5,3 3,39 86,76 6 3,7 37,3 96,9 5,68 7,9 7 7,3 38,53 9,95 99,75 76,37 8 9,8 37,9 86,9,8 84,4 V. DISCUSSION he shortest tme of processng heat transfer modelng for a sngle case war reached for MS.NET platform n envronment. In envronment (cluster of PC-s) the fastest combnaton was Sun Java and Lnux (there was no Wndows XP nstallaton). For the same envronment n dstrbuted case the leader was also Sun Java as platform and Lnux as operatng system (smlar scores are for synthetc tests [9]). The nterestng pont s the speed ups for these technologes - the networ usage by communcaton was a bottle-nec for.net and Mono - the speed up s not especally growng for four processors and more. The speed up for Sun Java s hgher for hgher number of processors. It proofs the necessary of parallelzaton for such a bg computatonal problem le heat transfer modelng. Smlar results were reached for sesmc feld modelng [8], but n ths case the networ transfer was smaller and speed ups results were close for all platforms. Mn/avg tme of processng [s] Speed up of computaton T Fg 7. The mnmal and average tmes for dstrbuted smulaton. 3,5,5,5 Number of processors Number of processors Fg 8. The speed up for dstrbuted smulaton. VI. SUMMARY here s an ablty of constructon the scentfc numercal code n component platforms descrbed n ths artcle. The problem of heat transfer modelng s presented and the way of parallelzaton s shown. The performance of dstrbuted solutons n case of parallelzaton s the man scope of expermental tests. Obtaned speed up results proofs, that parallelzaton s a good way to solve a problem of computatons effcency. ACKNOWLEDGMENT.NET Wn Mono Wn Java Wn Mono Lnux Java Lnux.NET Wn Mono Wn Java Wn Mono Lnux Java Lnux Ths wor was fnanced by the AGH - Unversty of Scence and Technology, Faculty of Geology, Geophyscs and Envronmental Protecton as a part of statutory proect number...56.

5 83 REFERENCES [] A. Pęta, Heat transfer modelng n deep geothermal applcaton, n Scence and supercomputng n Europe - report 6, Cneca, HPC- Europa, Pan-European Research Infrastructure on Hgh Performance Computng. Bologna 6, Italy, p [] M. Wróblewsa, A. Pęta, Deep lthosphere thermal modelng aganst surface temperature condton, n Near Surface 8-4th European meetng of Envronmental and engneerng geophyscs, 5 7 September 8, Cracow, Poland. [3] D. Relly., M. Relly: Java Networ Programmng and Dstrbuted Computng. Addson Wesley,. [4] M. MacDonald: Mcrosoft.NET Dstrbuted Applcatons: Integratng XML Web Servces and.net Remotng. Mcrosoft Press, 3 [5] H.J. Schong, E. Geschwnde: Mono Kc Start. Sams, 3. [6] E. Ptt, K. McNff: ava.rm: The Remote Method Invocaton Gude. Addson Wesley,. [7] J. C. Tannehll, D.A. Anderson, R.H. Pletcher: Computatonal Flud Mechancs and Heat Transfer, Second Edton, Taylor & Francs, Washngton, 997. [8] A. Kowal, A. Pórows T. Dane, A. Pęta, Analyss of selected component technologes effcency for parallel and dstrbuted sesmc wave feld modelng, n Innovatons and Advances n Computer Scences and Engneerng, Sprnger,. [9] A. Porows and D. Plodzen, "Effcency analyss of the server-sde numercal computatons," n Computer Networs, 6th Conference, CN 9, Wsla, Poland, June 6-, 9, Communcatons n Computer and Informaton Scence, Sprnger Berln Hedelberg, 9.

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