Massively Parallel Phase Field Simulations using HPC Framework walberla
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1 Massively Parallel Phase Field Simulations using HPC Framework walberla SIAM CSE 2015, March 15 th 2015 Martin Bauer, Florian Schornbaum, Christian Godenschwager, Johannes Hötzer, Harald Köstler and Ulrich Rüde Chair for System Simulation Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany
2 Outline Motivation walberla Framework Phase Field Method Overview Optimizations Performance Modelling Managing I/O Summary and Outlook 2
3 Motivation large domain required to reduce boundary influence some physical patterns only occur in highly resolved simulations ( spiral ) simulate big domains in 3D unoptimized, general purpose code phase field code from KIT available goal: write optimized parallel version for specific model 3
4 The walberla Framework
5 walberla Framework widely applicable Lattice-Boltzmann from Erlangen HPC software framework, originally developed for CFD simulations with Lattice Boltzmann Method (LBM) evolved into general framework for algorithms on structured grids coupling with in-house rigid body physics engine pe Vocal Fold Study (Florian Schornbaum) Free Surface Flow Fluid Structure Interaction (Simon Bogner) 5
6 Block Structured Grids structured grid domain is decomposed into blocks blocks are the container data structure for simulation data (lattice) blocks are the basic unit of load balancing 7
7 Hybrid Parallelization Distributed Memory Parallelization: MPI data exchange on borders between blocks via ghost layers sender process receiver process (slightly more complicated for non-uniform domain decompositions, but the same general ideas still apply) support for overlapping communication and computation some advanced models ( f.e. FreeSurface) require more complex communication patterns A Python Extension for the massively parallel framework walberla - PyHPC 14 Martin Bauer - Chair for System Simulation, FAU Erlangen-Nürnberg November 17,
8 Phase field in walberla
9 Phase field algorithm two lattices (fields): phase field φ with 4 entries per cell chemical potential μ with 2 entries per cell storing two time steps in src and dst fields spatial discretization: finite differences temporal discretization: explicit Euler method 10
10 Phase field algorithm two lattices (fields): phase field φ with 4 components chemical potential μ with 2 components storing two time steps in src and dst fields 11
11 Phase field algorithm FLOP per cell 940 Loads / Stores 34 12
12 Phase field algorithm FLOPs per cell 2214 Load/Stores:
13 Roofline Performance Model performance data per cell: FLOPs 3154 Loads / Stores 202 Loads from RAM 101 FLOP / double 31.2 from cache Sandy Bridge Architecture: RAM bandwidth/core 6.4 GB/s FLOP/s per 21.6 GFLOP/s Balance (FLOP/double) 25 compute bound 14
14 Optimizations of Phase Field algorithm
15 Optimization Roadmap single core optimizations based on results of performance model save floating point operations, pre-compute and store values where possible presented on example of μ-sweep here scaling performance behavior of parallelization challenges related to Input/Output performance data presented for SuperMUC 16
16 Implementation in walberla starting point: general, prototyping code new model specific implementation in walberla performance guided design no indirect or virtual calls optimized traversal over grid 18
17 Implementation in walberla Step 1: Replace / Remove expensive operations pre-compute common subexpressions fast inverse square root approximation replace division and sqrt operation with bit level operations and add/muls reduce number of divisions using table lookup where possible 19
18 Gibbs Energy subterm pre-computation z many quantities depend on local temperature only in this scenario temperature is a function of one coordinate: T = T(z) these quantities can be computed once for each x, y -slice 20
19 Gibbs Energy subterm pre-computation 21
20 SIMD single instruction multiple data ( SIMD ) architecture specific instructions Intel: SSE, AVX, AVX2 Blue Gene: QPX modern compiler do auto-vectorization still beneficial to write SIMD instructions explicitly via intrinsics problem: separate code for each architecture lightweight SIMD abstraction layer in walberla to write portable code a 3 a 2 a 1 a 0 + b 3 b 2 b 1 b 0 = ymm0 vaddpd ymm1 c 3 c 2 c 1 c 0 ymm0 22
21 SIMD 23
22 Buffering of staggered values pre-computed values to calculate divergence, values at staggered grid positions are required these values can be buffered more loads and stores, less floating point operations same technique can also be applied in φ sweep 24
23 Buffering of staggered values 80 x faster compared to original version 25
24 Intranode Scaling intranode weak scaling on SuperMUC 26
25 Single Node Optimization Summary Single Node Optimizations replace/remove expensive operations like square roots and divisions pre-compute and buffer values where possible SIMD intrinsics Percent Peak on SuperMUC φ-sweep 21 % μ-sweep 27 % Complete Program 25% Why not 100% Peak? unbalanced number of multiplications and addition divisions counted as 1 FLOP but they cost 43 times as much as a multiplication or addition 28
26 Scaling scaling on SuperMUC up to 32,768 cores ghost layer based communication communication hiding 29
27 Managing I/O I/O necessary to store results (frequently) and for checkpointing (seldom) for highly parallel simulations the output of results quickly becomes bottleneck Example: storing one time step of (940 x 940 x 2080) domain: 87 GB Solution: generate surface mesh from voxel data during simulation, locally on each process using a marching cubes algorithm one mesh for each phase boundary 31
28 Managing I/O surface meshes still unnecessarily fine resolved: one triangle per interface cell 32
29 Managing I/O quadric edge reduce algorithm ( cglib ) crucial: mesh reduction step preserves boundary vertices hierarchical mesh coarsening and reduction during simulation result: one coarse mesh with size in the order of several MB local fine meshes generated by marching cubes on coarse mesh on root 33
30 Summary
31 Summary / Outlook Summary efficient phase field algorithm necessary to simulate certain physical effects ( spiral ) systematic performance engineering several levels speedup by factor of 80 compared to original version reached around 25% peak performance on SuperMUC parallel output data processing during simulation to reduce result file size Outlook GPU implementation coupling to Lattice Boltzmann Method improve discretization scheme (implicit method) A Python Extension for the massively parallel framework walberla - PyHPC 14 Martin Bauer - Chair for System Simulation, FAU Erlangen-Nürnberg November 17, 2014
32 Thank you! Questions?
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