High Scalability of Lattice Boltzmann Simulations with Turbulence Models using Heterogeneous Clusters

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1 SIAM PP 2014 High Scalability of Lattice Boltzmann Simulations with Turbulence Models using Heterogeneous Clusters C. Riesinger, A. Bakhtiari, M. Schreiber Technische Universität München February 20, 2014 SIAM PP 2014, February 20,

2 Topics Motivation The Lattice Boltzmann Method Optimization Single GPU optimization: A-B vs. A-A Pattern Multi GPU optimization: Communication Schemes Results Runtime Lattice Updates Parallel Efficiency Conclusion & Outlook SIAM PP 2014, February 20,

3 Topics Motivation The Lattice Boltzmann Method Optimization Single GPU optimization: A-B vs. A-A Pattern Multi GPU optimization: Communication Schemes Results Runtime Lattice Updates Parallel Efficiency Conclusion & Outlook SIAM PP 2014, February 20,

4 Motivation Main Goal Development of a highly scalable code for heterogeneous clusters to investigate new ideas. Minor Goal Extend the software step by step with additional features (never loosing the main goal out of sight). SIAM PP 2014, February 20,

5 Motivation Main Goal Development of a highly scalable code for heterogeneous clusters to investigate new ideas. Minor Goal Extend the software step by step with additional features (never loosing the main goal out of sight). Properties of our Software application: algorithm: heterogenous system: development platform: Computation Fluid Dynamics Lattice Boltzmann Method CPUs + GPUs OpenCL Yet another Lattice Boltzmann Code SIAM PP 2014, February 20,

6 Features Features implemented so far: Implementation of LBM Tailored software design for heterogeneous clusters Overlapping communication with computation Support for free surfaces Considering turbulent flows Validation of the simulation results SIAM PP 2014, February 20,

7 Features Features implemented so far: Implementation of LBM Tailored software design for heterogeneous clusters Overlapping communication with computation Support for free surfaces Considering turbulent flows Validation of the simulation results Features to be implemented: Support for (complex) geometries Investigation of additional turbulence models Exploiting CPU power... SIAM PP 2014, February 20,

8 Features Features implemented so far: Implementation of LBM Tailored software design for heterogeneous clusters Overlapping communication with computation Support for free surfaces Considering turbulent flows Validation of the simulation results Features to be implemented: Support for (complex) geometries Investigation of additional turbulence models Expoiting CPU power... SIAM PP 2014, February 20,

9 The Lattice Boltzmann Method Motivation The Lattice Boltzmann Method Optimization Single GPU optimization: A-B vs. A-A Pattern Multi GPU optimization: Communication Schemes Results Runtime Lattice Updates Parallel Efficiency Conclusion & Outlook SIAM PP 2014, February 20,

10 The Lattice Boltzmann Method 1/3 Boltzmann Equation f t + v f = (f f eq ) }{{} Collision operator f ( x, v, t): f eq : Probability density function: Probability for finding particles at x and time t with velocity v Equilibrium distribution SIAM PP 2014, February 20,

11 The Lattice Boltzmann Method 1/3 Boltzmann Equation f t + v f = (f f eq ) }{{} Collision operator f ( x, v, t): f eq : Probability density function: Probability for finding particles at x and time t with velocity v Equilibrium distribution Lattice Boltzmann Method (LBM) LBM simulates fluid flow by... tracking virtual particles (more specifically, their distribution) colliding and streaming them (collision & streaming phase) only along a limited number of directions (DdQq discretization schemes) SIAM PP 2014, February 20,

12 The Lattice Boltzmann Method 2/3 Discretization Schemes d: number of dimensions q: number of density distributions/lattice vectors Collision & Streaming During collision phase, the collision operator is approximated (BGK model): f i ( x, t + δt) = f i ( x, t) + 1 i f i ) τ f eq i ( u) = ω i ρ (1 + 3( e i u) + 92 ( e i u) 2 32 ) u2 with ω i = 1 for i 0,..., 3, 16, 17, 1 for i 4,..., 15, and 1 for i = Movement of the virtual particles is simulated during streaming phase: (f eq f i ( x + e i, t + δt) = f i ( x, t + δt) SIAM PP 2014, February 20,

13 The Lattice Boltzmann Method 3/3 Densities & Velocities Only density distributions along the lattice vectores are stored. Densities & velocities are NOT explicitly stored per cell, but can be calculated: ρ = 18 i=0 f i ρ v = LBM for High Performance Computing 18 i=0 (f i e i ) Data access only for discretized density distributions Communication only with neighboring cells Calculations only use simple instructions SIAM PP 2014, February 20,

14 Topics Motivation The Lattice Boltzmann Method Optimization Single GPU optimization: A-B vs. A-A Pattern Multi GPU optimization: Communication Schemes Results Runtime Lattice Updates Parallel Efficiency Conclusion & Outlook SIAM PP 2014, February 20,

15 Single GPU optimization: The A-B Pattern Collision Density distributions of own cell are read Collision operator is executed Updated density distributions are written SIAM PP 2014, February 20,

