Institutul de Matematic i Informatic Laboratorul Modelare matematic

Institutul de Matematică şi Informatică Laboratorul Modelare matematică Proiecte internaţionale: Raportul privind realizarea proiectului 261499 HP-SEE, FP 7 EC în anul 2012 Dr. G. Secrieru 2012

Proiectul HP-SEE High-Performance Computing Infrastructure for South East Europe’s Research Communities (HP-SEE) 7 th Framework Programmer EUROPEAN COMMISSION Termenul: 09. 2010 – 06. 2013

Project HP-SEE Echipa de realizare a proiectului: dr. h. B. Rîbachin dr. dr G. Secrieru P. Bogatencov N. Iliuha E. Gutuleac/N. Şider 10/3/2020 3

Project HP-SEE GRNET IPP-BAS IFIN-HH TUBITAKULAKBIM NIIFI IPB UPT Coordinating Contractor Greece Bulgaria Romania Turkey Contractor Hungary Serbia Albania Uo. BL ETF UKIM UOM RENAM IIAP_NAS_RA GRENA AZRENA Contractor Contractor Bosnia-Herzegovina FYROM (Machedonia) Montenegro Moldova Armenia Georgia Azerbaijan 4

Project HP-SEE OBIECTIVELE PROIECTULUI: Stimularea cercetării performante cu acţiuni ce vizează consolidarea colaborării ştiinţifice şi constituirea iniţiativelor HPC pentru a contribui la dezvoltarea regională şi alinierea ţărilor din sud-estul Europei la tendinţele Pan-europene HPC. 5

Metode şi echipament utilizate Tehnologii moderne Open. MP şi MPI pentru elaborarea algoritmilor paraleli. Scheme numerice de calcul paralel pentru rezolvarea sistemelor de ecuaţii diferenţiale neliniare în derivate parţiale. Echipamentul utilizat constă din: clustere cu multe procesoare plasate în Moldova, Bulgaria şi Ungariaîn 10/3/2020 6

HPC Resources, available for MD AMR application deploying Cluster located at IICT of Bulgarian Academy of Sciences. 576 computing cores. The storage and management nodes have 128 cores. 7

HPC Resources, available for MD AMR application deploying SGI Ultra. Violet 1000 supercomputer at NIIFI, located in Pecs, Hungary. 1152 cores, 6057 GByte of memory 8

Local HPC resources for training, applications testing and debugging 48 -core IMI-RENAM cluster MS Windows Compute Cluster 2003 9

Supercalculatoare: Caracteristica actuală mondială Reitingul celor mai puternice supercalculatoare din lume stabilit la 12. 11. 2012 (Top 500) Locu Calculatorul Ţara Arhitectura Viteza 1015 (Peta. Flops) Nuclee 17. 59 560640 1 Titan SUA Cray XK 7 2 Sequoia SUA 16. 325 IBM Blue. Gene/Q 1572864 3 K computer Japonia RINKEN 10. 5 705024 26 Blade 2/1. 1 Xeon Rusia T-platforma 0. 9 78660 10

Formulation of the problem The system of equations of gravitational gas dynamics, which describe the process of collapse of a star, can be written as: In these equations, the value of the gravitational potential is determined from the Poisson equation ∆Φ=4πGρ The equation of state is used in the form of: e=1/2ρv 2+ε In the above equations: ρ - the density, v - velocity, P - pressure, ε - specific internal energy, e - full energy, t - time, xi - spatial coordinates, G = 6, 67*10– 11 kg-1 м 3 s-2 - constant gravitational 11 potential.

USING STRUCTURED ADAPTIVE COMPUTATIONAL GRID FOR SOLVING MULTIDAMR Method. IMENSIONAL COMPUTATIONAL PHYSICS TASKS If necessary, in the areas with large gradients of pressure, temperature, etc. , using the AMR method we can build sophisticated grid: 12

ADAPTIVE COMPUTATIONAL GRID FOR SOLVI AMR Method NG MULTIDIMENSIONAL COMPUTATIONAL PHYSICS At the foreground a coarse grid in the centers - balls. In TASKS the background is a fine mesh, which is 2 times less in each coordinate Interpolation of red dots with black and gray dots. 13

USING STRUCTURED ADAPTIVE COMPUTATIONAL GRID FOR SOLVICalculation algorithm NG MULTIDIMENSIONAL COMPUTATIONAL PHYSICS TASKS The solution of the three-dimensional Poisson equation has been tested on 5 levels of AMR nesting. In the test a homogeneous sphere of radius R and density ρ for the equation for the gravitational potential (4) is considered: (3) (4) The computational area is filled with values Ф from (3) in the sphere of radius R, outside sphere values are (3) are specified with bottom line. Then the values of the gravitational potential are calculating in the threedimensional formulation. The numerical solution was calculated for AMR hierarchy levels from one to five. 14

