University:
Boston University
Course:
MET CS 201 | Introduction to Programming
Academic year:

2024
Views:

236

Pages:

18
Author:

Tara Guerrero

Outline 1 PyCUDA 2 Automatic GPU Programming 3 GPU-DG: Challenges and Solutions Introduction Challenges Benefits of Metaprogramming GPU-DG: Performance and Generality Viscous Shock Capture Metaprogramming for GPU-DG Specialize code for user-given problem: Flux Terms Metaprogramming for GPU-DG Specialize code for user-given problem: Flux Terms Automated Tuning: Memory layout Loop slicing Gather granularity Metaprogramming for GPU-DG Specialize code for user-given problem: Flux Terms Automated Tuning: Memory layout Loop slicing Gather granularity Constants instead of variables: Dimensionality Polynomial degree Element properties Matrix sizes Metaprogramming for GPU-DG Specialize code for user-given problem: Flux Terms Automated Tuning: Memory layout Loop slicing Gather granularity Constants instead of variables: Dimensionality Polynomial degree Element properties Matrix sizes Loop Unrolling Metaprogramming for GPU-DG Specialize code for user-given problem: Flux Terms (*) Automated Tuning: Memory layout Loop slicing (*) Gather granularity Constants instead of variables: Dimensionality Polynomial degree Element properties Matrix sizes Loop Unrolling Loop Slicing for Differentiation 2.2 1.8 1.6 1.4 1.2 1.0 0.8 15 3.0 2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 ws Execution time [ms] Local differentiation, matrix-in-shared, order 4, with microblocking © ª 2.0 point size denotes wi ∈ 1, ,4 20 wp 25 30 Metaprogramming DG: Flux Terms ˆ ˆ ut ϕ + [∇ · F (u)]ϕ dx − 0= Dk [n̂ · F − (n̂ · F )∗ ]ϕ dSx ∂D {z } | k Flux term Metaprogramming DG: Flux Terms ˆ ˆ ut ϕ + [∇ · F (u)]ϕ dx − 0= Dk [n̂ · F − (n̂ · F )∗ ]ϕ dSx ∂D {z } | k Flux term Flux terms: vary by problem expression specified by user evaluated pointwise Metaprogramming DG: Flux Terms Example Example: Fluxes for Maxwell’s Equations n̂ · (F − F ∗ )E := 1 [n̂ × (JHK − αn̂ × JE K)] 2 Metaprogramming DG: Flux Terms Example Example: Fluxes for Maxwell’s Equations n̂ · (F − F ∗ )E := 1 [n̂ × (JHK − αn̂ × JE K)] 2 User writes: Vectorial statement in math. notation flux = 1/2∗cross(normal, h. int −h.ext −alpha∗cross(normal, e. int −e.ext)) Metaprogramming DG: Flux Terms Example Example: Fluxes for Maxwell’s Equations n̂ · (F − F ∗ )E := 1 [n̂ × (JHK − αn̂ × JE K)] 2 We generate: Scalar evaluator in C (6×) a flux += ( ((( val a field5 − val b field5 )∗ fpair −>normal[2] − ( val a field4 − val b field4 )∗ fpair −>normal[0]) + val a field0 − val b field0 )∗ fpair −>normal[0] − ((( val a field4 − val b field4 ) ∗ fpair −>normal[1] − ( val a field1 − val b field1 )∗ fpair −>normal[2]) + val a field3 − val b field3 ) ∗ fpair −>normal[1] )∗ value type (0.5); Hedge DG Solver High-Level Operator Description Maxwell’s Euler Poisson Compressible Navier-Stokes, . . . One Code runs. . . . . . on CPU, CUDA . . . on {CPU,CUDA}+MPI . . . in 1D, 2D, 3D . . . at any order Uses CPU, GPU code generation Open Source (GPL3) Written in Python, Outline 1 PyCUDA 2 Automatic GPU Programming 3 GPU-DG: Challenges and Solutions Introduction Challenges Benefits of Metaprogramming GPU-DG: Performance and Generality Viscous Shock Capture Nvidia GTX280 vs. single core of Intel Core 2 Duo E8400 300 250 GPU CPU GFlops/s 200 150 100 50 00 2 4 6 Polynomial Order N 8 10 Memory Bandwidth on a GTX 280 Global Memory Bandwidth [GB/s] 200 180 160 140 120 100 80 60 40 201 Gather Lift Diff Assy. Peak 2 3 4 5 6 Polynomial Order N 7 8 9 Multiple GPUs via MPI: 16 GPUs vs. 64 CPUs GFlops/s Flop Rates: 16 GPUs vs 64 CPU cores GPU 4000 CPU 3000 2000 1000 00 2 4 6 8 Polynomial Order N 10 GPU-DG in Double Precision GFlops/s GPU-DG: Double vs. Single Precision 400 350 300 250 200 150 100 50 00 Single Double Ratio 1.0 0.8 0.6 0.4 0.2 2 4 6 8 Polynomial Order N 100.0