16 Single GPU optimization: The A-B Pattern Collision Density distributions of own cell are read Collision operator is executed Updated density distributions are written Propagation Updated density distributions are copied to the corresponding neighboring cells SIAM PP 2014, February 20,

17 Single GPU optimization: The A-B Pattern Collision Density distributions of own cell are read Collision operator is executed Updated density distributions are written Propagation Updated density distributions are copied to the corresponding neighboring cells To avoid race conditions, two dedicated arrays for the density distributions are required! They are used in a ping pong like manner. SIAM PP 2014, February 20,

18 Single GPU optimization: The A-A Pattern Only one memory layout is used for all iterations. This saves memory by a factor of two twice as many cells per GPU α Step (odd iterations) Performed during odd iterations Only one collision is performed Memory belongs to own cell SIAM PP 2014, February 20,

19 Single GPU optimization: The A-A Pattern Only one memory layout is used for all iterations. This saves memory by a factor of two twice as many cells per GPU α Step (odd iterations) β Step (even iterations) Performed during odd iterations Only one collision is performed Memory belongs to own cell Performed during even iterations Two streamings and one collision Memory belongs to neighbors SIAM PP 2014, February 20,

20 Single GPU optimization: The A-A Pattern Only one memory layout is used for all iterations. This saves memory by a factor of two twice as many cells per GPU α Step (odd iterations) β Step (even iterations) Performed during odd iterations Only one collision is performed Memory belongs to own cell Performed during even iterations Two streamings and one collision Memory belongs to neighbors Data is always read and written to the same memory location. SIAM PP 2014, February 20,

21 OpenCL Features CommandQueue * Event Command Queue Contains a list of commands Commands can be executed in-order or out-of-order Event Can be used to determine the state of a command Mechanism to implement synchronization between commands Complex dependency graphs can be realized by dependencies of events SIAM PP 2014, February 20,

22 OpenCL Features CommandQueue * Event Command Queue Contains a list of commands Commands can be executed in-order or out-of-order Event Can be used to determine the state of a command Mechanism to implement synchronization between commands Complex dependency graphs can be realized by dependencies of events Only the concurrent execution of several command queues enables the parallel execution of several commands! SIAM PP 2014, February 20,

23 Single Boundary Kernel - Single Command Queue (SBK-SCQ) 1/2 communication (CPU CPU) X 0 X n Y 0 Y n Z 0 Z n X' 0 X' n Y' 0 Y' n Z' 0 Z' n CPU MPI_Isend() MPI_Irecv() communication (GPU CPU) one single command queue X 0 X n Y 0 Y n Z 0 Z n X' 0 X' n Y' 0 Y' n Z' 0 Z' n GPU one signle kernel for halo cells compute halo cells compute inner cells computations done by GPU computations done by CPU communication command queue idle times SIAM PP 2014, February 20,

24 Single Boundary Kernel - Single Command Queue (SBK-SCQ) 2/2 communication (CPU CPU) X 0 X n Y 0 Y n Z 0 Z n X' 0 X' n Y' 0 Y' n Z' 0 Z' n CPU MPI_Isend() MPI_Irecv() communication (GPU CPU) one single command queue X 0 X n Y 0 Y n Z 0 Z n X' 0 X' n Y' 0 Y' n Z' 0 Z' n GPU one signle kernel for halo cells compute halo cells compute inner cells computations done by GPU computations done by CPU communication command queue idle times SIAM PP 2014, February 20,

25 Multi Boundary Kernels - Single Command Queue (MBK-SCQ) 1/2 communication (CPU CPU) X 0 X n Y 0 Y n Z 0 Z n X' 0 X' n Y' 0 Y' n Z' 0 Z' n MPI_Isend() CPU communication (GPU CPU) one single command queue MPI_Irecv() X 0 X n Y 0 Y n Z 0 Z n X' 0 X' n Y' 0 Y' n Z' 0 Z' n GPU multiple kernels for halo cells compute halo cells compute inner cells computations done by GPU computations done by CPU communication command queue idle times SIAM PP 2014, February 20,

26 Multi Boundary Kernels - Single Command Queue (MBK-SCQ) 2/2 communication (CPU CPU) X 0 X n Y 0 Y n Z 0 Z n X' 0 X' n Y' 0 Y' n Z' 0 Z' n MPI_Isend() CPU communication (GPU CPU) one single command queue MPI_Irecv() X 0 X n Y 0 Y n Z 0 Z n X' 0 X' n Y' 0 Y' n Z' 0 Z' n GPU multiple kernels for halo cells compute halo cells compute inner cells computations done by GPU computations done by CPU communication command queue idle times SIAM PP 2014, February 20,