USING STRUCTURED ADAPTIVE COMPUTATIONAL GRID FOR SOLVING MULTIDIMENSIONAL COMPUTATIONAL PHYSICS TASKS Figure 1 shows the analytical solution for the gravitational potential, obtained from equation (4). Figure 2 - the numerical results, Figure 3 - two-dimensional cross-section of the X-axis of Fig. 2 Figure 1. Figure 2. Figure 3 15

USING STRUTURED ADAPTIVEMPUTATIONAL GRID FOR SGraphic representation of the error TASKS The difference between the analytical and numerical solutions: for the grid of 32 x 32 and two levels of grid for the grid of 512 x 512 and 5 -level grid It should be mentioned the significant refinement of result and consequently decreasing of the error by four orders. These results show the importance of applying the AMR method for raising accuracy of the solutions of multidimensional partial differential equations. 16

Results of AMR_PAR application execution on the WCC 2003 cluster of IMI in Open. MP mode, cores from 1 to 8 (2 x Quad. Core Intel Xeon E 5310, 1600 MHz, 8 GB of RAM) 17

Results of AMR_PAR application execution on HPCG cluster, IICT of the Bulgarian Academy of Sciences. Acceleration and Run Time dependences from CPU cores. For 128 x 128 dimention best number of cores — 4. 4 cores - walltime - 3, 3 min, CPU time -13, 2 min. 16 cores - walltime - 3, 7 min, CPU time - 59, 1 min 18

Calculated requirements of computational resources for the current Open. MP version of AMR_PAR application Next step is to run application using HP-SEE regional resources for largescale grid dimensions – up to 2048 x 2048, 5 -7 layers. After obtaining results of the modified application execution, it will be possible to make new benchmarking and propose new recommendations for application optimization. The results of calculations will be visualized in 2 -D images 19 and 3 -D models.

Rezumatul rezultatelor A fost elaborată şi realizată procedura transferării aplicaţiei AMR (Adaptive Mesh Refinement) din platforma MS Computer Cluster 2003 la platforma. Scientific Linux 5. 5 cu utilizarea pachetului specializat Intel® Parallel Studio XE 2011 for Linux. A fost modificată pentru testare aplicaţia AMR elaborată pentru rezolvarea unor probleme Specifice gazodinamice in cazul bi-dimensional şi tri-dimensional. Aplicaţia AMR a fost portată şi testată la resurselor clusterelor: - HPCG în institutul IICT din Academia de ştiinţe a Bulgariei; - Supecomputerul SGI Ultra. Violet 1000, plasat în or. Pecs, Ungaria. 20

Publicaţii : articole -6, teze -2, conferinţe – 5: Moscova, Belgrad, Minsc, Tbilisi, Chişinău • BOGATENCOV, P. ; SECRIERU G. Calculul performant: oportunităţi şi perspective pentru cercetare. Revistă“Ştiinţă şi inovare” (Akademos). Moldova, 2012, 1(24), 64 -69. ISSN 1857 -0461 • CЕКРИЕРУ Г. ; БОГАТЕНКОВ, П. ; РЫБАКИН, Б. ; ИЛЬЮХА Н. Развитие высокопроизводительной вычислительной инфраструктуры для научных исследований в Молдове. Труды 6 -ой Межд. Конф. «Параллельные вычисления и задачи управления (PACO’ 2012)» , T 3, 24 -26 octombrie 2012, Moscova, Rusia, 299 -305, ISBN: 978 -5 -91450 -124 -9. • BOGATENCOV, P. ; SECRIERU, G. , RYBAKIN, B. ; ILIUHA, N. Using Structured Adaptive Computational Grid For Solving Multidimensional Computational Physics Tasks. HP-SEE User Forum Belgrade, 17 -19 October 2012, Belgrad, Serbia. 5 -7. • BOGATENCOV, P. ; SECRIERU, G. ; ILIUHA, N. Access to the Regional Scientific computing Infrastructure. Четвертая Международная научная конференция «Суперкомпьютерные системы и их применение» . (SSA’ 2012), 23 -25 октября 2012, Минск, Беларусь, 42 -46. ISBN 978 -985 -6744 -76 -4. 21

Examenarea realizării proiectului • PSC 06 Meeting, care a avut loc 3 -5 aprilie 2012 în Ankara, Turcia. S-a examinat experienţa existentă de formare a relaţiilor cu industria în domeniul utilizării resurselor naţionale HPC (N. Iliuha). • HP-SEE Users Forum, care a avut loc 17 -19 octombrie 2012 în Belgrad, Serbia (dr. H. B. Rîbachin, dr. P. Bogatencov). 22

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