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Divide and Conquer QM Development

Muller, Ward, Goddard Linear Scaling Massive Parallelizability. Guess r. Form H. Diagonalize  r. Did r Change?. Yes. No. Done. Divide and Conquer QM Development. O(N 4 ) PS/Jaguar  O(N 2 ). O(N 3 ) Difficult to reduce: Krylof space, Conjugate gradient

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Divide and Conquer QM Development

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  1. Muller, Ward, Goddard Linear Scaling Massive Parallelizability Guess r Form H Diagonalize  r Did r Change? Yes No Done Divide and Conquer QM Development O(N4) PS/Jaguar  O(N2) O(N3) Difficult to reduce: Krylof space, Conjugate gradient Currently only important if N > 2000

  2. Break a big problem into small problems Physically based in quantum chemistry nbf Divide and Conquer Methods Divide and Conquer H Hamiltonian: Divided into fragments and buffer zones

  3. Linear Alkanes • 14-98 atoms • 170-817 bfns Divide and Conquer Results • Linear scaling AND parallel!

  4. Divide, Conquer, and Recombine • Buffer zones don’t scale • Metallic Systems • Same problem n times • Hierarchically recombine • E-value decomp of off-diagonal sections • Can also approximate.

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