27 Multi Boundary Kernels - Multi Command Queues (MBK-SCQ) communication (CPU CPU) X 0 X n Y 0 Y n Z 0 Z n X' 0 X' n Y' 0 Y' n Z' 0 Z' n X 0 X n Y 0 Y n Z 0... CPU MPI_Isend() MPI_Isend() multiple command queues for halo cells MPI_Irecv() communication (GPU CPU) X 0 X n Y 0 Y n Z 0 Z n X' 0 X' n Y' 0 Y' n Z' 0 Z' n X 0 X n Y 0 Y n Z 0 Z N multiple kernels for halo cells multiple kernels for halo cells GPU compute halo cells compute inner cells compute halo cells computations done by GPU communication computations done by CPU command queue idle times SIAM PP 2014, February 20,

28 Topics Motivation The Lattice Boltzmann Method Optimization Single GPU optimization: A-B vs. A-A Pattern Multi GPU optimization: Communication Schemes Results Runtime Lattice Updates Parallel Efficiency Conclusion & Outlook SIAM PP 2014, February 20,

Test Configuration Tödi Cluster in Switzerland CPUs: AMD Opteron Interlagos 6272 number of cores per CPU: 16 total number of CPUs: 272 total number of CPU cores: 4352

29 Test Configuration Tödi Cluster in Switzerland CPUs: AMD Opteron Interlagos 6272 number of cores per CPU: 16 total number of CPUs: 272 total number of CPU cores: 4352 GPUs: NVIDIA Tesla K20x number of CUDA cores per GPU: 2688 total number of GPUs: 272 (256 used) total number of CUDA cores: SIAM PP 2014, February 20,

30 Runtime (Weak Scaling) Runtime (Weak Scaling) Optimal Runtime Basic SBC-SCQ MBC-SCQ MBC-MCQ 3,91 3,8 normalized Runtime (linear scale) 3,3 2,8 2,3 1,8 1,3 0,8 1,00 1,00 1,00 1,00 1,10 1,13 1,17 1,18 1,02 1,19 1,20 1,02 1,18 1,23 1,20 1,11 2,23 1,96 1,48 1,44 1,37 1,71 1,70 1,55 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 2,98 2,08 2,15 2,06 2,61 2,48 2, Number of GPUs (logarithmic scale) SIAM PP 2014, February 20,

31 Lattice Updates (Weak Scaling) Lattice Updates (Weak Scaling) Optimal Scaling Basic SBC-SCQ MBC-SCQ MBC-MCQ 205,25 GLUPS (logarithmic) ,60 1,77 1,74 1,57 1,60 3,21 3,02 2,94 3,05 2,90 6,41 5,98 5,78 6,09 5,67 12,83 11,58 11,53 11,19 10,82 25,66 19,26 19,36 18,14 13,07 51,31 33,19 32,68 31,94 23,00 102,62 54,75 51,75 48,19 34,35 87,45 89,44 82, Number of GPUs (logarithmic) 53,98 SIAM PP 2014, February 20,

32 Parallel Efficiency (Weak Scaling) Parallel Efficiency (Weak Scaling) Optimal Efficiency Efficiency Basic Efficiency SBC-SCQ Efficiency MBC-SCQ Efficiency MBC-MCQ Parallel Efficiency (linear scale) 1,1 1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00 0,98 0,98 0,85 0,85 0,91 0,84 0,83 0,88 0,82 0,83 0,90 0,84 0,68 0,70 0,73 0,58 0,59 0,64 0,51 0,45 0,48 0,46 0,49 0,38 0,40 0,41 0,34 0, Number of GPUs (logarithmic scale) SIAM PP 2014, February 20,

33 Topics Motivation The Lattice Boltzmann Method Optimization Single GPU optimization: A-B vs. A-A Pattern Multi GPU optimization: Communication Schemes Results Runtime Lattice Updates Parallel Efficiency Conclusion & Outlook SIAM PP 2014, February 20,

34 Conclusion & Outlook Conclusion Biggest gain in performance is achieved by using SBK-SCQ instead of a basic scheme More sophisticated schemes (MBK-MCQ) achieve results similar to less sophisticated schemes (SBK-SCQ) Looks like NVIDIA OpenCL does not support overlapping of command queues Degree of parallel efficiency decreases linearly with number of GPUs! SIAM PP 2014, February 20,

35 Conclusion & Outlook Conclusion Biggest gain in performance is achieved by using SBK-SCQ instead of a basic scheme More sophisticated schemes (MBK-MCQ) achieve results similar to less sophisticated schemes (SBK-SCQ) Looks like NVIDIA OpenCL does not support overlapping of command queues Degree of parallel efficiency decreases linearly with number of GPUs! Outlook Improve poor parallel efficiency ( 40%), by running multiple command queues in parallel by considering the network topology Exploit CPUs not just for communication but also for computation SIAM PP 2014, February 20,

36 Technische Universita t Mu nchen Final slide SIAM PP 2014, February 20,

Computational Science and Engineering (Int. Master s Program)

Computational Science and Engineering (Int. Master s Program) Technische Universität München Master s Thesis MPI Parallelization of GPU-based Lattice Boltzmann Simulations Author: Arash Bakhtiari 1 st