Simon Layton, Boston University - Nvidia

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Component (5) - Solver Cycle

‣Smooth errors on all levels

k=1

V-Cycle

- Simplest option

- lots of SpMV!

Restriction

k=M

Interpolation

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Component (5) - Solver Cycle ‣Smooth errors on all levels k=1 V-Cycle - Simplest option - lots of SpMV! Restriction k=M Interpolation 10

GPU Implementation - Justification ‣Algorithm entirely parallel! - Fine-grained parallelism available ‣If we get ~2x+ speedup, massive savings in runtime - Bigger runs! - Less time to solution! 11

Page 1 and 2: Classical Algebraic Multigrid for E
Page 3 and 4: What is Multigrid and why do we car
Page 5 and 6: Matrix as a graph ‣Variables as v
Page 7 and 8: Component (2) - Selector ‣Choose
Page 9: Component (4) - Galerkin Product
Page 13 and 14: Interpolator (again) ‣Interpolati
Page 15 and 16: Repeated Set Union Ĉ i = C s i [ [
Page 17 and 18: Results - Convergence ‣Regular Po
Page 19 and 20: Profiling ‣1,000,000 unknowns ‣
Page 21: Conclusions & Further Work ‣Class

Simon Layton, Boston University - Nvidia

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