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Lecture notes in computer science

High Performance Computing for Eigenvalue Solver in Density-Matrix Renormalization Group Method: Parallelization of the Hamiltonian Matrix-Vector Multiplication

Susumu Yamada, Masahiko Okumura, Masahiko Machida

Published Jan 1, 2008• 5 citations
Publisher
DOI
10.1007/978-3-540-92859-1_5

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There has been recent interest in the deployment of ab initio density matrix renormalization group (DMRG) computations on high performance computing platforms. Here, we introduce a reformulation of the conventional distributed memory ab initio DMRG algorithm that connects it to the conceptually simpler and advantageous sum of the sub-Hamiltonian approach. Starting from this framework, we further explore a hierarchy of parallelism strategies that includes (i) parallelism over the sum of sub-Hamiltonians, (ii) parallelism over sites, (iii) parallelism over normal and complementary operators, (iv) parallelism over symmetry sectors, and (v) parallelism within dense matrix multiplications. We describe how to reduce processor load imbalance and the communication cost of the algorithm to achieve higher efficiencies. We illustrate the performance of our new open-source implementation on a recent benchmark ground-state calculation of benzene in an orbital space of 108 orbitals and 30 electrons, with a bond dimension of up to 6000, and a model of the FeMo cofactor with 76 orbitals and 113 electrons. The observed parallel scaling from 448 to 2800 central processing unit cores is nearly ideal.