Simon Layton, Boston University - Nvidia

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What is Multigrid and why do we care?

‣Hierarchical

- Repeatedly reduce size of the problem

‣ Optimal Complexity

- O(N)

‣Parallel & scalable

- 100k+ cores (Hypre)

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Problem Statement ‣Solve sparse linear systems from engineering problems Au = b ‣Pressure Poisson equation in fluids r 2 = r·u ⇤ - 90%+ of total run time! 2

What is Multigrid and why do we care? ‣Hierarchical - Repeatedly reduce size of the problem ‣ Optimal Complexity - O(N) ‣Parallel & scalable - 100k+ cores (Hypre) 3

Page 1: Classical Algebraic Multigrid for E
Page 5 and 6: Matrix as a graph ‣Variables as v
Page 7 and 8: Component (2) - Selector ‣Choose
Page 9 and 10: Component (4) - Galerkin Product
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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