Research of the new Intel Xeon Phi architecture for solving a wide range of scientific problems at JINR

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1 Research of the new Intel Xeon Phi architecture for solving a wide range of scientific problems at JINR Podgainy D.V., Streltsova O.I., Zuev M.I. on behalf of Heterogeneous Computations team HybriLIT LIT, Joint Institute for Nuclear Research

2 The main objective Investigation of the new Intel Xeon Phi 7200 (KNL) architecture for solving scientific problems at JINR (Dubna, Moscow region) using parallel programming technologies. Research includes: Calculations using application programs: - Calculation of the parameters of long Josephson junctions; - Bayesian analysis of realistic models of the equations of state of super dense nuclear matter; - Solving 2D Sine-Gordon equations on Ivy Bridge and KNL processors.

3 Intel Xeon Phi systems Heterogeneous cluster HybriLIT Intel Xeon Phi 7250 (1.4 GHz) 16 GB 68 cores 4 threads per core Intel Omni-Path Intel Xeon Phi 7290 (1.5 GHz) 16 GB 72 cores 4 threads per core Intel Omni-Path 2x Intel Xeon E5-2695v3 (2.3 GHz) RAM 128 GB 14 cores 2 threads per core Ethernet 1Gbit/s

4 Long Josephson Junctions Atanasova P.Kh., Bashashin M.V., Rahmonov I.R., Shukrinov Yu.M., Streltsova O.I., Volokhova A.V., Zemlyanaya E.V., Zuev M.I. (JINR, Plovdiv University (Bulgaria)) We consider a model that takes into account the inductive and capacitive coupling between the JJs. LJJ system consists of superconducting layers with intermediate dielectric (insulator) layers of length L. Phase dynamic of the LJJ system with capacitive and inductive coupling between the contacts is described by a system of equations with respect to the phase difference l and voltage Vl at each l-th contact: l t DCVl scvl 1 scvl 1 2 N V 1 l Ll,n 2n sin l l I t x t n 1 where L inductive coupling matrix. 1 L= S S 0 0 S 1 S 0 0 S S 1 V0 dl jc dissipation parameter, inductive coupling parameter S takes a S superconducting layers, I insulator (dielectric) layers value in the range 0< S <0.5. Dc the effective electrical thickness of JJ, normalized to the thickness of the dielectric layer. sc capacitive coupling parameter. Vl voltage at l-th JJ, I - external current. All quantities converted to dimensionless. Boundary conditions: l 0, t l L, t x x He

5 Long Josephson junctions. The numerical approach Numerical solution of the system (1-3). We introduce a uniform discrete grid in the space coordinate x with step x and in the time coordinate t with step t. To approximate the derivatives with respect to spatial coordinates, we use the standard three-point finite-difference formulas. The resulting system of ordinary differential equations for the values of the phase voltages and the differences in the discrete grid points is solved numerically using the four-step Runge-Kutta (RK) procedure.

6 Long Josephson junctions. The numerical approach Calculation of Current-Voltage Characteristic (CVC). We calculate dependence <V> on I. At each time step, we calculate integral L 1 V t V x, t dx (4) using Simpson's formula. Next, the integral V l l T max L 1 T 0 min Is calculated by means of rectangles formula. Finally, the voltage is averaged by the number of contacts V N l 1 l T T max min V l l V t dt (6) (5)

7 Long Josephson junctions. Results Number of contacts= 10, Number of nodes= 1000, x= ,14 176,16 Computation time, sec Less is better ,9 172,7 178,28 171,81 171,25 171, , Intel Xeon E v3 (28 cores) 2x Intel Xeon E v3 (56 cores) Default -O3 O3 -xmic-avx512 Intel Xeon Phi 7290 (72 cores)

8 Bayesian analysis of realistic models of the equations of state of super dense nuclear matter Ayriyan A., Blaschke D., Grigorian H., Poghosyan G. (JINR, KIT (Germany))

9 Bayesian analysis. Software package for BA of EoS models 1. Construction of hybrid models of EoS The fourth-order Runge-Kutta File Interface method with adaptive step 2. Calculation of netron star structure (solving of the TolmanOppenheimer-Volkoff equations) File Interface 3. Extracting the stable configuration File Interface 4. Determination of the a priori probabilities MPI realization 5. Calculation of conditional probabilities of the observations 6. Calculation of a posteriori probabilities of the models 7. Creation of the demonstration materials (graphs).

10 Laboratory of Information Technologies (JINR) Bayesian analysis. Get the a posteriori probabilities Alvarez, Ayriyan, Benic, Blaschke, Grigorian, Typel. Eur. Phys. J. A (2016) 52, 69

11 Bayesian analysis. Results of MPI realisation of TOV solver 4 х Intel Xeon Phi 7250, AVX512 Intel Omni-Path (100Gbs) 4 х Intel Xeon E5-2695v3, AVX2

12 Solving 2D Sine-Gordon equations on Ivy Bridge and KNL processors Hristov I., Hristova R. (LIT, JINR)

13 Solving 2D Sine-Gordon equations on Ivy Bridge and KNL processors. Numerical Scheme We follow the approach for construction of the numerical scheme from [1]. We solve the problem numerically in rectangular domain by using second order central finite differences with respect to all derivatives. As a result at every mesh point of the domain we have to solve a system with the tridiagonal matrix S. Because of the specific tridiagonal structure of S we need only 9*Neq - 12 floating point operations per solving one system, where Neq are the number of equations. [1] Kazacha G.S., Serdyukova S.I. Numerical Investigation of the Behaviour of Solutions of the SineGordon Equation with a Singularity for Large t, Zhurnal Vychislitelnoi Matematiki i Matematicheskoi Fiziki, 1993, Vol. 33, Issue 3, P

14 Solving 2D Sine-Gordon equations on Ivy Bridge and KNL processors. Parallelization strategy (Thread and SIMD levels of parallelism) 1. To achieve good data locality we take into account the column major order for multidimensional arrays of Fortran language. 2. We use two levels of parallelism thread level and SIMD level (automatic vectorization) for our pure OpenMP implementation. 3. The smallest piece of work is the calculation of 8 consecutive linear systems and solving them. Both calculations of right-hand sides and solving 8 linear systems at once are vectorized. The above pieces of work are distributed between OpenMP threads.

15 Solving 2D Sine-Gordon equations on Ivy Bridge and KNL processors. Performance results

16 Solving 2D Sine-Gordon equations on Ivy Bridge and KNL processors. Results of computations

17 Conclusions Long Josephson junctions Bayesian analysis 2D Sine-Gordon equations

18 Acknowledgements

19 Thank you for your attention! Any questions?