Simon Layton, Boston University - Nvidia

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Component (3) - Interpolator / Restrictor ‣Transfer residuals between levels - Construct next level Distance 2 - Looks at neighbours of neighbours 8
Component (4) - Galerkin Product ‣Generate next level in hierarchy A k+1 = R k A k P k 1.5 1 0.5 < 1% 2% 2% < 1% 13% Triple matrix product 0 39% −0.5 ‣ −1 Prolongate & correct 44% Restrict residual Compute R Compute A Compute P Smooth Other −1.5 −1.5 −1 −0.5 0 0.5 1 1.5 Bottleneck! 9
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: Component (2) - Selector ‣Choose
Page 11 and 12: GPU Implementation - Justification
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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